Averages and measures of spread — Paper 4 · IGCSE Mathematics 0580

9 Answer the whole of this question on one sheet of graph paper. The heights (h cm) of 270 students in a school are measured and the results are shown in the table. h Frequency 120 < h 130 15 130 < h 140 24 140 < h 150 36 150 < h 160 45 160 < h 170 50 170 < h 180 43 180 < h 190 37 190 < h 200 20 (a) Write down the modal group. [1] (b) (i) Calculate an estimate of the mean height. [4] (ii) Explain why the answer to part (b)(i) is an estimate. [1] (c) The following table shows the cumulative frequencies for the heights of the students. h Cumulative frequency h 120 0 h 130 p h 140 q h 150 r h 160 120 h 170 170 h 180 213 h 190 250 h 200 270 Write down the values of p, q and r. [2] (d) Using a scale of 1cm to 5 units, draw a horizontal h-axis, starting at h = 120. Using a scale of 1cm to 20 units on the vertical axis, draw a cumulative frequency diagram. [5] (e) Use your diagram to find (i) the median height, [1] (ii) the upper quartile, [1] (iii) the inter-quartile range, [1] (iv) the 60th percentile. [1] (f) All the players in the school’s basketball team are chosen from the 30 tallest students. Use your diagram to find the least possible height of any player in the basketball team. [2]

19 marks

Mark scheme: 9 (a) 160 < h Y 170 B1 (b) (i) Mid values 125, 135, 145, 155, 165, 175, M1 Allow 1 slip 185, 195 (15 x 125 + 24 x 135 + 36 x 145 + 45 M1 Dep on mid values ± 0.5, allow 1 slip in mid- x 155 + 50 x 165 + 43 x 175 + 37 x 185 values (43830) + 20 x 195) ÷ 270 M1 Dep on previous method 162 or better A1 (162.333..) www4 (ii) Mid-values are an estimate of each B1 e.g. exact values not given interval o.e. (c) p = 15, q = 39, r = 75 B2 B1 for 2 correct. If no labels, take in order given (d) Correct scales S1 9 points correctly plotted ft P3ft P2ft for 7 or 8 correct acc. 1 mm P1ft for 5 or 6 correct Curve or line through 9 points C1ft Dep on ‘S’ shape within 1 small square of 2 points (e) (i) 162 to 164 B1 (ii) 176 to 178 B1 (iii) 28 to 30 B1 (iv) 167.5 to 168.5 B1 (f) Uses 240 or 241 on cumul, freq. axis M1 e.g. annotates graph or shows values in working 186.5 to 188 A1 ww2 [19] IGCSE – NOVEMBER 2005 0580/0581 4 IGCSE – NOVEMBER 2005 0580/0581 4 IGCSE – NOVEMBER 2005 0580/0581 4

This question in 0580/41 Oct/Nov 2005

9 (a) The numbers 0, 1, 1, 1, 2, k, m, 6, 9, 9 are in order (k ≠ m). Their median is 2.5 and their mean is 3.6. (i) Write down the mode. [1] (ii) Find the value of k. [1] (iii) Find the value of m. [2] (iv) Maria chooses a number at random from the list. The probability of choosing this number is 1 . Which number does she choose? [1] 5 (b) 100 students are given a question to answer. The time taken (t seconds) by each student is recorded and the results are shown in the table. t 0<t 20 20<t 30 30<t 35 35<t 40 40<t 50 50<t 60 60<t 80 Frequency 10 10 15 28 22 7 8 (i) Calculate an estimate of the mean time taken. [4] (ii) Two students are picked at random. What is the probability that they both took more than 50 seconds? Give your answer as a fraction in its lowest terms. [3] Answer part (c) on a sheet of graph paper. (c) The data in part (b) is re-grouped to give the following table. t 0<t 30 30<t 60 60<t 80 Frequency p q 8 (i) Write down the values of p and q. [2] (ii) Draw an accurate histogram to show these results. Use a scale of 1 cm to represent 5 seconds on the horizontal time axis. Use a scale of 1 cm to 0.2 units of frequency density (so that 1 cm2 on your histogram represents 1 student). [4]

18 marks

Mark scheme: 9 (a) (i) 1 B1 (ii) 3 B1 (iii) 29 + their k + m M1 = 3 . 6 o.e. 10 (m =) 4 A1 (iv) 9 B1 (b) (i) mid-values 10, 25, 32.5, 37.5, 45, 55, 70 M1 At least 6 correct s.o.i. seen (10 x 10) + (10 x 25) + (15 x 32.5) + (28 x M1* Dep on first M1 or mid-values 37.5) + (22 x 45) + (7 x 55) + (8 x 70) ±0.5 Allow 1 more slip. [3822.5] Total ÷ 100 M1 Dep on second M1* 38.2 (38.225) A1 (ii) 15 14 M1 × 100 99 210 A1 o.e. 9900 7 A1 Final Answer 330 (c) (i) p = 20 B1 q = 72 B1 (ii) Horizontal scale correct S1 Implied by correct use. Ignore the vertical scale. For each block of correct width For scale error (halved), award Height 3.3 cm H1 H1, H1, H1 for correct ft heights. Height 12 cm H1 Height 2 cm H1 After H0, H0, H0, give SC1 for correct frequency densities written. (0.67, 2.4, 0.4) 18

This question in 0580/41 May/June 2006

6 Answer the whole of this question on a sheet of graph paper. Kristina asked 200 people how much water they drink in one day. The table shows her results. Amount of water (x litres) Number of people 0 < x 0.5 8 0.5 < x 1 27 1 < x 1.5 45 1.5 < x 2 50 2 < x 2.5 39 2.5 < x 3 21 3 < x 3.5 7 3.5 < x 4 3 (a) Write down the modal interval. [1] (b) Calculate an estimate of the mean. [4] (c) Make a cumulative frequency table for this data. [2] (d) Using a scale of 4 cm to 1 litre of water on the horizontal axis and 1 cm to 10 people on the vertical axis, draw the cumulative frequency graph. [5] (e) Use your cumulative frequency graph to find (i) the median, [1] (ii) the 40th percentile, [1] (iii) the number of people who drink at least 2.6 litres of water. [2] (f) A doctor recommends that a person drinks at least 1.8 litres of water each day. What percentage of these 200 people do not drink enough water? [2]

18 marks

Mark scheme: 6 (a) 1.5 < x ≤ 2 B1 (b) (8×0.25 + 27×0.75 + 45×1.25 +…….. M1 For mid-values (allow two slips) ……….. 3×3.75) M1 For Σfx (allow two slips) dep on first M1, or mid-values ± 0.05 their 345.5 ÷ 200 M1 for ÷ 200 dep on second M1 1.7275, 1.727, 1.728 or 1.73 cso A1 www 4 (c) 8, 35, 80, 130, 169, 190, 197, 200 B2 If B0, allow M1 for clear attempt to add accumulatively (d) axes correct scale S1 Not reversed and must reach 200 vertically, even if not labelled 8 points plotted ft part (c) P3dep dep on at least M1 in (c) (0.5, 8), (1, 35), (1.5, 80), (2, 130), (2.5, 8 points from their values 169), (3, 190), (3.5, 197), For x-values (upper boundary values), (4, 200) points must touch grid line For y-values, even, must touch grid line, odd must be inside square. P2 for 6 or 7 points ft P1 for 4 or 5 points ft curve (or polygon) either correct or C1 Allow 1 mm tolerance through 8 points and correct shape Ignore any bars drawn if they do not compromise the points and graph (e) (i) 1.65-1.75 B1 (ii) 1.5 B1 (iii) 23 – 29 integers only B2 If B0 allow SC1 for non-integer in correct range, or 172 – 177 seen (may be written on graph) (f) 54 – 56.5 B2 SC1 for figures 108 – 113 or 87 – 92 Accept if written on graph www 2 [18] IGCSE – May/June 2007 0580 and 0581 04

This question in 0580/41 May/June 2007

2 (a) Grade 1 2 3 4 5 6 7 Number of students 1 2 4 7 4 8 2 The table shows the grades gained by 28 students in a history test. (i) Write down the mode. [1] (ii) Find the median. [1] (iii) Calculate the mean. [3] (iv) Two students are chosen at random. Calculate the probability that they both gained grade 5. [2] (v) From all the students who gained grades 4 or 5 or 6 or 7, two are chosen at random. Calculate the probability that they both gained grade 5. [2] (vi) Students are chosen at random, one by one, from the original 28, until the student chosen has a grade 5. Calculate the probability that this is the third student chosen. [2] (b) Claude goes to school by bus. The probability that the bus is late is 0.1 . If the bus is late, the probability that Claude is late to school is 0.8 . If the bus is not late, the probability that Claude is late to school is 0.05 . (i) Calculate the probability that the bus is late and Claude is late to school. [1] (ii) Calculate the probability that Claude is late to school. [3] (iii) The school term lasts 56 days. How many days would Claude expect to be late? [1]

16 marks

Mark scheme: 2 (a) (i) 6 B1 (ii) 4.5 B1 (iii) 1( × 1 + 2 × 2 + 4 × 3 + 7 × 4 + 4 × 5 + M1 Allow 1 slip 8 × 6 + 2 × 7 ) (127) ÷ 28 M1dep dep on 1st M1 4.54 A1 www 3 4.53571… (iv) 4 3 M1 Accept all probabilities as fracts/dec/% × -1 once for words or 2 sf, do not accept 28 27 ratios i.s. cancelling after correct answer. 1 A1 www2 e.g. ( 75612 , 0.0159 etc) o.e. 63 (v) 4 3 M1 × 21 20 1 A1 www2 e.g. ( 42012 , 0.0286 etc) o.e. 35 (vi) 24 23 4 M1 × × 28 27 26 92 A1 www2 e.g. ( 196562208 , 0.112) o.e. 819 (b) (i) 0.08 o.e. B1 (ii) 0.9 × 0.05 M1 their (b)(i) + 0.9 × 0.05 M1dep dep on 1st M1 0.125 o.e. A1 www3 (iii) 7 B1 ft their (ii) × 56 either correct to 3sf or better or r.o.t. [16] IGCSE – October/November 2007 0580/0581 04

This question in 0580/41 Oct/Nov 2007

2 A normal die, numbered 1 to 6, is rolled 50 times. For Examiner's 1 Use 2 4 The results are shown in the frequency table. Score 1 2 3 4 5 6 Frequency 15 10 7 5 6 7 (a) Write down the modal score. Answer(a) [1] (b) Find the median score. Answer(b) [1] (c) Calculate the mean score. Answer(c) [2] (d) The die is then rolled another 10 times. The mean score for the 60 rolls is 2.95. Calculate the mean score for the extra 10 rolls. Answer(d) [3]

7 marks

Mark scheme: 2 (a) 1 B1 (b) 2.5 o.e. B1 (c) 2.96 c.a.o. B2 If B0, M1 for 15 × 1 + 10 × 2 + 7 × 3 + 5 × 4 + 6 × 5 + 7 × 6 (allow one slip) implied by 148 seen Ignore subsequent rounding (d) 60 × 2.95 (= 177) M1 their 177 – their 148 (or 50 × their 2.96) M1 Dependent on first M and only if positive or M1 for (Mean of new rolls =) 2.9 c.a.o. www3 A1 their 148( 50 × their .296 ) + x ( or 10 x ) = .295 60 then M1 for x ( or 10 x ) = 60 × .295 − their 148 (or 50 × their 2.96) and only if positive [7] IGCSE – May/June 2009 0580, 0581 04 48

This question in 0580/41 May/June 2009

8 Fifty students are timed when running one kilometre. For Examiner's The results are shown in the table. Use Time 4.0 < t Y 4.5 4.5 < t Y 5.0 5.0 < t Y 5.5 5.5 < t Y 6.0 6.0 < t Y 6.5 6.5 < t Y 7.0 (t minutes) Frequency 2 7 8 18 10 5 (a) Write down the modal time interval. Answer(a) min [1] (b) Calculate an estimate of the mean time. Answer(b) min [4] (c) A new frequency table is made from the results shown in the table above. Time 4.0 < t Y 5.5 5.5 < t Y 6.0 6.0 < t Y 7.0 (t minutes) Frequency 18 (i) Complete the table by filling in the two empty boxes. [1] (ii) On the grid below, complete an accurate histogram to show the information in this new For table. Examiner's Use 40 30 Frequency density 20 10 0 t 4 5 6 7 8 Time (minutes) [3] (iii) Find the number of students represented by 1 cm2 on the histogram. Answer(c)(iii) [1]

10 marks

Mark scheme: 8 (a) 5.5 < t Y 6 B1 Condone poor notation (b) 4.25, 4.75, 5.25, 5.75, 6.25, 6.75 M1 At least 5 correct mid-values seen where x is in the correct interval allow (2 × 4.25 + 7 × 4.75 + 8 × 5.25 + 18 × 5.75 M1 ∑fx + 10 × 6.25 + 5 × 6.75) (= 283.5) one further slip M1 Depend on second method ÷ 50 or their ∑f 5.67 www4 A1 After M3 allow 5.7 isw conversion to mins/secs and reference to classes (c) (i) 17, 15 B1 (ii) Rectangular bars of heights 11.3 B1ft ft their 17 divided by 1.5 and 15 B1ft ft their 15 11.3 plot between 11 and 12 include lines and 15 to be touching the 15 line Correct widths of 1.5 and 1 – no gaps B1 (iii) 2.5 cao B1 [10] IGCSE – October/November 2009 0580 04

This question in 0580/41 Oct/Nov 2009

2 40 students are asked about the number of people in their families. Examiner's Use The table shows the results. Number of people in family 2 3 4 5 6 7 Frequency 1 1 17 12 6 3 (a) Find (i) the mode, Answer(a)(i) [1] (ii) the median, Answer(a)(ii) [1] (iii) the mean. Answer(a)(iii) [3] (b) Another n students are asked about the number of people in their families. The mean for these n students is 3. Find, in terms of n, an expression for the mean number for all (40 + n) students. Answer(b) [2]

7 marks

Mark scheme: 2 (a) (i) 4 1 (ii) 5 1 (iii) 4.75 3 M1 for 1 × 2 + 1 × 3 + 17 × 4 + 12 × 5 + 6 × 6 + 3 × 7 condone one slip then M1 dependent result (190) ÷ 40 190 + 3n (b) 2 SC1 for their 190 + 3n 40 + n

This question in 0580/41 May/June 2010

6 The masses of 60 potatoes are measured. Examiner's The table shows the results. Use Mass (m grams) 10 I m Y 20 20 I m Y 40 40 I m Y 50 Frequency 10 30 20 (a) Calculate an estimate of the mean. Answer(a) g [4] (b) On the grid, draw an accurate histogram to show the information in the table. 2 Frequency density 1 m 0 10 20 30 40 50 Mass (grams) [3]

7 marks

Mark scheme: 6 (a) 32.5 cao www4 4 M1 for mid-values seen M1 for use of Σfx with x’s anywhere in each interval (10 × 15 + 30 × 30 + 20 × 45) M1 ÷ 60 dependent on second M1 (b) Histogram drawn 3 B1 Bars correct positions and widths – no gaps B2 Heights of bars 1, 1.5 and 2 (B1 for any two correct or for heights in the ratio 2:3:4)

This question in 0580/41 May/June 2010

7 200 students were asked how many hours they exercise each week. Examiner's Use The table shows the results. Time (t hours) 0ItY5 5ItY10 10ItY15 15ItY20 20ItY25 25ItY30 30ItY35 35ItY40 Number of 12 15 23 30 40 35 25 20 students (a) Calculate an estimate of the mean. Answer(a) h [4] (b) Use the information in the table above to complete the cumulative frequency table. Time (t hours) t Y=5 t Y=10 t Y=15 t Y=20 t Y=25 t Y=30 t Y=35 t Y=40 Cumulative frequency 12 27 50 80 120 200 [1] For Examiner's Use 200 180 160 140 120frequency 100 80Cumulative 60 40 20 t 0 5 10 15 20 25 30 35 40 Time (t hours) (c) On the grid, draw a cumulative frequency diagram to show the information in the table in part (b). [4] (d) On your cumulative frequency diagram show how to find the lower quartile. [1] (e) Use your cumulative frequency diagram to find (i) the median, Answer(e)(i) [1] (ii) the inter-quartile range, Answer(e)(ii) [1] (iii) the 64th percentile, Answer(e)(iii) [1] (iv) the number of students who exercise for more than 17 hours. Answer(e)(iv) [2]

15 marks

Mark scheme: 7 (a) 12 × 2.5 + 15 × 7.5 + 23 × 12.5 + 30 × M1 mid-values any three soi 17.5 + 40 × 22.5 + 35 × 27.5 + 25 × M1 Use of Σfx dep on x anywhere in each interval 32.5 + 20 × 37.5 (including lower bound) – allow 2 slips or omissions ÷ 200 M1 Depend on second M 21.9 www 4 A1 (b) 155, 180 1 (c) 8 points plotted ft, ignoring (0, 0) P3ft P2ft for 6 or 7 plotted , P1ft for 4 or 5 plotted Reasonable increasing curve or C1ft Condone starting at (5, 12) and ft only if shape polygon through their 8 points correct. (d) Either horizontal or vertical line at 1 least 1 cm long at y = 50 on the curve (e) (i) 22 – 23 1 (ii) 13.5 – 14.5 1 (iii) 25.5 – 26.5 1 (iv) 136 – 140 must be integer 2 SC1 for 60 – 64 seen and must be integer 2 2

This question in 0580/42 May/June 2010

10 (a) For a set of six integers, the mode is 8, the median is 9 and the mean is 10. For Examiner's The smallest integer is greater than 6 and the largest integer is 16. Use Find the two possible sets of six integers. Answer(a) First set , , , , , Second set , , , , , [5] (b) One day Ahmed sells 160 oranges. He records the mass of each orange. The results are shown in the table. Mass (m grams) 50 < m Y 80 80 < m Y 90 90 < m Y 100 100 < m Y 120 120 < m Y 150 Frequency 30 35 40 40 15 (i) Calculate an estimate of the mean mass of the 160 oranges. Answer(b)(i) g [4] (ii) On the grid, complete the histogram to show the information in the table. For Examiner's Use 5 4 3 Frequency density 2 1 0 m 50 60 70 80 90 100 110 120 130 140 150 Mass (grams) [4] Question 11 is printed on the next page.

13 marks

Mark scheme: 10 (a) 7, 8, 8, 10, 11, 16 5 Mark answer spaces only or clearly indicated and 8, 8, 8, 10, 10, 16 lists. Allow numbers in any order but must be lists of 6 integers B4 for either correct list If not B4 then B1 for a series with mode 8 and B1 for a series with median 9 and B1 for a series with sum 60 (b) (i) (30 × 65 + 35 × 85 + 40 × 95 + 4 M1 for mid-values soi (allow 1 error/omission) with x in correct 40 × 110 + 15 × 135) ÷ 160 and M1 for use of ∑fx interval including both boundaries allow one further error/omission and M1 (dependent on second M) for ÷ 160 94.7 (94.68 – 94.69) www 4 (ii) Heights of 4, 2, 0.5 with correct 4 B3 for 2 correct interval widths or B2 for 1 correct or B1 for all three freq. densities correct but no/incorrect graph

This question in 0580/43 Oct/Nov 2010

8 The table below shows the marks scored by a group of students in a test. For Examiner's Use Mark 11 12 13 14 15 16 17 18 Frequency 10 8 16 11 7 8 6 9 (a) Find the mean, median and mode. Answer(a) mean = median = mode = [6] (b) The table below shows the time (t minutes) taken by the students to complete the test. Time (t) 0 I=t Y=10 10 I=t Y=20 20 I=t Y=30 30 I=t Y=40 40 I=t Y=50 50 I=t Y=60 Frequency 2 19 16 14 15 9 (i) Cara rearranges this information into a new table. Complete her table. Time (t) 0 I=t Y=20 20 I=t Y=40 40 I=t Y=50 50 I=t Y=60 Frequency 9 [2] (ii) Cara wants to draw a histogram to show the information in part (b)(i). Complete the table below to show the interval widths and the frequency densities. 0 I=t Y=20 20 I=t Y=40 40 I=t Y=50 50 I=t Y=60 Interval 10 width Frequency 0.9 density [3] (c) Some of the students were asked how much time they spent revising for the test. For Examiner's 10 students revised for 2.5 hours, 12 students revised for 3 hours and n students revised for Use 4 hours. The mean time that these students spent revising was 3.1 hours. Find n. Show all your working. Answer(c) n = [4]

15 marks

Mark scheme: 8 14.2 3 M1 for Σ fx (10 × 11 + 8 × 12 + 16 × 13 + 11 × 14 + 7 × 15 + 8 × 16 + 6 × 17 + 9 × 18 ) (1065) (allow one error or omission) M1dep for ÷ Σf (10 + 8 + 16 + 11 + 7 + 8 + 6 + 9) (75) (allow one further error or omission) 14 2 M1 for 37th, 37.5th or 38th seen 13 1 (b) (i) 21, 30, 15 2 B1 for 2 correct (ii) 20 20 10 (10) 3 1, 1, 1 for each correct vertical pair 1.05 1.5 1.5 (0.9) (c) 10 × 5.2 + 12 × 3 + 4 n ( = )1.3 M2 M1 for either numerator or denominator seen 10 + 12 + n multiplying across and collecting terms M1 dep on linear numerator and denominator their (68.2 − 25 − 36) = their (4 − 3.1) × n (n =) 8 www 4 A1 IGCSE – May/June 2011 0580 41

This question in 0580/41 May/June 2011

6 For Time Examiner's 0 I t Y 20 20 I t Y 35 35 I t Y 45 45 I t Y 55 55 I t Y 70 70 I t Y 80 Use (t mins) Frequency 6 15 19 37 53 20 The table shows the times taken, in minutes, by 150 students to complete their homework on one day. (a) (i) In which interval is the median time? Answer(a)(i) [1] (ii) Using the mid-interval values 10, 27.5, ……..calculate an estimate of the mean time. Answer(a)(ii) min [3] (b) (i) Complete the table of cumulative frequencies. Time t Y 20 t Y 35 t Y 45 t Y 55 t Y 70 t Y 80 (t mins) Cumulative 6 21 frequency [2] (ii) On the grid, label the horizontal axis from 0 to 80, using the scale 1 cm represents 5 minutes and the vertical axis from 0 to 150, using the scale 1 cm represents 10 students. Draw a cumulative frequency diagram to show this information. [5] For Examiner's Use (c) Use your graph to estimate (i) the median time, Answer(c)(i) min [1] (ii) the inter-quartile range, Answer(c)(ii) min [2] (iii) the number of students whose time was in the range 50 I t Y 60, Answer(c)(iii) [1] (iv) the probability, as a fraction, that a student, chosen at random, took longer than 50 minutes, Answer(c)(iv) [2] (v) the probability, as a fraction, that two students, chosen at random, both took longer than 50 minutes. Answer(c)(v) [2]

19 marks

Mark scheme: 6 (a) (i) 45 < t Y 55 1 Allow any indication e.g. 4th interval (ii) 52.6 (52.63….. ) www 3 3 M1 for 6 × 10 + 15 × 27.5 + 19 × 40 + 37 × 50 + 53 × 62.5 + 20 × 75 (= 7895) Allow 1 error/omission and M1 dep for ÷ 150 (b) (i) 40, 77, 130, 150 2 B1 for 2 or 3 correct values (ii) Correct scales S1 6 correct plots ft P3ft ft from (i) if increasing values. (35, 21) must be inside square 20 – 22 but (55, 77) may be inside or edge of square P2 for 4 or 5 correct plots ft P1 for 2 or 3 correct plots ft Curve or ruled lines through the 6 C1ft ft their points if increasing points condone graph starting at (20, 6) (c) (i) 54 to 55 1 (ii) 18.5 – 22.5 2 B1 for UQ = 62.5 to 65 or LQ = 42.5 to 44 seen (iii) Their reading at 60 – their reading at 1 50 150 − their reading at 50 ( ±2) their reading at 50( ±2) (iv) oe 2 SC1 for oe 150 150 k (v) If their (iv) is , then ft their 2ft In (iv) and (v), condone answers as decimals to 150 3 sf k k − 1 Penalise first occurence only of 2sf decimals × 150 149 isw cancelling/conversion k k − 1 M1 for × 150 149 IGCSE – May/June 2011 0580 42

This question in 0580/42 May/June 2011

3 The table shows information about the heights of 120 girls in a swimming club. For Examiner's Use Height (h metres) Frequency 1.3 I h Y 1.4 4 1.4 I h Y 1.5 13 1.5 I h Y 1.6 33 1.6 I h Y 1.7 45 1.7 I h Y 1.8 19 1.8 I h Y 1.9 6 (a) (i) Write down the modal class. Answer(a)(i) m [1] (ii) Calculate an estimate of the mean height. Show all of your working. Answer(a)(ii) m [4] (b) Girls from this swimming club are chosen at random to swim in a race. Calculate the probability that (i) the height of the first girl chosen is more than 1.8 metres, Answer(b)(i) [1] (ii) the heights of both the first and second girl chosen are 1.8 metres or less. Answer(b)(ii) [3] (c) (i) Complete the cumulative frequency table for the heights. For Examiner's Use Height (h metres) Cumulative frequency h Y 1.3 0 h Y 1.4 4 h Y 1.5 17 h Y 1.6 50 h Y 1.7 h Y 1.8 114 h Y 1.9 [1] (ii) Draw the cumulative frequency graph on the grid. 120 110 100 90 80 70 Cumulative 60 frequency 50 40 30 20 10 0 h 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Height (m) [3] (d) Use your graph to find (i) the median height, Answer(d)(i) m [1] (ii) the 30th percentile. Answer(d)(ii) m [1]

15 marks

Mark scheme: 3 (a) (i) 1.6 < h ≤ 1.7 1 Condone alt. notation used for class (ii) {1.35 × 4 + 1.45 ×13 + 1.55 ×33 M3 (194/120) + 1.65 × 45 + 1.75 × 19 + 1.85 M1 for mid-values soi (allow one slip) × 6}÷ 120 and M1 for use of ∑fx with x in correct interval (allow one more slip) and M1 depend on 2nd M for dividing by 120 1.62 or 1.616 to 1.617 A1 www4 6 Accept dec/% to 3 sf or better but not ratio (b) (i) oe 1 120 isw cancelling/conversion (also for (ii)) 2147 k k − 1 k (ii) oe (0.902(1..)) 3 M2 for × where is 1 – their (b)(i) 2380 120 119 120 or if k = 114 or M1 for 1 – their (b)(i) or for 114/120 seen After 0 scored SC2 for ans 1/476 oe or SC1 for 6/120 × 5/119 (c) (i) 95, 120 1 (ii) Plots 7 points correctly P2ft P1ft for 5 or 6 correct plots exact or in correct square Curve or lines through 7 points C1ft ft their increasing curve within 1 mm of points (d) (i) 1.61 to 1.63 1ft ft their 60th reading on inc. curve to nearest 0.01 (ii) 1.555 to 1.57 1ft ft their 36th reading on inc. curve 20

This question in 0580/41 Oct/Nov 2011

5 For Examiner′s Height (h cm) 150 < h Ğ 160 160 < h Ğ 165 165 < h Ğ 180 180 < h Ğ 190 Use Frequency 5 9 18 10 The table shows information about the heights of a group of 42 students. (a) Using mid-interval values, calculate an estimate of the mean height of the students. Show your working. Answer(a) … cm [3] (b) Write down the interval which contains the lower quartile. Answer(b) … [1] (c) Complete the histogram to show the information in the table. One column has already been drawn for you. 2 Frequency density 1 0 150 155 160 165 170 175 180 185 190 Height (cm) [4] _____________________________________________________________________________________

8 marks

Mark scheme: 5 (a) 171.25 (or 171 or 171.2 or 171.3) 3 M1 for 5 × 155 + 9 × 162.5 + 18 × 172.5 + 10 × 185 [= 7192.5] www and M1 (dep on M1) for their Σfx ÷ 42 (b) 160 < x ≤ 165 oe 1 (c) Blocks with heights of 1.8, 1.2, 1, with 4 B3 for 2 correct blocks correct interval widths and no gaps or B2 for 1 correct block or B1 for 3 correct frequency densities or heights or 3 correct widths IGCSE – May/June 2013 0580 41 Qu. Answer Marks Part marks 15 7

This question in 0580/41 May/June 2013

9 Sam asked 80 people how many minutes their journey to work took on one day. For Examiner′s The cumulative frequency diagram shows the times taken (m minutes). Use 80 70 60 50 Cumulative 40 frequency 30 20 10 m 0 10 20 30 40 50 Time (minutes) (a) Find (i) the median, Answer(a)(i) … min [1] (ii) the lower quartile, Answer(a)(ii) … min [1] (iii) the inter-quartile range. Answer(a)(iii) … min [1] (b) One of the 80 people is chosen at random. For Examiner′s Use Find the probability that their journey to work took more than 35 minutes. Give your answer as a fraction. Answer(b) … [2] (c) Use the cumulative frequency diagram to complete this frequency table. Time (m minutes) 0 < m Y 10 10 < m Y 15 15 < m Y 30 30 < m Y 40 40 < m Y 50 Frequency 30 12 18 [2] (d) Using mid-interval values, calculate an estimate of the mean journey time for the 80 people. Answer(d) … min [3] (e) Use the table in part (c) to complete the histogram to show the times taken by the 80 people. One column has already been completed for you. 4 3 Frequency 2 density 1 m 0 10 20 30 40 50 Time (minutes) [5] _____________________________________________________________________________________

15 marks

Mark scheme: 9 (a) (i) 14 1 (ii) 8 1 (iii) 30 – their (ii) 1FT 11 69 (b) 2 SC1 for 80 80 (c) 16, 4 2 B1 for each correct value (d) 18.0625 rot to 3sf or better or 3 M1 for Σmf for m as mid values of 5, 12.5, 22.5, 18.1 www 35 and 45 (= 1445) and M1 dep for Σmf ÷ 80, dep on M1 earned (e) Correct widths with no gaps 1 2nd block w = 5, fd = 2.4 1 3rd block w = 15 fd = 1.2 1 4th block w = 10 and fd = 1.6 1FT Strict FT from their (c) 5th block w = 10 and fd = 0.4 1FT Strict FT from their (c) After 0 scored for blocks, SC1 for 4 correct fds soi by correct heights

This question in 0580/43 May/June 2013

7 120 students are asked to answer a question. For Examiner′s The time, t seconds, taken by each student to answer the question is measured. Use The frequency table shows the results. Time 0 < t Y 10 10 < t Y 20 20 < t Y 30 30 < t Y 40 40 < t Y 50 50 < t Y 60 Frequency 6 44 40 14 10 6 (a) Calculate an estimate of the mean time. Answer(a) … s [4] (b) (i) Complete the cumulative frequency table. Time t Y 10 t Y 20 t Y 30 t Y 40 t Y 50 t Y 60 Cumulative frequency 6 104 120 [2] (ii) On the grid below, draw a cumulative frequency diagram to show this information. 120 100 80 Cumulative 60 frequency 40 20 t 0 10 20 30 40 50 60 Time (seconds) [3] (iii) Use your cumulative frequency diagram to fi nd the median, the lower quartile and For Examiner′s the 60th percentile. Use Answer(b)(iii) Median … s Lower quartile … s 60th percentile … s [4] (c) The intervals for the times taken are changed. (i) Use the information in the frequency table on the opposite page to complete this new table. Time 0 < t Y 20 20 < t Y 30 30 < t Y 60 Frequency 40 [2] (ii) On the grid below, complete the histogram to show the information in the new table. One column has already been drawn for you. 4 3.5 3 2.5 Frequency density 2 1.5 1 0.5 t 0 10 20 30 40 50 60 Time (seconds) [3] _____________________________________________________________________________________

18 marks

Mark scheme: 7 (a) 24.7 or 24.66 to 24.67 4 M1 for midpoints soi (condone 1 error or omission) (5, 15, 25, 35, 45, 55) and M1 for use of ∑fx with x in correct interval including both boundaries (condone 1 further error or omission) and M1 (dependent on second M) for ∑fx ÷ 120 (b) (i) 50, 90, 114 2 B1 for 2 correct (ii) Correct curve 3 Ignore section to left of t = 10 or ruled polygon B1 for 6 correct horizontal plots and B1FT for 6 correct vertical plots If 0 scored SC1 for 5 out of 6 correct plots and B1FT for curve or polygon through at least 5 of their points dep on an increasing curve/polygon that reaches 120 vertically (iii) 21.5 to 23 B1 15 to 16.5 B1 24 to 26 4 B2 or B1 for 72 or 72.6 seen (c) (i) 50, 30 2 B1 each (ii) Correct histogram 3FT B1 for blocks of widths 0 – 20, 30 – 60 (no gaps) B1FT for block of height 2.5 or their 50 ÷ 20 and B1FT for block of height 1 or their 30 ÷ 30 IGCSE – October/November 2013 0580 41

This question in 0580/41 Oct/Nov 2013

5 (a) 80 students were asked how much time they spent on the internet in one day. For Examiner′s This table shows the results. Use Time (t hours) 0 < t Y 1 1 < t Y 2 2 < t Y 3 3 < t Y 5 5 < t Y 7 7 < t Y 10 Number of students 15 11 10 19 13 12 (i) Calculate an estimate of the mean time spent on the internet by the 80 students. Answer(a)(i) … hours [4] (ii) On the grid, complete the histogram to show this information. 16 14 12 10 Frequency 8 density 6 4 2 t 0 1 2 3 4 5 6 7 8 9 10 Time (hours) [4] 3 For (b) The probability that Chaminda uses the internet on any day is 5 . Examiner′s Use 3 The probability that Niluka uses the internet on any day is 4 . (i) Complete the tree diagram. Chaminda Niluka 3 Uses the 4 internet Uses the 3 internet 5 Does not … use the internet … Uses the internet … Does not use the internet Does not … use the internet [2] (ii) Calculate the probability, that on any day, at least one of the two students uses the internet. Answer(b)(ii) … [3] (iii) Calculate the probability that Chaminda uses the internet on three consecutive days. Answer(b)(iii) … [2] _____________________________________________________________________________________

15 marks

Mark scheme: 5 (a) (i) 3.81 or 3.812 to 3.813 or 4 M1 for midpoints soi (condone 1 error or omission 3h 49min nfww and M1 for use of ∑fx with x in correct interval including both boundaries (condone 1 further error or omission) and M1 (dep on 2nd M1) for ∑fx ÷ 80 (305 ÷ 80) (ii) Correct histogram 4 B1 for each correct block and B1 for correct widths 2 1 3 1 2 1 (b) (i) , , , oe 2 B1 for or both s in correct place 5 4 4 4 5 4 18  9  2 1 (ii) nfww 3 M2 FT for 1 – their × their 20  10  5 4 3 3 3 1 2 3 or × + × their + their × oe 5 4 5 4 5 4 or 2 1 M1 FT for their × their 5 4 3 1 2 3 or × their + their × oe 5 4 5 4 27 3 3 3 (iii) [0.216] 2 M1 for × × 125 5 5 5 2 2 2

This question in 0580/43 Oct/Nov 2013

7 (a) 1.0 0.8 0.6 Frequency density 0.4 0.2 m 0 10 20 30 40 50 60 70 80 90 100 Mass (grams) The histogram shows some information about the masses (m grams) of 39 apples. (i) Show that there are 12 apples in the interval 70 < m Y 100 . Answer(a)(i) [1] (ii) Calculate an estimate of the mean mass of the 39 apples. Answer(a)(ii) … g [5] (b) The mean mass of 20 oranges is 70 g. One orange is eaten. The mean mass of the remaining oranges is 70.5 g. Find the mass of the orange that was eaten. Answer(b) … g [3] __________________________________________________________________________________________

9 marks

Mark scheme: 24 7 (a) (i) (100 – 70) × 0.4 [= 12] or better 1 Accept × 39 oe 78 (ii) 60.9 or 60.89… nfww 5 B1 for 3 or 4 correct extra frequencies 3, 6, 10, 8 soi M1 for at least 4 of mid-interval values 15, 40, 55, 65, 85 soi M1 for Σfx where x is any value in each interval allow their frequencies provided integers and they must be shown [3 × 15 + 6 × 40 + 10 × 55 + 8 × 65 + 12 × 85] [2375] M1 (dependent on second M1) for ÷ 39 or ÷ (3 + 6 + 10 + 8 +12) (b) 60.5 3 M2 for 20 × 70 – 19 × 70.5 oe or M1 for either 20 × 70 or 19 × 70.5 600 600

This question in 0580/42 May/June 2014

6 A company tested 200 light bulbs to fi nd the lifetime, T hours, of each bulb. The results are shown in the table. Lifetime Number (T hours) of bulbs 0 < T Y 1000 10 1000 < T Y 1500 30 1500 < T Y 2000 55 2000 < T Y 2500 72 2500 < T Y 3500 33 (a) Calculate an estimate of the mean lifetime for the 200 light bulbs. Answer(a) … hours [4] (b) (i) Complete the cumulative frequency table. Lifetime (T hours) T Y 1000 T Y 1500 T Y 2000 T Y 2500 T Y 3500 Number of bulbs [2] (ii) On the grid, draw a cumulative frequency diagram to show this information. 200 150 Cumulative frequency 100 50 T 0 500 1000 1500 2000 2500 3000 3500 Lifetime (hours) [3] (iii) The company says that the average lifetime of a bulb is 2200 hours. Estimate the number of bulbs that lasted longer than 2200 hours. Answer(b)(iii) … [2] (c) Robert buys one energy saving bulb and one halogen bulb. 9 The probability that the energy saving bulb lasts longer than 3500 hours is . 10 3 The probability that the halogen bulb lasts longer than 3500 hours is . 5 Work out the probability that exactly one of the bulbs will last longer than 3500 hours. Answer(c) … [4] __________________________________________________________________________________________

15 marks

Mark scheme: 6 (a) 2000 or 1998.75 or 1998.8 or 4 M1 for midpoints soi (condone 1 error or omission) 1999 nfww (500, 1250, 1750, 2250, 3000) and with x in correct interval M1 for use of ∑fx including both boundaries (condone 1 further error or omission) (5000, 37500, 96250, 162000, 99000) and M1 (dep on 2nd M1) for ∑fx ÷ 200 (b) (i) 10, 40, 95, 167, 200 2 B1 for 2 correct (ii) Correct curve or ruled polygon 3 B1FT their (b)(i) for 5 correct heights within 1mm vertically and B1 for 5 points at upper ends of intervals on correct vertical line and B1FT (dep on at least B1) for increasing curve or polygon through 5 points After 0 scored, SC1FT for 4 correct points plotted (iii) 68 to 80 2 M1 for 120 to 132 seen 21 9 2 1 3 (c) oe 4 M3 for × + × oe or better 50 10 5 10 5 or 9 2 1 3 18 3 M2 for × or × or oe or oe 10 5 10 5 50 50 or 1 2 M1 for sight of and 10 5 Qu Answers Mark Part Marks

This question in 0580/41 Oct/Nov 2014

9 (a) Ricardo asks some motorists how many litres of fuel they use in one day. The numbers of litres, correct to the nearest litre, are shown in the table. Number of litres 16 17 18 19 20 Number of motorists 11 10 p 4 8 (i) For this table, the mean number of litres is 17.7 . Calculate the value of p. Answer(a)(i) p = … [4] (ii) Find the median number of litres. Answer(a)(ii) … litres [1] (b) Manuel completed a journey of 320 km in his car. The fuel for the journey cost $1.28 for every 6.4 km travelled. (i) Calculate the cost of fuel for this journey. Answer(b)(i) $ … [2] (ii) When Manuel travelled 480 km in his car it used 60 litres of fuel. Manuel’s car used fuel at the same rate for the journey of 320 km. Calculate the number of litres of fuel the car used for the journey of 320 km. Answer(b)(ii) … litres [2] (iii) Calculate the cost per litre of fuel used for the journey of 320 km. Answer(b)(iii) $ … [2] (c) Ellie drives a car at a constant speed of 30 m/s correct to the nearest 5 m/s. She maintains this speed for 5 minutes correct to the nearest 10 seconds. Calculate the upper bound of the distance in kilometres that Ellie could have travelled. Answer(c) … km [5] __________________________________________________________________________________________

16 marks

Mark scheme: 16 × 11 + 17 × 10 + 18 p + 19 × 4 + 20 × 8 9 (a) (i) 7 4 M2 for = 177. 11 + 10 + 4 + 8 + p or better or M1 for sum of two correct products or better or for [total =] 11 + 10 + 4 + 8 + p and B1 for 582 + 18p = 17.7 (33 + p) (ii) 17 1FT STRICT FT median for their p if integer 320 (b) (i) 64 2 M1 for × 1.28 oe 4.6 320 (ii) 40 2 M1 for × 60 oe 480 (iii) 1.6[0] 2FT FT their (b)(i) / their (b)(ii) evaluated correctly to 2dp 480 M1 for their (b)(i) / their (b)(ii) or × 1.28 ÷ 60 4.6 (c) 9.9125 cao 5 B4 for answer 9912.5 or M1 for 25 to 35 × 290 to 310 oe and B1 for 32.5 used and B1 for 305 or 5 mins 5 secs used and M1 indep for any correct conversion seen m to km

This question in 0580/43 Oct/Nov 2014

9 The table shows the height, h cm, of 40 children in a class. Height (h cm) 120 < h  130 130 < h  140 140 < h  144 144 < h  150 150 < h  170 Frequency 3 14 4 6 13 (a) Write down the class interval containing the median. Answer(a) … < h  … [1] (b) Calculate an estimate of the mean height. Answer(b) … cm [4] (c) Complete the histogram. 2 1.5 Frequency density 1 0.5 0 h 120 130 140 150 160 170 Height (cm) [4] __________________________________________________________________________________________

9 marks

Mark scheme: 9 (a) 140 < h ≤ 144 1 (b) 144.875 nfww 4 M1 for at least 4 correct mid-values soi M1 for ∑fx where x is in the correct interval, allow one further error/omission M1 dep for ÷ 40 dependent on second method mark (c) 4 correct blocks 4 B3 for 3 correct blocks B2 for 2 correct blocks B1 for 1 correct block or at least 3 correct frequency densities (1.4, 1, 1, 0.65 )

This question in 0580/42 Feb/March 2015

6 The table shows the time, t minutes, that 400 people take to complete a test. Time taken 0  t  10 10  t  24 24  t  30 30  t  40 40  t  60 60  t  70 (t mins) Frequency 10 90 135 85 70 10 (a) (i) Write down the modal time interval. Answer(a)(i) … min [1] (ii) Calculate an estimate of the mean time taken to complete the test. Answer(a)(ii) … min [4] (b) (i) Complete the table of cumulative frequencies. Time taken t  10 t  24 t  30 t  40 t  60 t  70 (t mins) Cumulative 10 100 400 frequency [2] (ii) On the grid opposite, draw a cumulative frequency diagram to show this information. 400 350 300 250 Cumulative frequency 200 150 100 50 t 0 10 20 30 40 50 60 70 Time taken (minutes) [3] (c) Use your graph to estimate (i) the median time, Answer(c)(i) … min [1] (ii) the inter-quartile range, Answer(c)(ii) … min [2] (iii) the 15th percentile, Answer(c)(iii) … min [2] (iv) the number of people who took more than 50 minutes. Answer(c)(iv) … [2]

17 marks

Mark scheme: 6 (a) (i) 24 < t Y 30 1 (ii) 30.9 or 30.875 nfww 4 M1 for midpoints soi (condone 1 error or omission) 5, 17, 27, 35, 50, 65 soi M1 for use of ∑fx with x in correct interval including both boundaries (condone 1 further error or omission) (50, 1530, 3645, 2975, 3500, 650) and M1 (dep on 2nd M1) for ∑fx ÷ 400 (b) (i) [10 100] 235 320 390 [400] 2 B1 for any two correct SC1 for 235, n, n + 70 n > 235 (ii) Correct curve or polygon 3 B1 for correct horizontal placement B1FT for correct vertical placement B1FT dep on at least B1 for reasonable increasing curve or polygon through their 6 points If zero scored SC1 for 5 out of 6 points correctly plotted (c) (i) 27.5 to 29 1 (ii) 12 to 14 2 B1 for 36 to 38 or 24 seen (iii) 18 to 20 2 B1 for 60 seen or marked on grid (iv) 30 to 45 2 B1 for 355 to 370 seen

This question in 0580/41 May/June 2015

7 (a) A group of 50 students estimated the mass, M grams, of sweets in a jar. The results are shown in the table. Mass (M grams) Number of students 0 < M  200 5 200 < M  300 9 300 < M  350 18 350 < M  400 12 400 < M  500 6 (i) Calculate an estimate of the mean. Answer(a)(i) … grams [4] (ii) Complete this histogram to show the information in the table. 0.4 0.3 Frequency 0.2 density 0.1 M 0 100 200 300 400 500 Mass (grams) [3] (b) A group of 50 adults also estimated the mass, M grams, of the sweets in the jar. The histogram below shows information about their estimates. Use the histograms to make two comparisons between the distributions of the estimates of the students and the adults. 0.4 0.3 Frequency 0.2 density 0.1 M 0 100 200 300 400 500 Mass (grams) Answer(b) 1 … … 2 … … [2] __________________________________________________________________________________________

9 marks

Mark scheme: 7 (a) (i) 316 4 M1 for 100, 250, 325, 375, 450 soi M1 for Σfm with m’s in intervals including boundaries [15800] M1 (dep on 2nd M1) for their Σfm ÷ 50 (ii) Three correct blocks with heights 3 B2 for two correct blocks 0.09, 0.36, 0.24 with correct widths or and no gaps B1 for one correct block or three correct frequency densities soi (b) Students have a greater range of B1 estimates oe [On average] adults estimated a B1 greater mass oe

This question in 0580/42 May/June 2015

6 120 students take a mathematics examination. (a) The time taken, m minutes, for each student to answer question 1 is shown in this table. Time (m minutes) 0 < m G 1 1 < m G 2 2 < m G 3 3 < m G 4 4 < m G 5 5 < m G 6 Frequency 72 21 9 11 5 2 Calculate an estimate of the mean time taken. Answer(a) … min [4] (b) (i) Using the table in part (a), complete this cumulative frequency table. Time (m minutes) m G 1 m G 2 m G 3 m G 4 m G 5 m G 6 Cumulative frequency 72 120 [2] (ii) Draw a cumulative frequency diagram to show the time taken. 120 110 100 90 80 70 Cumulative frequency 60 50 40 30 20 10 0 m 1 2 3 4 5 6 Time (minutes) [3] (iii) Use your cumulative frequency diagram to find (a) the median, Answer(b)(iii)(a) … min [1] (b) the inter-quartile range, Answer(b)(iii)(b) … min [2] (c) the 35th percentile. Answer(b)(iii)(c) … min [2] (c) A new frequency table is made from the table shown in part (a). Time (m minutes) 0 < m G 1 1 < m G 3 3 < m G 6 Frequency 72 (i) Complete the table above. [2] (ii) A histogram was drawn and the height of the first block representing the time 0 < m G 1 was 3.6 cm. Calculate the heights of the other two blocks. Answer(c)(ii) … cm and … cm [3] __________________________________________________________________________________________

19 marks

Mark scheme: 6 (a) 1.35 nfww 4 M1 for 0.5, 1.5, 2.5, 3.5, 4.5, 5.5 soi, M1 for Σfm soi by 162 where m is in correct interval including boundaries M1dep for Σfm ÷ 120 or Σfm ÷ Σf dependent on second M1 earned (b) (i) 93, 102, 113, 118 2 SC1FT for 1 error (ii) Correct diagram 3 B1FT for correct vertical plots and B1 for correct horizontal plots and B1FT dep on at least B1 for reasonable increasing curve or polygon through their 6 points If zero scored, SC1FT for 5 out of 6 correct plots (iii) (a) 0.6 to 0.85 1 (b) 1.3 to 1.7 2 B1 for UQ = 1.7 to 1.9 or LQ = 0.2 to 0.4 (c) 0.3 to 0.6 2FT Allow in correct range provided there is no evidence of reading at 35 or FT their reading at 42 B1 for 42 soi (c) (i) 30 and 18 2 B1 for each (ii) 0.75 and 0.3 3FT FT (their 30) ÷ 40 and (their 18) ÷ 60 B2FT for either 0.75 or 0.3 or M1 for their 30 ÷ 2 or ÷ 20 or for their 18 ÷ 3 or ÷ 20

This question in 0580/41 Oct/Nov 2015

3 Leo measured the rainfall each day, in millimetres, for 120 days. The cumulative frequency table shows the results. Rainfall (r mm) r  20 r  25 r  35 r  40 r  60 r  70 Cumulative 5 13 72 90 117 120 frequency (a) On the grid below, draw a cumulative frequency diagram to show these results. 120 100 80 Cumulative frequency 60 40 20 r 0 10 20 30 40 50 60 70 Rainfall (mm) [3] (b) (i) Find the median. Answer(b)(i) … mm [1] (ii) Use your diagram to find the number of days when the rainfall was more than 50 mm. Answer(b)(ii) … [2] (c) Use the information in the cumulative frequency table to complete the frequency table below. Rainfall (r mm) 0  r  20 20  r  25 25  r  35 35  r  40 40  r  60 60  r  70 Frequency 5 59 3 [2] (d) Use your frequency table to calculate an estimate of the mean. You must show all your working. Answer(d) … mm [4] (e) In a histogram drawn to show the information in the table in part (c), the frequency density for the interval 25  r  35 is 5.9 . Calculate the frequency density for the intervals 20  r  25 , 40  r  60 and 60  r  70 . Answer(e) 20  r  25 … 40  r  60 … 60  r  70 … [4]

16 marks

Mark scheme: 3 (a) Correct diagram 3 B1 for correct vertical plots and B1 for correct horizontal plots and B1 dep on at least B1 for reasonable increasing curve or polygon through their 6 points If zero scored, SC1 for 5 out of 6 correct plots (b) (i) 32 to 34 1 (ii) 120 – reading at r = 50 2FT B1FT for reading at r = 50 seen (c) 8 18 27 2 B1 for 2 correct 1 (d) 4 M1 for mid-values soi 35.2 or 35 or 35.16 to 35.17 6 with x in the correct interval M1 FT for ∑fx nfww including boundaries 120 M1dep for ∑fx ÷ dependent on second M1 earned (e) 1.6 4FT FT from (c) their 8 ÷ 5 and their 27 ÷ 20 1.35 B3FT for any 2 correct 0.3 or B2FT for first or second answer correct or B1 for 0.3 only 0 6

This question in 0580/42 Oct/Nov 2015

6 The table shows information about the masses, m grams, of 160 apples. Mass (m grams) 30 < m  80 80 < m  100 100 < m  120 120 < m  200 Frequency 50 30 40 40 (a) Calculate an estimate of the mean. Answer(a) … g [4] (b) On the grid, complete the histogram to show the information in the frequency table. 2.5 2 1.5 Frequency density 1 0.5 m 0 40 80 120 160 200 Mass (grams) [3] (c) An apple is chosen at random from the 160 apples. Find the probability that its mass is more than 120 g. Answer(c) … [1] (d) Two apples are chosen at random from the 160 apples, without replacement. Find the probability that (i) they both have a mass of more than 120 g, Answer(d)(i) … [2] (ii) one has a mass of more than 120 g and one has a mass of 80 g or less. Answer(d)(ii) … [3] __________________________________________________________________________________________

13 marks

Mark scheme: 6 (a) 101.5625 or 102 or 101.5 to 101.6 4 M1 for 55, 90, 110, 160 soi nfww M1 for Σfm with frequencies and each m in or on a boundary of a correct interval 2750, 2700, 4400, 6400 M1 dep on 2nd M for ÷ 160 (b) Correct histogram drawn with 3 B1 for each correct block correct widths and heights If zero scored, SC1 for correct heights or 1, 1.5 and 2 (no gaps) frequency densities 40 (c) oe 1 160 1560 40 39 (d) (i) oe 2 M1 for × 25440 160 159 4000 40 50 50 40 (ii) oe 3 M2 for × + × oe 25 440 160 159 160 159 or M1 for one of these products soi

This question in 0580/43 Oct/Nov 2015

4 Coins are put into a machine to pay for parking cars. The probability that the machine rejects a coin is 0.05 . (a) Adhira puts 2 coins into the machine. (i) Calculate the probability that the machine rejects both coins. … [2] (ii) Calculate the probability that the machine accepts at least one coin. … [1] (b) Raj puts 4 coins into the machine. Calculate the probability that the machine rejects exactly one coin. … [3] (c) The table shows the amount of money, $a, received for parking each day for 200 days. Amount ($a) 200 1 a G 250 250 1 a G 300 300 1 a G 350 350 1 a G 400 400 1 a G 450 450 1 a G 500 Frequency 13 19 27 56 62 23 Calculate an estimate of the mean amount of money received each day. $ … [4] (d) The histogram shows the length of time that 200 cars were parked. 1.2 1.1 1 0.9 0.8 0.7 Frequency density 0.6 0.5 0.4 0.3 0.2 0.1 0 50 100 150 200 250 300 350 400 Time in minutes (i) Calculate the number of cars that were parked for 100 minutes or less. … [1] (ii) Calculate the percentage of cars that were parked for more than 250 minutes. … % [2]

13 marks

Mark scheme: 14 (a) (i) 2 M1 for 0.052 oe 0.0025 or oe 400 399 (ii) 1FT FT for 1 – (their (a)(i)) oe 0.9975 or oe 400 6859 (b) 3 M2 for 4(0.05 × 0.953) oe 0.171 or 0.1714 to 0.1715 or 40 000 M1 for 0.05 × 0.953 oe seen or for the 4 combinations correctly identified

This question in 0580/43 May/June 2016

4 200 people run 10 km. The table shows some information about the times, t minutes, taken to run the 10 km. Time 30 1 t G 40 40 1 t G 45 45 1 t G 50 50 1 t G 55 55 1 t G 60 60 1 t G 80 (t minutes) Frequency 8 22 95 55 14 6 (a) Howard takes 40 minutes to run the 10 km. Calculate his average speed in kilometres per hour. … km/h [2] (b) Calculate an estimate of the mean time. … min [4] (c) Complete the histogram to show the information in the table. 20 18 16 14 12 Frequency density 10 8 6 4 2 0 t 30 40 50 60 70 80 Time (minutes) [4] (d) (i) Use the frequency table opposite to complete the cumulative frequency table. Time t G 40 t G 45 t G 50 t G 55 t G 60 t G 80 (t minutes) Cumulative 8 30 194 200 frequency [1] (ii) Draw a cumulative frequency diagram to show the information in the table above. 200 180 160 140 120 Cumulative frequency 100 80 60 40 20 0 t 30 40 50 60 70 80 Time (minutes) [3] (iii) Use your diagram to find (a) the median, … min [1] (b) the 90th percentile, … min [1] (c) the number of people who took more than 58 minutes to run the 10 km. … [2]

18 marks

Mark scheme: 4 (a) 15 2 M1 for 10 ÷ 40 [× 60] (b) 49.2 nfww 4 M1 for 35, 42.5, 47.5, 52.5, 57.5, 70 soi M1 for Σ fx 8 × 35 + 22 × 42.5 + 95 × 47.5 + 55 × 52.5 + 14 × 57.5 + 6 × 70 M1 dep for their Σ fx ÷ 200 (c) Fully correct histogram 4 B3 for 4 correct blocks or B2 for 2 or 3 correct blocks or B1 for 1 correct block If zero scored, SC1 for correct frequency densities 0.8, 19, 11, 2.8, 0.3 soi (d) (i) 125, 180 1 (ii) Correct diagram 3 B1FT their (d)(i) for 6 correct heights within correct square(including boundaries) or touching correct line if should be on a grid line and B1 for 6 points at upper ends of intervals on correct vertical line and B1FT (dep on at least B1) for increasing curve or polygon through 6 points If zero scored, SC1FT for 5 correct points plotted (iii) (a) 48 to 49 1 (b) 55 1 (c) 8 to 14 2FT B1FT for 186 to 192 seen

This question in 0580/42 Oct/Nov 2016

7 The table shows information about the time taken by 400 people to complete a race. Time taken 45 1 m G 50 50 1 m G 60 60 1 m G 70 70 1 m G 90 90 1 m G 100 100 1 m G 120 (m minutes) Frequency 23 64 122 136 26 29 (a) Calculate an estimate of the mean time taken. … min [4] (b) (i) Complete the cumulative frequency table. Time taken m G 50 m G 60 m G 70 m G 90 m G 100 m G 120 (m minutes) Cumulative 23 400 frequency [2] (ii) On the grid, draw a cumulative frequency diagram to show this information. 400 300 Cumulative 200frequency 100 0 m 40 50 60 70 80 90 100 110 120 Time taken (minutes) [3] (iii) Use your diagram to estimate (a) the median, … min [1] (b) the inter-quartile range, … min [2] (c) the 60th percentile. … min [2]

14 marks

Mark scheme: 7 (a) 72.7 or 72.70 to 72.71 nfww 4 M1 for midpoints soi (condone 1 error or omission) (47.5, 55, 65, 80, 95, 110) M1 for use of ∑fx with x in correct interval including both boundaries (condone 1 further error or omission) (1092.5, 3520, 7930, 10880, 2470, 3190) M1 (dep on 2nd M1) for ∑fx ÷ 400 (b) (i) [23] 87 209 345 371 [400] 2 B1 for 2 or 3 correct (ii) Correct graph 3 B1FT their (b)(i) for 6 correct heights B1 for 6 points at upper ends of intervals on correct vertical line B1FT (dep on at least B1) for increasing curve or polygon through 6 points After 0 scored, SC1FT their (b)(i) for 5 correct points plotted (iii) (a) 69 to 70 1 (b) 20 to 23 2FT FT their cumulative freq curve M1 for correct UQ or LQ for their cumulative freq curve (c) 72 to 75 2 M1 for 240 soi

This question in 0580/42 Feb/March 2017

2 The time taken for each of 90 cars to complete one lap of a race track is shown in the table. Time (t seconds) 70 1 t G 71 71 1 t G 72 72 1 t G 73 73 1 t G 74 74 1 t G 75 Frequency 17 24 21 18 10 (a) Write down the modal time interval. … 1 t G … [1] (b) Calculate an estimate of the mean time. … s [4] (c) (i) Complete the cumulative frequency table. Time (t seconds) t G 71 t G 72 t G 73 t G 74 t G 75 Cumulative frequency 17 [2] (ii) On the grid, draw a cumulative frequency diagram to show this information. 90 80 70 60 50 Cumulative frequency 40 30 20 10 0 t 70 71 72 73 74 75 Time (seconds) [3] (iii) Find the median time. … s [1] (iv) Find the inter-quartile range. … s [2] (d) One lap of the race track measures 3720 metres, correct to the nearest 10 metres. A car completed the lap in 75 seconds, correct to the nearest second. Calculate the upper bound for the average speed of this car. Give your answer in kilometres per hour. … km/h [4]

17 marks

Mark scheme: 2(a) 71 < t ⩽ 72 1 2(b) 72.3 or 72.27 to 72.28 nfww 4 M1 for midpoints soi (condone 1 error or omission) M1 for use of ∑fx with x in correct interval including both boundaries M1 (dep on 2nd M1) for ∑fx ÷ 90 2(c)(i) 41, 62, 80, 90 2 B1 for 2 correct values 2(c)(ii) Correct curve 3 B1FT their (c)(i) for 5 correct heights B1 for 5 points plotted at upper ends of intervals B1FT (dep on at least B1) for increasing curve or increasing polygon through 5 points If zero scored, SC1FT for 4 correct points plotted 2(c)(iii) 72.1 to 72.4 1 2(c)(iv) 1.9 to 2.2 2 M1 for UQ = 73.2 to 73.4 or LQ = 71.2 to 71.3 2(d) 180 cao nfww 4 B3 for 50 [m/s] nfww OR 3725 ÷ 1000 M3 for 74.5 ÷ 3600 OR M2 for 3725 ÷ 74.5 or M1 for 3725 or 74.5 seen or for (3715 to 3725) ÷ (74.5 to 75.5) M1 indep for multiply by 3.6 oe

This question in 0580/41 May/June 2017

3 (a) 200 students estimate the capacity, x millilitres, of a cup. The results are shown in the frequency table. Capacity (x ml) 0 1 x G 100 100 1 x G 150 150 1 x G 200 200 1 x G 250 250 1 x G 400 Frequency 20 55 66 35 24 (i) Calculate an estimate of the mean. … ml [4] (ii) Complete the histogram. 1.5 1 Frequency density 0.5 0 x 0 100 200 300 400 Capacity (ml) [4] (b) The 200 students also estimate the mass, m grams, of a small rock. The results are shown in the cumulative frequency table. Mass (m grams) m G 50 m G 100 m G 150 m G 200 m G 250 Cumulative frequency 28 64 104 168 200 (i) On the grid, draw a cumulative frequency diagram. 200 150 Cumulative frequency 100 50 0 m 0 50 100 150 200 250 Mass (g) [3] (ii) Find (a) the 65th percentile, … g [1] (b) the number of students who estimated more than 75 g. … [2]

14 marks

Mark scheme: 3(a)(i) 175.5 nfww 4 M1 for at least four of 50, 125, 175, 225, 325 soi M1 for Σ fx with x inside or on boundary of each interval their Σ fx M1 (dep on second M1) for 200 3(a)(ii) Fully correct histogram 4 B1 for each correct bar If zero scored, B1 for 0.2, 1.32, 0.7, 0.16 seen 3(b)(i) Fully correct cumulative 3 B1 for correct horizontal plots frequency diagram B1 for correct vertical plots B1FT dep on at least B1 earned for points joined with smooth increasing curve or polygon If zero scored, SC1 for 4 correct plotted points 3(b)(ii)(a) 170 to 175 1 3(b)(ii)(b) 152 to 158 2 M1 for 42 to 48 written

This question in 0580/42 May/June 2017

8 (a) The table shows the marks gained by 10 students in their physics test and their mathematics test. Physics 63 61 14 27 72 75 44 40 28 50 mark Mathematics 52 80 16 36 79 75 51 35 24 63 mark (i) Complete the scatter diagram below. The first six points have been plotted for you. 80 70 60 50 Mathematics mark 40 30 20 10 0 10 20 30 40 50 60 70 80 Physics mark [2] (ii) What type of correlation is shown in the scatter diagram? … [1] (b) The marks of 30 students in a spelling test are shown in the table below. Mark 0 1 2 3 4 5 Frequency 2 4 5 5 6 8 Find the mean, median, mode and range of these marks. Mean = … Median = … Mode = … Range = … [7] (c) The table shows the marks gained by some students in their English test. Mark 52 75 91 Number of students x 45 11 The mean mark for these students is 70.3 . Find the value of x. x = … [3]

13 marks

Mark scheme: 8(a)(i) 4 points correctly plotted 2 B1 for 2 or 3 points correctly plotted 8(a)(ii) Positive 1 8(b) mean 3.1 3 sum of products M2 for 30 or M1 for at least 4 correct products soi median 3 2 M1 for 15.5 oe indicated mode 5 1 range 5 1 8(c) 24 nfww 3 x × 52 + 45 × 75 + 11 × 91 M1 for [ = 70.3] x + 45 + 11 M1 for clearing their fraction

This question in 0580/43 May/June 2017

5 The histogram shows the distribution of the masses, m grams, of 360 apples. Key: the shaded square represents 10 apples Frequency density 0 m 140 160 180 200 220 240 Mass (grams) (a) Use the histogram to complete the frequency table. Mass (m grams) Number of apples 140 < m G 170 170 < m G 180 180 < m G 190 190 < m G 210 92 210 < m G 240 42 [3] (b) Calculate an estimate of the mean mass of the 360 apples. … g [4]

7 marks

Mark scheme: 5(a) 54, 76, 96 3 B1 for each 5(b) 187 or 186.8 to 186.9 nfww 4 M1 for 155, 175, 185, 200, 225 soi M1 for Σfm with their frequencies from (a) 155 × their 54 + 175 × their 76 + 185 × their 96 + 200 × 92 + 225 × 42 M1 (dep on second M1) for their Σfm ÷ 360

This question in 0580/41 Oct/Nov 2017

6 (a) There are 100 students in group A. The teacher records the distance, d metres, each student runs in one minute. The results are shown in the cumulative frequency diagram. 100 90 80 70 60 Cumulative 50 frequency 40 30 20 10 0 d 100 200 300 400 Distance (metres) Find (i) the median, … m [1] (ii) the upper quartile, … m [1] (iii) the inter-quartile range, … m [1] (iv) the number of students who run more than 350 m. … [2] (b) There are 100 students in group B. The teacher records the distance, d metres, each of these students runs in one minute. The results are shown in the frequency table. Distance 100 1 d G 200 200 1 d G 250 250 1 d G 280 280 1 d G 32 0 320 1 d G 400(d metres) Number of 20 22 30 16 12students (i) Calculate an estimate of the mean distance for group B. … m [4] (ii) Complete the histogram to show the information in the frequency table. 1 0.8 0.6 Frequency density 0.4 0.2 0 d 100 200 300 400 Distance (metres) [4] (c) For the 100 students in group B, the median is 258 m. Complete the statement. On average, the students in group A run … than the students in group B. [1]

14 marks

Mark scheme: 6(a)(i) 280 1 6(a)(ii) 320 1 6(a)(iii) 90 1 6(a)(iv) 10 2 M1 for 90 written 6(b)(i) 250.2 nfww cao 4 M1 for at least 4 correct mid-values M1 for Σfx M1 dep on second M1 for Σfx ÷ 100 6(b)(ii) Correct completion of 4 B1 for each correct block histogram If zero scored, then SC1 for correct frequency densities seen 6(c) [22 m] further oe 1

This question in 0580/42 Oct/Nov 2017

4 The table shows information about the time, t minutes, taken for each of 150 girls to complete an essay. Time (t minutes) 60 1 t G 65 65 1 t G 70 70 1 t G 80 80 1 t G 100 100 < t G 150 Frequency 10 26 34 58 22 (a) Write down the interval that contains the median time. … 1 t G … [1] (b) Calculate an estimate of the mean time. … min [4] (c) Rafay looks at the frequency table. (i) He says that it is not possible to work out the range of the times. Explain why he is correct. … … [1] (ii) He draws a pie chart to show this information. Calculate the sector angle for the interval 65 1 t G 70 minutes. … [2] (d) A girl is chosen at random. Work out the probability that she took more than 100 minutes to complete the essay. … [1] (e) Two girls are chosen at random. Work out the probability that, to complete the essay, (i) they both took 65 minutes or less, … [2] (ii) one took 65 minutes or less and the other took more than 100 minutes. … [3] (f) The information in the frequency table is shown in a histogram. The height of the block for the 60 1 t G 65 interval is 5 cm. Complete the table. Time (t minutes) 60 1 t G 65 65 1 t G 70 70 1 t G 80 80 1 t G 100 100 1 t G 150 Height of block 5 (cm) [3]

17 marks

Mark scheme: 4(a) 80 < t ⩽100 1 4(b) 86 nfww 4 M1 for midpoints soi M1 for use of Σfx with x in correct interval including both boundaries M1 (dep on 2nd M1) for Σfx ÷ 150 4(c)(i) Reference to not knowing the 1 individual values so we do not know the highest or the lowest values 4(c)(ii) 62.4 2 M1 for 26 ÷ 150 or 360 ÷ 150 soi 4(d) 22 1 oe 150 4(e)(i) 90 2 10 9 oe M1 for × 22350 150 149 100 After zero scored, SC1 for answer oe 22500 4(e)(ii) 440 3 10 22 22 10 oe M2 for × + × oe 22350 150 149 150 149 or 10 22 22 10 M1 for × or × oe 150 149 150 149 440 After zero scored, SC1 for answer oe 22500 4(f) 13, 8.5, 7.25, 1.1 3 B2 for 3 correct or B1 for 1 correct or for 3 correct FD.s 5.2, 3.4, 2.9, 0.44 oe

This question in 0580/43 Oct/Nov 2017

2 The time taken for each of 120 students to complete a cooking challenge is shown in the table. Time (t minutes) 20 1 t G 25 25 1 t G 30 30 1 t G 35 35 1 t G 40 40 1 t G 45 Frequency 44 32 28 12 4 (a) (i) Write down the modal time interval. … 1 t G … [1] (ii) Write down the interval containing the median time. … 1 t G … [1] (iii) Calculate an estimate of the mean time. … min [4] (iv) A student is chosen at random. Find the probability that this student takes more than 40 minutes. … [1] (b) (i) Complete the cumulative frequency table. Time (t minutes) t G 20 t G 25 t G 30 t G 35 t G 40 t G 45 Cumulative 0 44 frequency [2] (ii) On the grid, draw a cumulative frequency diagram to show this information. 120 110 100 90 80 70 Cumulative frequency 60 50 40 30 20 10 0 t 20 25 30 35 40 45 Time (minutes) [3] (iii) Find the median time. … min [1] (iv) Find the interquartile range. … min [2] (v) Find the number of students who took more than 37 minutes to complete the cooking challenge. … [2]

17 marks

Mark scheme: 2(a)(i) 20 [< t ⩽] 25 1 2(a)(ii) 25 [< t ⩽] 30 1 2(a)(iii) 28.3 or 28.33.. 4 M1 for 22.5, 27.5, 32.5, 37.5, 42.5 soi M1 for ∑fx where x is in the correct interval including boundaries M1dep for ∑fx ÷ 120 or ∑fx ÷ (44 + 32 + 28 + 12 + 4) 2(a)(iv) 4 1 oe isw 120 2(b)(i) 76, 104, 116, 120 2 B1 for one error FT other values or for 3 correct 2(b)(ii) Correct curve 3 B1 for correct horizontal placement for 6 plots B1FT for correct vertical placement for 6 plots B1FT dep on at least B1 for reasonable increasing curve or polygon through their 6 points If 0 scored SC1FT for 5 out of 6 points correctly plotted 2(b)(iii) 27 to 27.5 1 2(b)(iv) 8.5 to 9.5 2 B1 for [UQ=] 32 to 32.5 or [LQ=] 23 to 23.5 2(b)(v) 8, 9, 10, 11 or 12 2 B1 for 108 to 112 seen or B1FT their graph reading at 37 mins seen

This question in 0580/42 May/June 2018

3 (a) The scatter diagram shows the physics mark and the chemistry mark for each of 12 students. 7 6 5 4 Chemistry mark 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Physics mark (i) What type of correlation is shown in the scatter diagram? … [1] (ii) On the scatter diagram, draw a line of best fit. [1] (iii) Find an estimate of the chemistry mark for another student who has a physics mark of 4. … [1] (b) A teacher records the number of days each of the 24 students in her class are absent. The frequency table shows the results. Number of days 0 1 2 3 4 5 Frequency 10 8 3 2 0 1 Find the mode, the median and the mean. Mode = … Median = … Mean = … [5] (c) Three sizes of eggs are sold in a shop. The table shows the number of eggs of each size sold in one day. Size Small Medium Large Mass (m grams) 46 1 m G 52 52 1 m G 62 62 1 m G 80 Number of eggs sold 78 180 162 (i) Calculate an estimate of the mean mass. … g [4] (ii) On the grid, draw a histogram to show the information in the table. 20 18 16 14 12 Frequency 10 density 8 6 4 2 0 m 40 50 60 70 80 Mass (grams) [4]

16 marks

Mark scheme: 3(a)(i) Positive 1 Ignore strong, weak, etc. 3(a)(ii) Correct ruled line 1 3(a)(iii) 2 1 3(b) [mode = ] 0 5 B1 [median = ] 1 B1 [mean = ] 1.04 or 1.041 to 1.042 B3 or M2 for ([10 × 0] + 8 × 1 + 3 × 2 + 2 × 3 + [0 × 4] + 1 × 5) ÷ 24 oe or M1 for [10 × 0] + 8 × 1 + 3 × 2 + 2 × 3 + [0 × 4] + 1 × 5 oe 3(c)(i) 60.9 or 60.91... nfww 4 M1 for 49, 57, 71 correct M1 for use of Σfx with x in the correct interval including both boundaries M1 (dep on 2nd M1) for their (78 × 49 + 180 × 57 + 162 × 71) ÷ (78 + 180 + 162) 3(c)(ii) Correct histogram 4 B1 for correct widths in correct position B1 height 13 B1 height 18 B1 height 9 If 0 scored B1 for 13, 18 and 9 seen

This question in 0580/43 May/June 2018

4 A school nurse records the height, h cm, of each of 180 children. The table shows the information. Height 60 1 h G 70 70 1 h G 90 90 1 h G 100 100 1 h G 110 110 1 h G 115 115 1 h G 125 (h cm) Frequency 8 26 35 67 28 16 (a) Calculate an estimate of the mean. Give your answer correct to 1 decimal place. … cm [4] (b) In a histogram showing the information, the height of the bar for the interval 60 1 h G 70 is 0.4 cm. Calculate the height of the bar for each of the following intervals. 115 1 h G 125 … cm 110 1 h G 115 … cm 70 1 h G 90 … cm [3] (c) Complete the cumulative frequency table below. Height h G 70 h G 90 h G 100 h G 110 h G 115 h G 125 (h cm) Cumulative 180 frequency [2] (d) On the grid opposite, draw a cumulative frequency diagram. 180 160 140 120 100 Cumulative frequency 80 60 40 20 0 h 60 70 80 90 100 110 120 130 Height (cm) [3] (e) Use your cumulative frequency diagram to find an estimate of (i) the interquartile range, … cm [2] (ii) the 70th percentile, … cm [2] (iii) the number of children with height greater than 106 cm. … [2]

18 marks

Mark scheme: 4(a) 100.2 nfww 4 M1 for midpoints soi 65, 80, 95, 105, 112.5, 120 M1 for use of ∑fx with x in correct interval including both boundaries M1dep for ∑fx ÷ 180 dep on previous M1 4(b) 0.8 3 B1 for each 2.8 If zero scored, SC1 for 1.6, 5.6 and 1.3 0.65 seen 4(c) 8 34 69 136 164 2 B1 for one error FT other values or for 3 or 4 correct 4(d) Correct diagram 3 B1FT for correct vertical placement for 6 plots B1 for correct horizontal placement for 6 plots B1FT dep on at least B1 for reasonable increasing curve or polygon through their 6 points If zero scored, SC1FT for 5 out of 6 correct plots 4(e)(i) 15 to 17 2 B1 for [LQ =] 93 to 94 or [UQ =] 109 to 110 4(e)(ii) 107 to 109 2 B1 for 126 seen 4(e)(iii) 66 to 72 2 FT their graph for 2 marks B1 for answer 106 to 114 or B1FT their graph reading at 106 cm seen

This question in 0580/41 Oct/Nov 2018

5 (a) A factory recycles metal. The mass, x tonnes, of metal is measured each week. The table shows the results for 52 weeks. Mass (x tonnes) 100 1 x G 200 200 1 x G 250 250 1 x G 300 300 1 x G 500 Frequency 8 20 12 12 (i) Calculate an estimate of the mean. … tonnes [4] (ii) 0.5 0.4 0.3 Frequency density 0.2 0.1 0 x 0 100 200 300 400 500 Mass (tonnes) On the grid, draw a histogram to show the information in the table. [4] (b) Another factory also recycles metal. The mass, x tonnes, of metal is measured each day for a number of days. The cumulative frequency diagram shows the results. 100 90 80 70 60 Cumulative frequency 50 40 30 20 10 0 x 0 10 20 30 40 50 60 70 80 Mass (tonnes) (i) For how many days was the mass measured? … [1] (ii) Find an estimate of the median. … tonnes [1] (iii) Find an estimate of the upper quartile. … tonnes [1] (iv) Find an estimate of the interquartile range. … tonnes [1] (v) Find an estimate of the number of days when the mass was greater than 20 tonnes. … [2]

14 marks

Mark scheme: 5(a)(i) 265 or 265.3 to 265.4 nfww 4 M1 for mid-values 150, 225, 275, 400 soi M1 for Σ fx where x is in correct interval including boundaries M1 dep for Σ fx ÷ 52 dependent on second M1 5(a)(ii) Correct histogram 4 B1 for each correct block If 0 scored, SC1 for the four frequency densities seen 5(b)(i) 100 1 5(b)(ii) 56 1 5(b)(iii) 62 1 5(b)(iv) 24 1 5(b)(v) 88 2 M1 for evidence of 12 written

This question in 0580/43 Oct/Nov 2018

7 (a) 20 students each record the mass, p grams, of their pencil case. The table below shows the results. Mass 0 1 p G 50 50 1 p G 100 100 1 p G 125 125 1 p G 150 150 1 p G 200 ( p grams) Frequency 2 5 4 6 3 (i) Calculate an estimate of the mean mass. … g [4] (ii) Use the frequency table above to complete the cumulative frequency table. Mass p G 50 p G 100 p G 125 p G 150 p G 200 ( p grams) Cumulative 20 frequency [2] (iii) A student is chosen at random. Find the probability that this student has a pencil case with a mass greater than 150 g. … [1] (b) Some students each record the mass, m kg, of their school bag. Adil wants to draw a histogram to show this information. Complete the table below. Mass (m kg) 0 1 m G 4 4 1 m G 6 6 1 m G 7 7 1 m G 10 Frequency 32 42 Height of bar on 1.6 2 1.2 2.8 histogram (cm) [2] (c) The frequency table below shows information about the number of books read by some students in a reading marathon. Number of 1 2 3 4 5 6 7 8 books read Frequency 2 2 16 10 9 4 x 2 (i) The mean number of books read is 4.28 . Find the value of x. x = … [3] (ii) Write down the mode. … [1] (iii) Write down the median. … [1]

14 marks

Mark scheme: 7(a)(i) 111.25 4 M1 for midpoints soi (25, 75, 112.5, 137.5, 175) M1 for ∑fx with x in correct interval including both boundaries M1 (dep on 2nd M1) for ∑fx ÷ 20 7(a)(ii) 2 7 11 17 2 B1 for three correct 7(a)(iii) 3 1 oe 20 7(b) 20 6 2 B1 for one correct value or [SF = ] 5 or 1 oe 5 7(c)(i) 5 nfww 3 M2 for ∑fx ÷ ∑f = 4.28 oe or M1 for 179 + 7x oe or 4.28 × (45 + x ) oe seen 7(c)(ii) 3 1 7(c)(iii) 4 1

This question in 0580/42 Feb/March 2019

4 (a) The test scores of 14 students are shown below. 21 21 23 26 25 21 22 20 21 23 23 27 24 21 (i) Find the range, mode, median and mean of the test scores. Range = … Mode = … Median = … Mean = … [6] (ii) A student is chosen at random. Find the probability that this student has a test score of more than 24. … [1] (b) Petra records the score in each test she takes. The mean of the first n scores is x. The mean of the first (n – 1) scores is (x + 1). Find the nth score in terms of n and x. Give your answer in its simplest form. … [3] (c) During one year the midday temperatures, t°C, in Zedford were recorded. The table shows the results. Temperature (t°C) 0 1 t G 10 10 1 t G 15 15 1 t G 20 20 1 t G 25 25 1 t G 35 Number of days 50 85 100 120 10 (i) Calculate an estimate of the mean. … °C [4] (ii) Complete the histogram to show the information in the table. 25 20 15 Frequency density 10 5 0 0 5 10 15 20 25 30 35 t Temperature (°C) [4]

18 marks

Mark scheme: 4(a)(i) range = 7 1 mode = 21 1 median = 22.5 2 M1 for evidence of middle value mean = 22.7 or 22.71… 2 M1 for use of Σ x ÷ 14 4(a)(ii) 3 1 oe 14 4(b) x − n + 1 final answer 3 M2 for nx − ( n − 1)( x + 1) or M1 for ( n − 1)( x + 1) 4(c)(i) 16.6 or 16.60 to 16.61 nfww 4 M1 for 5, 12.5, 17.5, 22.5, 30 soi M1 for Σfx where x is in correct interval, including boundaries M1 dep on second M1 for Σfx 50 + 85 + 100 + 120 + 10 4(c)(ii) Correct histogram 4 B1 for each correct block If 0 scored, SC1 for 5, 20, 24, 1 seen

This question in 0580/41 May/June 2019

9 100 students were each asked how much money, $m, they spent in one week. The frequency table shows the results. Amount ($m) 0 1 m G 5 5 1 m G 10 10 1 m G 20 20 1 m G 30 30 1 m G 50 Frequency 16 38 30 9 7 (a) Calculate an estimate of the mean. $ … [4] (b) Complete the cumulative frequency table below. Amount ($m) m G 5 m G 10 m G 20 m G 30 m G 50 Cumulative 16 100 frequency [2] (c) On the grid, draw the cumulative frequency diagram. 100 80 60 Cumulative frequency 40 20 0 0 10 20 30 40 50 m Amount ($) [3] (d) Use your cumulative frequency diagram to find an estimate for (i) the median, $ … [1] (ii) the interquartile range, $ … [2] (iii) the number of students who spent more than $25. … [2]

14 marks

Mark scheme: 9(a) 12.8[0] 4 M1 for midpoints soi M1 for use of ∑fm with m in correct interval including both boundaries M1 (dep on 2nd M1) for ∑fm ÷ 100 9(b) 54 84 93 2 B1 for 2 correct or 1 error and 2 correct or FT 9(c) correct diagram with all points 3 B1FT their (b) for plots at 5 correct heights correctly plotted B1 for 5 points at upper ends of intervals on correct vertical line B1FT (dep on at least B1) for increasing curve or polygon through 5 points After 0 scored, SC1FT for 4 correct points plotted 9(d)(i) 9 to 9.8 final answer 1 9(d)(ii) 8.5 to 11.5 2 B1 for [UQ =] 15.5 to 17.5 or [LQ =] 6 to 7 seen 9(d)(iii) 10, 11 or 12 2 B1 for 88 to 90 seen or for answer between 10 and 12

This question in 0580/42 May/June 2019

6 The table shows the time, t seconds, taken by each of 120 boys to solve a puzzle. Time 20 1 t G 30 30 1 t G 35 35 1 t G 40 40 1 t G 60 60 1 t G 100 (t seconds) Frequency 38 27 21 16 18 (a) Calculate an estimate of the mean time. … s [4] (b) On the grid, complete the histogram to show the information in the frequency table. 6 5 4 Frequency density 3 2 1 0 20 30 40 50 60 70 80 90 100 t Time (seconds) [4]

8 marks

Mark scheme: 6(a) 40.5 or 40.45[8..] or 40.46 nfww 4 M1 for 25, 32.5, 37.5, 50, 80 soi M1 for Σft M1 dep for theirΣft ÷ 120 6(b) Fully correct histogram 4 B1 for each correct bar If 0 scored, SC1 for frequency densities of 5.4, 4.2, 0.8 and 0.45 seen

This question in 0580/43 May/June 2019

6 (a) The cumulative frequency diagram shows information about the times taken by 200 students to solve a problem. 200 180 160 140 120 Cumulative 100 frequency 80 60 40 20 0 0 10 20 30 40 50 60 Time (minutes) Use the cumulative frequency diagram to find an estimate for (i) the median, … min [1] (ii) the interquartile range, … min [2] (iii) the number of students who took more than 40 minutes. … [2] (b) Roberto records the value of each of the coins he has at home. The table shows the results. Value (cents) 1 2 5 10 20 50 Frequency 3 1 3 2 4 2 (i) Find the range. … cents [1] (ii) Find the mode. … cents [1] (iii) Find the median. … cents [1] (iv) Work out the total value of Roberto’s coins. … cents [2] (v) Work out the mean. … cents [1] (c) The histogram shows information about the masses of 100 boxes. 10 9 8 7 6 Frequency 5 density 4 3 2 1 0 0 5 10 15 20 25 30 Mass (kilograms) Calculate an estimate of the mean. … kg [6]

17 marks

Mark scheme: 6(a)(i) 34 1 6(a)(ii) 18 2 B1 for [l.q. = ] 25 or [u.q. = ] 43 seen 6(a)(iii) 60 2 M1 for 140 written 6(b)(i) 49 1 6(b)(ii) 20 1 6(b)(iii) 10 1 6(b)(iv) 220 2 M1 for 3 × 1 + 1 × 2 + 3 × 5 + 2 × 10 + 4 × 20 + 2 × 50 6(b)(v) 14.7 or 14.66 to 14.67 1 FT their (iv) ÷ 15 6(c) 13.25 nfww 6 B2 for frequencies 30, 40, 30 soi or B1 for 2 of these M1 for 5, 12.5, 22.5 M1 Σ fx with their frequencies (if seen) and each x in correct interval including boundaries Σfx M1 dependent for (dependent on 100 second M1) OR Alternative Method B2 for frequencies 15, 15, 40, 10, 10, 10 soi or B1 for 2 of 15, 40, 10 M1 for 2.5, 7.5, 12.5, 17.5, 22.5, 27.5 M1 Σ fx with their frequencies (if seen) and each x in correct interval including boundaries Σfx M1 dependent for (dependent on 100 second M1)

This question in 0580/41 Oct/Nov 2019

5 The cumulative frequency diagram shows information about the distance, d km, travelled by each of 60 male cyclists in one weekend. 60 50 40 Cumulative 30 frequency 20 10 0 d 0 20 40 60 80 100 120 Distance (km) (a) Use the cumulative frequency diagram to find an estimate of (i) the median, … km [1] (ii) the lower quartile, … km [1] (iii) the interquartile range. … km [1] (b) For the same weekend, the interquartile range for the distances travelled by a group of female cyclists is 40 km. Make one comment comparing the distribution of the distances travelled by the males with the distribution of the distances travelled by the females. … … [1] (c) A male cyclist is chosen at random. Find the probability that he travelled more than 50 km. … [2] (d) (i) Use the cumulative frequency diagram to complete this frequency table. Distance (d km) Number of male cyclists 0 1 d G 40 18 40 1 d G 50 9 50 1 d G 60 60 1 d G 70 70 1 d G 90 90 1 d G 120 2 [2] (ii) Calculate an estimate of the mean distance travelled. … km [4]

12 marks

Mark scheme: 5(a)(i) 52 1 5(a)(ii) 36 1 5(a)(iii) 26 1 FT 62 – their (a)(ii) evaluated correctly 5(b) Valid comment 1 Strict FT their (a)(iii), e.g. distances for females are more varied 5(c) 11 2 27 oe M1 for 27 written or answer of oe 20 60 5(d)(i) [18 9] 14 12 5 [2] 2 B1 for 1 correct value 5(d)(ii) 48.75 nfww 4 M1 for midpoints soi M1 for use of ∑fx with their frequencies M1 (dep on 2nd M1) for ∑fx ÷ (60 or by their ∑f )

This question in 0580/43 Oct/Nov 2019

2 The heights, h metres, of the 120 boys in an athletics club are recorded. The table shows information about the heights of the boys. Height (h metres) 1.3 1 h G 1.4 1.4 1 h G 1.5 1.5 1 h G 1.6 1.6 1 h G 1 .7 1.7 1 h G 1.8 1.8 1 h G 1.9 Frequency 7 18 30 24 27 14 (a) (i) Write down the modal class. … 1 h G … [1] (ii) Calculate an estimate of the mean height. … m [4] (b) (i) One boy is chosen at random from the club. Find the probability that this boy has a height greater than 1.8 m. … [1] (ii) Three boys are chosen at random from the club. Calculate the probability that one of the boys has a height greater than 1.8 m and the other two boys each have a height of 1.4 m or less. … [4] (c) (i) Use the frequency table on page 4 to complete the cumulative frequency table. Height h G 1.4 h G 1.5 h G 1.6 h G 1.7 h G 1.8 h G 1.9(h metres) Cumulative 7 25frequency [2] (ii) On the grid, draw a cumulative frequency diagram to show this information. 120 110 100 90 80 Cumulative 70 frequency 60 50 40 30 20 10 0 h 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Height (m) [3] (d) Use your diagram to find an estimate for (i) the median height, … m [1] (ii) the 40th percentile. … m [2]

18 marks

Mark scheme: 2(a)(i) 1.5 < h ⩽ 1.6 1 2(a)(ii) 1.62 or 1.623… nfww 4 M1 for 1.35, 1.45, 1.55, 1.65, 1.75 1.85 soi M1 for Σfx M1 dep for their Σfx ÷ 120 2(b)(i) 14 1 oe 120 2(b)(ii) 21 4  14 7 6  oe M3 for 3  × ×  20060  120 119 118  14 7 6 or M2 for × × isw 120 119 118 14 7 6 or M1 for , , 120 119 118 343 After 0 scored, SC1 for answer or 864000 343 oe 288000 2(c)(i) 55, 79, 106, 120 2 B1 for 2 or 3 correct 2(c)(ii) Correct diagram 3 B1 for correct horizontal plots B1FT for correct vertical plots B1FT dep on at least B1 for reasonable increasing curve or polygon through their 6 points If 0 scored SC1 for 5 out of 6 points correctly plotted 2(d)(i) 1.62 to 1.63 1 2(d)(ii) 1.57 to 1.58 2 B1 for 48 soi

This question in 0580/41 May/June 2020

3 The speed, v km/h, of each of 200 cars passing a building is measured. The table shows the results. Speed (v km/h) 0 1 v G 20 20 1 v G 40 40 1 v G 45 45 1 v G 50 50 1 v G 60 60 1 v G 80 Frequency 16 34 62 58 26 4 (a) Calculate an estimate of the mean. … km/h [4] (b) (i) Use the frequency table to complete the cumulative frequency table. Speed (v km/h) v G 20 v G 40 v G 45 v G 50 v G 60 v G 80 Cumulative frequency 16 50 196 200 [1] (ii) On the grid, draw a cumulative frequency diagram. 200 180 160 140 120 Cumulative frequency 100 80 60 40 20 0 v 0 10 20 30 40 50 60 70 80 Speed (km/h) [3] (iii) Use your diagram to find an estimate of (a) the upper quartile, … km/h [1] (b) the number of cars with a speed greater than 35 km/h. … [2] (c) Two of the 200 cars are chosen at random. Find the probability that they both have a speed greater than 50 km/h. … [2] (d) A new frequency table is made by combining intervals. Speed (v km/h) 0 1 v G 40 40 1 v G 50 50 1 v G 80 Frequency 50 120 30 On the grid, draw a histogram to show the information in this table. 15 10 Frequency density 5 0 v 0 10 20 30 40 50 60 70 80 Speed (km/h) [3]

16 marks

Mark scheme: 3(a) 41.4 4 M1 for 10, 30, 42.5, 47.5, 55, 70 M1 for Σ fx where x lies in or on the boundary of each interval. Σfx M1 dep for dep on second M1 200 3(b)(i) 112, 170 1 3(b)(ii) Correct diagram 3 B1 for correct horizontal plot B1FT for correct vertical plots B1 FT dep on at least B1 earned for reasonable increasing curve or polygon through their 6 points If 0 scored SC1FT for 5 out of 6 points plotted correctly 3(b)(iii)(a) 48 1 3(b)(iii)(b) 160 2 M1 for 40 seen 3(c) 87 2 30 29 oe M1 for × oe 3980 200 199 3(d) Correct histogram 3 B1 for each column If 0 scored SC1 for correct frequency densities soi 1.25, 12, 1

This question in 0580/42 May/June 2020

3 (a) Here is some information about the masses of potatoes in a sack: • The largest potato has a mass of 174 g. • The range is 69 g. • The median is 148 g. • The lower quartile is 121 g. • The interquartile range is 38 g. On the grid below, draw a box-and-whisker plot to show this information. 100 110 120 130 140 150 160 170 180 Mass (g) [4] (b) The table shows the marks scored by some students in a test. Mark 5 6 7 8 9 10 Frequency 8 2 12 2 0 1 Calculate the mean mark. … [3]

7 marks

Mark scheme: 3(a) correct diagram 4 B1 for median line correctly drawn at 148 B1 for 105 soi B1 for whisker at 159 soi 3(b) 6.48 3 M1 for (5 × 8) + (6 × 2) + (12 × 7) + … M1dep for their ∑fx ÷ their (8 + 2 + 12 + 2 + 0 + 1)

This question in 0580/43 May/June 2020

3 (a) Women Men 0 60 120 180 240 300 360 420 Time (minutes) The box-and-whisker plots show the times spent exercising in one week by a group of women and a group of men. Below are two statements comparing these times. For each one, write down whether you agree or disagree, giving a reason for your answer. Agree or Statement Reason disagree On average, the women spent less time exercising than the men. The times for the women show less variation than the times for the men. [2] (b) The frequency table shows the times, t minutes, each of 100 children spent exercising in one week. Time (t minutes) 0 1 t G 60 60 1 t G 100 100 1 t G 160 160 1 t G 220 220 1 t G 320 Frequency 41 24 23 8 4 (i) Calculate an estimate of the mean time. … min [4] (ii) The information in the frequency table is shown in this cumulative frequency diagram. 100 80 60 Cumulative frequency 40 20 0 t 0 60 120 180 240 300 360 Time (minutes) Use the cumulative frequency diagram to find an estimate of (a) the 60th percentile, … min [1] (b) the number of children who spent more than 3 hours exercising. … [2] (iii) A histogram is drawn to show the information in the frequency table. The height of the bar for the interval 60 1 t G 100 is 10.8 cm. Calculate the height of the bar for the interval 160 1 t G 220 . … cm [2]

11 marks

Mark scheme: 3(a) Disagree: the median for the women is 2 B1 for each correct statement oe greater (than the median for the men) oe Disagree: the men have a smaller [interquartile] range of times oe 3(b)(i) 87.4 nfww 4 M1 for mid-points soi (30, 80, 130, 190, 270) M1 for use of Σfm with m in correct interval including both boundaries M1 (dep on 2nd M1) for Σfm ÷ (41 + 24 + 23 + 8 + 4) 3(b)(ii)(a) 90 1 3(b)(ii)(b) 8 2 B1 for 92 seen 3(b)(iii) 2.4 2 24 8 M1 for or 40 60 1 Or B1 for [multiplier] 18 or 18

This question in 0580/41 Oct/Nov 2020

7 (a) The box-and-whisker plot shows information about the marks scored by some students in a test. 0 10 20 30 40 50 60 70 80 90 100 Mark (i) Write down the median mark. … [1] (ii) Work out the range. … [1] (iii) Jais scored a mark in the test that was higher than the marks scored by 75% of the students. Write down a possible mark for Jais. … [1] (iv) This box-and-whisker plot shows information about the marks scored by the same students in a second test. 0 10 20 30 40 50 60 70 80 90 100 Mark Make one comparison between the distributions of marks in the two tests. … … [1] (b) The table shows information about the height, h cm, of each of 50 plants. Height (h cm) 0 1 h G 20 20 1 h G 30 30 1 h G 34 34 1 h G 40 40 1 h G 60 Frequency 4 9 20 15 2 Calculate an estimate of the mean. … cm [4] (c) Some apples are weighed and the mass, m grams, of each apple is recorded. The table shows the results. Mass (m grams) 100 1 m G 110 110 1 m G 115 115 1 m G 125 125 1 m G 140 Frequency 50 x 44 51 The histogram shows some of the information from the table. 8 6 Frequency density 4 2 0 m 100 110 120 130 140 Mass (grams) (i) Work out the value of x. x = … [1] (ii) Complete the histogram. [2]

11 marks

Mark scheme: 7(a)(i) 70 1 7(a)(ii) 78 1 7(a)(iii) Value in range 86 <V ≤ 90 1 7(a)(iv) One general comment interpreting 1 the median comparison nfww e.g. Students did better on second test oe OR One general comment interpreting IQR/range comparison nfww e.g. Students marks were more consistent on the 2nd test oe 7(b) 31.2 4 M1 for mid-values soi M1 for Σfm where m is any value in interval including boundaries M1 (dep on second M1) for their Σfm ÷ 50 7(c)(i) 38 1 7(c)(ii) Blocks of heights 4.4 and 3.4 with 2 B1 for each correct block correct widths If B0 scored, SC1 for both correct frequency densities soi

This question in 0580/42 Feb/March 2021

4 (a) The mass, m kg, of each of 40 parcels in a warehouse is recorded. The table shows information about the masses of these parcels. Mass (m kg) 0.5 1 m G 1 1 1 m G 2 2 1 m G 4 4 1 m G 7 7 1 m G 12 Frequency 4 7 15 10 4 (i) Complete the histogram to show this information. 9 8 7 6 5 Frequency density 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 m Mass (kg) [3] (ii) Calculate an estimate of the mean mass of the parcels. … kg [4] (iii) A parcel is picked at random from the 40 parcels. Find the probability that this parcel has a mass of 2 kg or less. … [1] (iv) Two parcels are picked at random without replacement from those with a mass greater than 2 kg. Work out the probability that one of them has a mass greater than 7 kg and the other has a mass of 4 kg or less. … [3] (b) A van delivers parcels from a different warehouse. The box-and-whisker plot shows information about the masses of the parcels in the van. 0 1 2 3 4 5 6 7 8 9 Mass (kg) (i) Find the median. … kg [1] (ii) Find the interquartile range. … kg [1] (iii) Two parcels are removed from the van at the first delivery. The masses of these parcels are 2.4 kg and 5.8 kg. Describe the effect that removing these parcels has on the median mass of the remaining parcels. Give a reason for your answer. … … [2]

15 marks

Mark scheme: 4(a)(i) Correct histogram 3 B1 for each correct block If 0 scored, SC1 for any two of fds 7.5, 3.33…, 0.8 oe soi 4(a)(ii) 3.7875 or 3.79 or 3.787 or 3.788 4 M1 for 0.75, 1.5, 3, 5.5, 9.5 soi M1 for Σfx M1 dep for their Σfx ÷ 40 4(a)(iii) 11 1 oe 40 4(a)(iv) 30 3 4 15 oe M2 for [2 ×] × oe 203 29 28 4 15 or M1 for or oe seen 29 29  4 26  After 0 scored, SC1 for [ 2 ×]  ×   40 39  oe 120 or for answer oe 841 4(b)(i) 4.6 1 4(b)(ii) 3.2 1 4(b)(iii) [median] remains the same oe 2 B1 for each statement and one is below [the median/middle] and one is above oe

This question in 0580/42 May/June 2021

3 (a) Zoe’s test scores last term were 6 7 7 7 8 9 9 10 10. Find (i) the range, … [1] (ii) the mode, … [1] (iii) the median. … [1] (b) The cumulative frequency diagram shows information about the time taken by each of 200 students to solve a problem. 200 180 160 140 120 Cumulative 100 frequency 80 60 40 20 0 0 2 4 6 8 10 12 14 16 18 20 Time (minutes) Use the diagram to find an estimate of (i) the median, … min [1] (ii) the interquartile range. … min [2] (c) The test scores of 200 students are shown in the table. Score 5 6 7 8 9 10 Frequency 3 10 43 75 48 21 Calculate the mean. … [3] (d) The height, in cm, of each of 200 plants is measured. The histogram shows the results. 4 3 Frequency 2 density 1 0 50 60 70 80 90 100 110 120 130 140 150 160 Height (cm) Calculate an estimate of the mean height. You must show all your working. … cm [6]

15 marks

Mark scheme: 3(a)(i) 4 1 3(a)(ii) 7 1 3(a)(iii) 8 1 3(b)(i) 14 1 3(b)(ii) 4 2 B1 for [ l.q. =] 11 or [u.q =] 15 3(c) 8.09 3 M1 for 5 × 3 + 10 × 6 + 43 × 7 + 75 × 8 + 48 × 9 + 21 × 10 M1 dep ÷ 200 3(d) 30, 70, 40, 36, 24 seen B2 B1 for 3 or 4 correct or M1 for 1 × (80 – 50), 3.5 × (100 – 80), 4 × (110 – 100), 3.6 × (120 – 110) and 0.6 × (160 – 120) oe (their 30 × 65 + their 70 × 90 M3 M1 for midpoints soi + their 40 × 105 + their 36 × 115 M1 for Σfx , x in interval or boundary of + their 24 × 140) ÷ 200 interval M1 dep on second M1 for ÷ 200 99.75 A1

This question in 0580/43 May/June 2021

3 The cumulative frequency diagram shows information about the mass, m kg, of each of 80 boys. 80 60 Cumulative frequency 40 20 0 m 30 40 50 60 70 80 90 Mass (kg) (a) m 30 40 50 60 70 80 90 Mass (kg) On the grid, draw a box-and-whisker plot to show the information in the cumulative frequency diagram. [4] (b) Use the cumulative frequency diagram to find an estimate of (i) the 30th percentile, … kg [2] (ii) the number of boys with a mass greater than 75 kg. … [2] (c) (i) Use the cumulative frequency diagram to complete this frequency table. Mass 30 1 m G 40 40 1 m G 50 50 1 m G 60 60 1 m G 70 70 1 m G 80 80 1 m G 90(m kg) Frequency 8 12 14 10 [1] (ii) Calculate an estimate of the mean mass of the boys. … kg [4] (iii) Two boys are chosen at random from those with a mass greater than 70 kg. Find the probability that one of them has a mass greater than 80 kg and the other has a mass of 80 kg or less. … [3]

16 marks

Mark scheme: 3(a) Correct box-and-whisker plot 4 B1 for lowest value and highest value at 30 and 90 B1 for LQ and UQ at 50 and 72 B1 for median at 63 3(b)(i) 56 2 M1 for 24 soi 3(b)(ii) 16 2 B1 for 64 written 3(c)(i) 14, 22 1 3(c)(ii) 61.5 4 M1 for 35, 45, 55, 65, 75, 85 soi M1 for Σ fx M1 dep for their Σ fx ÷ (8 + 12 +their 14 + their 22 + 14 +10) or Σ fx ÷ 80 3(c)(iii) 35 3  10 14  oe M2 for [2]  ×  oe 69  24 23  10 14 or M1 for or oe seen 24 24 35 If 0 scored, SC1 for answer oe 72

This question in 0580/41 Oct/Nov 2021

2 (a) The cumulative frequency diagram shows information about the floor area, a m 2, of each of 80 houses. 80 70 60 50 Cumulative 40frequency 30 20 10 0 a 40 60 80 100 120 140 160 180 200 Floor area (m2) Use the diagram to find an estimate of (i) the median, … m2 [1] (ii) the lower quartile, … m2 [1] (iii) the interquartile range, … m2 [1] (iv) the number of houses with a floor area greater than 120 m2. … [2] (b) The information about the 80 floor areas is shown in this frequency table. Floor area 2 40 1 a G 60 60 1 a G 80 8 0 1 a G 100 100 1 a G 130 130 1 a G 160 160 1 a G 200 ( a m ) Frequency 14 17 18 15 9 7 (i) Calculate an estimate of the mean floor area. … m2 [4] (ii) Complete the histogram to show the information in the frequency table. 1.0 Frequency 0.5density 0 a 40 60 80 100 120 140 160 180 200 Floor area (m2) [4] (iii) Two of the houses are picked at random. Find the probability that one of the houses has a floor area greater than 130 m 2 and the other has a floor area 60 m 2 or less. … [3]

16 marks

Mark scheme: 2(a)(i) 90 1 2(a)(ii) 68 1 2(a)(iii) 52 1 FT 120 – their (a)(ii) 2(a)(iv) 20 2 B1 for 60 in working or as answer 2(b)(i) 97.5 4 M1 for mid-points soi (50, 70, 90, 115, 145, 180) M1 for use of Σfm with m in correct interval including both boundaries M1 for (dep on 2nd M1) for Σfm ÷ 80 2(b)(ii) Bars with heights 0.9, 0.5, 0.3, 0.175 4 B1 for each correct bar and with correct widths If 0 scored, SC1 for 3 or 4 correct frequency densities 2(b)(iii) 28 3 16 14 oe M2 for [2 ×] × oe 395 80 79 16 16 14 or M1 for or oe or oe or 80 79 80 14 oe seen 79 7 If 0 scored, SC1 for answer oe 100

This question in 0580/42 Oct/Nov 2021

8 (a) Jean asks 600 people to choose their favourite sport. The pie chart shows some of this information. Football 105° 60° 27° Tennis Rugby (i) Show that 100 people choose tennis. [1] (ii) Work out how many people choose rugby. … [2] (iii) 125 people choose cricket and the rest choose swimming. Complete the pie chart to show this information. [2] (b) The heights of some plants are measured: • smallest height = 0.6 cm • range = 8.1 cm • median = 5.2 cm • lower quartile = 3.4 cm • interquartile range = 4.1 cm. On the grid, draw a box-and-whisker plot to show this information. 0 1 2 3 4 5 6 7 8 9 10 Height (cm) [3] (c) A dice is rolled 100 times. The frequency table shows the results. Score 1 2 3 4 5 6 Frequency 16 25 17 19 8 15 Find (i) the range, … [1] (ii) the mode, … [1] (iii) the median. … [1] (d) 50 students answer a mathematics question. The table shows the time, t seconds, taken by each student to answer the question. Time (t seconds) 10 1 t G 20 2 0 1 t G 25 25 1 t G 30 30 1 t G 50 50 1 t G 80 Frequency 2 8 12 16 12 Calculate an estimate of the mean. … s [4]

15 marks

Mark scheme: 8(a)(i) 60 1 × 600 oe 360 8(a)(ii) 45 2 27 M1 for × 600 oe 360 8(a)(iii) Correct straight line on the pie chart 2 B1 for 75 8(b) Correct diagram 3 B1 for any three of 0.6, 3.4, 5.2, 7.5, 8.7 correctly placed B1 for 7.5 and 8.7 seen 0.6 3.4 5.2 7.5 8.7 8(c)(i) 5 1 8(c)(ii) 2 1 8(c)(iii) 3 1 8(d) 39.2 4 M1 for mid-values soi M1 for Σfx with x in correct interval including boundaries Σfx M1 dep for dep on second M1 50

This question in 0580/43 Oct/Nov 2021

5 The table shows information about the mass, m grams, of each of 120 letters. Mass (m grams) 0 1 m G 50 50 1 m G 100 100 1 m G 200 200 1 m G 500 Frequency 43 31 25 21 (a) Calculate an estimate of the mean mass. … g [4] (b) Iraj draws a histogram to show this information. He makes the height of the first bar 17.2 cm. Calculate the height of each of the remaining bars. height of bar for 50 1 m G 100 … cm height of bar for 100 1 m G 200 … cm height of bar for 200 1 m G 500 … cm [3] (c) Complete the cumulative frequency table. Mass (m grams) m G 50 m G 100 m G 200 m G 500 Cumulative frequency [2] (d) Draw a cumulative frequency diagram. 120 100 80 Cumulative 60 frequency 40 20 0 m 0 100 200 300 400 500 Mass (g) [3] (e) Use the cumulative frequency diagram to find an estimate for (i) the median, … g [1] (ii) the upper quartile, … g [1] (iii) the 40th percentile, … g [2] (iv) the number of letters with a mass m where 250 1 m G 400 . … [2]

18 marks

Mark scheme: 5(a) 5 4 M1 for midpoints soi 121 or 120.8… or 120 6 M1 for use of ∑fx with x in correct interval including both boundaries but not if x is 50, 50, 100 and 300 M1 (dep on 2nd M1) for ∑fx ÷ 120 5(b) 12.4 5 1.4 3 B1 for each If 0 scored SC1 for fd’s [0.86,] 0.62, 0.25 and 0.07 oe 5(c) 43 74 99 120 2 B1 for 2 or 3 correct 5(d) Correct diagram 3 B1 for correct horizontal placement for 4 plots B1FT for correct vertical placement for 4 plots B1FT dep on at least B1 for reasonable increasing curve or polygon through their 4 points If 0 scored SC1 FT for 3 out of 4 points correctly plotted 5(e)(i) Strict FT their median reading 1 5(e)(ii) Strict FT their UQ reading 1 5(e)(iii) Strict FT their reading at 40th 2 B1 for 48 written or mark at cf = 48 on graph percentile 5(e)(iv) Strict FT their reading at 400 2 B1 for either correct reading at 250 or 400 – their reading at 250

This question in 0580/42 Feb/March 2022

1 (a) The list shows 15 midday temperatures, in degrees Celsius, in Suntown. 17 21 21 18 23 22 25 19 21 17 19 18 21 24 23 (i) Complete the stem-and-leaf diagram to show this information. 1 7 2 Key: 1|7 represents 17 °C [2] (ii) Find the median. … °C [1] (iii) Find the upper quartile. … °C [1] (iv) Rahul draws a pie chart to show this information. Calculate the sector angle for the number of days the temperature is 18 °C. … [2] (b) 0 50 100 150 200 Mass (grams) The box-and-whisker plot shows information about the masses, in grams, of some apples. (i) Find the median. … g [1] (ii) Find the range. … g [1] (iii) Find the interquartile range. … g [1] (c) (i) The time, t minutes, spent on homework in one week by each of 200 students is recorded. The table shows the results. Time (t minutes) 40 1 t G 60 60 1 t G 80 80 1 t G 90 90 1 t G 100 100 1 t G 150 Frequency 6 10 70 84 30 Calculate an estimate of the mean. … min [4] (ii) A new table with different class intervals is completed. Time (t minutes) 40 1 t G 90 90 1 t G 150 Frequency 86 114 On a histogram the height of the bar for the 40 1 t G 90 interval is 17.2 cm. Calculate the height of the bar for the 90 1 t G 150 interval. … cm [2]

15 marks

Mark scheme: 1(a)(i) 1 7 7 8 8 9 9 2 1 1 1 1 2 3 3 4 5 2 B1 for one row correctly ordered or for fully correct unordered stem-and-leaf diagram or for a correct diagram with one error or omission 1(a)(ii) 21 1 1(a)(iii) 23 1 1(a)(iv) 48 2 M1 for   2 360 15  or   360 2 15  1(b)(i) 120 1 1(b)(ii) 130 1 1(b)(iii) 60 1 1(c)(i) 93.4 4 M1 for mid-values soi M1 for fx M1 dep on second M for 200   fx 1(c)(ii) 19 2 M1 for 86 50 or 114 60

This question in 0580/41 May/June 2022

7 Information about the mass, m kg, of each of 150 children is recorded in the frequency table. Mass (m kg) 0 1 m G 10 10 1 m G 20 20 1 m G 25 25 1 m G 40 40 1 m G 50 Frequency 12 38 32 50 18 (a) Calculate an estimate of the mean mass. … kg [4] (b) Draw a histogram to show the information in the table. 8 7 6 5 Frequency density 4 3 2 1 0 m 0 10 20 30 40 50 Mass (kg) [4] (c) (i) Use the frequency table to complete this cumulative frequency table. Mass (m kg) m G 10 m G 20 m G 25 m G 40 m G 50 Cumulative frequency [2] (ii) Calculate the percentage of children with a mass greater than 10 kg. … % [2]

12 marks

Mark scheme: 7(a) 25.2 or 25.23… 4 M1 for midpoints soi M1 for use of ∑fx with x in correct interval including both boundaries M1 (dep on 2nd M1) for ∑fx ÷ 150 7(b) 5 correct blocks 4 B3 for 4 correct blocks or B2 for 3 correct blocks or B1 for 2 correct blocks or block widths 10, 10, 5, 15, 10 If 0 scored SC1 for 4 correct frequency densities from 1.2, 3.8, 6.4, 3.33[3…] and 1.8 oe soi 7(c)(i) 12, 50, 82, 132, 150 2 B1 for 3 or 4 correct 7(c)(ii) 92 2 M1 for 150 −12 oe seen If 0 scored, SC1 for answer 8[%]

This question in 0580/42 May/June 2022

5 The time, t minutes, taken by each of 80 people to travel to work is recorded. The table shows information about these times. Time 0 1 t G 5 5 1 t G 10 10 1 t G 20 20 1 t G 35 35 1 t G 60 (t minutes) Frequency 3 7 18 28 24 (a) (i) Write down the class interval containing the median time. … 1 t G … [1] (ii) Calculate an estimate of the mean time. … min [4] (b) (i) One of these 80 people is chosen at random. Find the probability that this person took longer than 10 minutes to travel to work. Give your answer as a fraction in its simplest form. … [2] (ii) Two people are chosen at random from those taking 20 minutes or less to travel to work. Calculate the probability that one of these people took 5 minutes or less and the other took more than 5 minutes. … [3] (c) (i) Use the frequency table on page 8 to complete the cumulative frequency table. Time t G 5 t G 10 t G 20 t G 35 t G 60 (t minutes) Cumulative 3 10 80 frequency [1] (ii) On the grid, draw a cumulative frequency diagram to show this information. 80 70 60 50 Cumulative frequency 40 30 20 10 0 0 10 20 30 40 50 60 t Time (minutes) [3] (iii) Find an estimate for the 80th percentile. … min [2] (iv) Find an estimate for the percentage of people who took longer than 45 minutes to travel to work. Show all your working. … % [3]

19 marks

Mark scheme: 5(a)(i) 20 < t ⩽ 35 1 5(a)(ii) 28 nfww 4 M1 for midpoints soi M1 for use of ∑fm with m in correct interval including both boundaries M1 (dep on 2nd M1) for ∑fm ÷ 80 5(b)(i) 7 2 18  28  24 cao M1 for oe 8 80 5(b)(ii) 25 3  3 25  oe M2 for [2 ]  or [2 ]   126  28 27   25 3   oe    28 27  3 25 or M1 for either or or 28 27 25 3 or 28 27 75 If 0 scored, SC1 for answer oe 392 5(c)(i) 28 and 56 1 5(c)(ii) Correct diagram 3 B1FT their (c)(i) for plots at 5 correct heights B1 for 5 plots at upper ends of intervals on correct vertical line B1FT (dep on at least B1) for increasing curve or polygon through 5 points After 0 scored, SC1FT for 4 correct points plotted 5(c)(iii) Strict FT their reading at 80th percentile 2 B1 for 64 written or a mark at cf = 64 on for an increasing curve/polygon graph or a mark on curve at (t, 64) 5(c)(iv) Correct integer reading at t = 45 M1 FT their cf graph for all three marks 80  (their readingat t  45) M1 [ 100] 80 (their readingat t  45) or  100 80 Percentage consistent with their reading A1 If no working shown then SC1 for a correct percentage that follows from a correct reading from their graph.

This question in 0580/43 May/June 2022

5 (a) 100 students each record the time, t minutes, taken to eat a pizza. The cumulative frequency diagram shows the results. 100 80 60 Cumulative frequency 40 20 0 t 0 5 10 15 Time (minutes) Find an estimate of (i) the median, … min [1] (ii) the interquartile range, … min [2] (iii) the number of students taking more than 11 minutes to eat a pizza. … [2] (b) 150 students each record how far they can throw a tennis ball. The table shows the results. Distance 0 1 d G 20 20 1 d G 30 30 1 d G 35 35 1 d G 45 45 1 d G 60 (d metres) Frequency 4 38 40 53 15 (i) Calculate an estimate of the mean. … m [4] (ii) A histogram is drawn to show this information. The height of the bar representing 30 1 d G 35 is 12 cm. Calculate the height of each of the other bars. Distance (d metres) Frequency Height of bar (cm) 0 1 d G 20 4 20 1 d G 30 38 30 1 d G 35 40 12 35 1 d G 45 53 45 1 d G 60 15 [3] (iii) Two students are chosen at random. Find the probability that they both threw the ball more than 45 m. … [2]

14 marks

Mark scheme: 5(a)(i) 9.4 1 5(a)(ii) 2.4 2 B1 for [uq =] 10.4 or [lq =] 8 but not as final answer 5(a)(iii) 18 2 B1 for 82 seen 5(b)(i) 13 4 M1 for midpoints 10, 25, 32.5, 40, 52.5 34.65 or 34 soi 20 M1 for fx where values of x are in interval or on boundary fx M1 dep on second M for 150 5(b)(ii) 0.3, 5.7, ..., 7.95, 1.5 3 B2 for any two correct or B1 for one correct or for at least three frequency densities seen 0.2, 3.8, 8, 5.3, 1 oe or M1 for [factor] 1.5 5(b)(iii) 7 2 15 14 oe M1 for  745 150 149

This question in 0580/41 Oct/Nov 2022

3 Kai and Ann carry out a survey on the distances travelled, in kilometres, by 200 cars. Kai completes this frequency table for the data collected. Distance (d km) 80 1 d G 100 100 1 d G 150 150 1 d G 200 200 1 d G 300 300 1 d G 400 Frequency 7 33 76 52 32 (a) (i) Calculate an estimate of the mean. … km [4] (ii) Ann uses this frequency table for the same data. There is a different interval for the final group. Distance (d km) 80 1 d G 100 100 1 d G 150 150 1 d G 200 200 1 d G 300 300 1 d G 360 Frequency 7 33 76 52 32 Without calculating an estimate of the mean for this data, find the difference between Ann’s and Kai’s estimate of the mean. You must show all your working. … km [2] (iii) A histogram is drawn showing the information in Kai’s frequency table. The height of the block for the interval 200 1 d G 300 is 2.6 cm. Calculate the height of the block for each of the following intervals. 80 1 d G 100 … cm 150 1 d G 200 … cm 300 1 d G 400 … cm [3] (b) One car is picked at random. Find the probability that the car has travelled more than 300 km. … [1] (c) Two of the 200 cars are picked at random. Find the probability that (i) both cars have travelled 150 km or less, … [2] (ii) one car has travelled more than 200 km and the other car has travelled 100 km or less. … [3]

15 marks

Mark scheme: 3(a)(i) 211.275 4 M1 for mid-points soi (90, 125, 175, 250, 350) M1 for use of fm with m in correct interval including both boundaries M1 for (dep on 2nd M1) for fm  200 3(a)(ii) 32  350 – 32  330 oe or better, or the reverse of this M1 3.2 or – 3.2 final answer B1 3(a)(iii) 1.75 3 B2 for two correct heights or B1 for one correct height or 3 correct frequency densities 7.6 1.6 or M1 for scale factor of 5 or 0.2 3(b) 4 1 oe 25 3(c)(i) 39 2 40 39 oe M1 for  oe 995 200 199 3(c)(ii) 147 3 oe 4975 84 7 M2 for [2]  oe 200 199 84 7 84 7 or B1 for and or and oe 200 199 199 200 147 If 0 scored, SC1 for answer oe 5000

This question in 0580/42 Oct/Nov 2022

3 The height, h cm, of each of 100 plants is recorded. The table shows information about the heights of these plants. Height 10 1 h G 15 15 1 h G 25 25 1 h G 40 40 1 h G 60 60 1 h G 70 (h cm) Frequency 8 18 28 33 13 (a) Complete the histogram to show this information. The first two blocks have been drawn for you. 2.5 2 1.5 Frequency density 1 0.5 0 10 20 30 40 50 60 70 h Height (cm) [3] (b) Calculate an estimate of the mean height. … cm [4]

7 marks

Mark scheme: 3(a) Correct histogram 3 B1 for each correct block 28 33 13 If 0 scored, SC1 for two of , , or 1.87 or 1.866 to 15 20 10 1.867, 1.65, 1.3 3(b) 38.65 4 M1 for 12.5, 20, 32.5, 50, 65 soi M1 for fx where x is in the correct interval including boundaries M1dep for fx ÷100

This question in 0580/43 Oct/Nov 2022

2 (a) 100 students take part in a reaction test. The table shows the results. Reaction time (seconds) 6 7 8 9 10 11 Number of students 3 32 19 29 11 6 (i) Write down the mode. … s [1] (ii) Find the median. … s [1] (iii) Calculate the mean. … s [3] (iv) Two students are chosen at random. Find the probability that both their reaction times are greater than or equal to 9 seconds. … [2] (b) The box-and-whisker plot shows the heights, h cm, of some students. h 100 110 120 130 140 150 160 Height (cm) (i) Find the range. … cm [1] (ii) Find the interquartile range. … cm [1] (c) The mass of each of 200 potatoes is measured. The table shows the results. Mass (m grams) 50 1 m G 110 110 1 m G 200 200 1 m G 300 Frequency 60 99 41 (i) Calculate an estimate of the mean. … g [4] (ii) Complete the histogram to show the information in the table. 1.5 1 Frequency density 0.5 0 m 50 100 150 200 250 300 Mass (grams) [2]

15 marks

Mark scheme: 2(a)(i) 7 1 2(a)(ii) 8 1 2(a)(iii) 8.31 3 M1 for 3×6 + 32×7 + 19×8 + 29×9 + 11×10 + 6×11 oe  fx M1dep on M1 for 100 2(a)(iv) 23 2 k k − 1 oe M1 for  oe, k < 100 110 100 99 46 45 or B1 for and 100 99 2(b)(i) 53 1 2(b)(ii) 20 1 2(c)(i) 151.975 4 M1 for 80, 155, 250 soi M1 for  fx where x is in correct interval including boundaries  fx M1 dep for dep on second M1 200 2(c)(ii) Correct histogram completed with widths 110 to 200 and 200 to 2 B1 for one correct block 300 and heights 1.1 and 0.41 If 0 scored, SC1 for 1.1 and 0.41 seen

This question in 0580/42 Feb/March 2023

3 (a) The table shows information about the mass of each of 1000 eggs. Mass (m grams) 40 1 m G 50 50 1 m G 56 56 1 m G 64 64 1 m G 70 Frequency 126 520 154 200 (i) Calculate an estimate of the mean. … g [4] (ii) An egg is picked at random from the 1000 eggs. Find the probability that this egg has a mass greater than 56 g. Give your answer as a fraction in its simplest form. … [2] (b) One year, a farmer makes a profit of $24 730 selling eggs. Write this profit (i) correct to 2 significant figures $ … [1] (ii) in standard form. $ … [1] (c) On a farm, there are 500 hens, correct to the nearest 10. (i) In one year, the mean number of eggs laid per hen was 320 eggs, correct to the nearest 20. Calculate the upper bound for the total number of eggs all the hens lay in that year. … [3] (ii) Another farm has 800 hens, correct to the nearest 20. Calculate the lower bound for the difference between the number of hens on the two farms. … [2]

13 marks

Mark scheme: 3(a)(i) 55.87 4 M1 for midpoints soi M1 for use of where m is in the correct fm interval including boundaries M1 (dep on 2nd M1) for ÷1000 fm 3(a)(ii) 177 2 154  200 cao M1 for oe 500 1000 3(b)(i) 25000 1 3(b)(ii) 2.473  10 4 1 3(c)(i) 166 650 or 165816 nfww 3 M2 for (500 + 5) × ‘320 to 340’ or ‘500 to 510’ × (320 + 10) or M1 for 500  5 or 500  5 or 320 10 or 320 10 Alternative method M2 for 504 × ‘320 to 340’ or ‘500 to 510’ × 329 or M1 for 504 or 329 3(c)(ii) 285 or 286 nfww 2 M1 for 800 10

This question in 0580/41 May/June 2023

4 The table shows information about the heights of 80 children. Height 1.2 1 h G 1.4 1.4 1 h G 1.5 1.5 1 h G 1.65 1.65 1 h G 1. 8 1.8 1 h G 1.9 (h metres) Frequency 2 13 24 32 9 (a) (i) Write down the interval containing the median. … 1 h G … [1] (ii) Calculate an estimate of the mean height. … m [4] (b) (i) One of these children is chosen at random. Calculate the probability that they have a height of 1.4 m or less. … [1] (ii) Two of these children are chosen at random. Calculate the probability that both children are taller than 1.5 m but only one of them is taller than 1.8 m. … [3] (c) (i) Complete the cumulative frequency table for the heights. Height h G 1.4 h G 1.5 h G 1.65 h G 1.8 h G 1.9 (h metres) Cumulative 2 frequency [2] (ii) On the grid, draw the cumulative frequency diagram. 80 70 60 50 Cumulative 40frequency 30 20 10 0 h 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Height (m) [3] (d) Use your diagram to find an estimate of (i) the interquartile range … m [2] (ii) the 60th percentile. … m [2]

18 marks

Mark scheme: 4(a)(i) 1.65 < h ≤ 1.8 1 4(a)(ii) 1.63875 4 M1 for midpoints soi M1 for use of ∑fh with h in correct interval including both boundaries M1dep on 2nd M1 for ∑fh ÷ 80 4(b)(i) 1 1 oe 40 4(b)(ii) 63 3 56 9 oe M2 for  [ 2] oe 395 80 79 56 9 9 56 or B1 for or or or oe seen 80 79 80 79 If 0 or B1 scored, instead award SC2 for 117 answer oe 632 63 or SC1 for answer oe 400 4(c)(i) 15, 39, 71, 80 2 B1 for 3 correct or M1 for 1 error in addition with other values then consistent 4(c)(ii) Correct curve 3 B1 for correct horizontal placement for 5 plots B1FT for correct vertical placement for 5 plots B1FT dep on at least B1 for reasonable increasing curve or polygon through their 5 points If 0 scored SC1 FT for 4 out of 5 points correctly plotted 4(d)(i) Strict FT their UQ – their LQ 2dep B1dep for their UQ or their LQ seen Dep on increasing curve/polygon for 2 marks or B1 4(d)(ii) Strict FT their reading at 48 2dep B1 for 48 written

This question in 0580/42 May/June 2023

6 (a) The cumulative frequency table shows information about the speed of each of 200 cars as they pass a speed camera. Speed v G 70 v G 80 v G 90 v G 95 v G 100 v G 120 (v km/h) Cumulative 12 46 115 155 177 200 frequency (i) On the grid, draw the cumulative frequency diagram. 200 180 160 140 120 Cumulative 100 frequency 80 60 40 20 0 v 60 70 80 90 100 110 120 Speed (km/h) [3] (ii) Use your cumulative frequency diagram to find an estimate of (a) the median … km/h [1] (b) the interquartile range … km/h [2] (c) the number of cars with a speed greater than 110 km/h. … [2] (b) The frequency table shows information about the mass of each of 50 trucks. Mass 2000 1 m G 2600 2600 1 m G 3500 3500 1 m G 5000 5000 1 m G 5700 (m kg) Frequency 12 15 16 7 (i) Calculate an estimate for the mean mass of the trucks. … kg [4] (ii) In a histogram showing this information, the height of the first block is 6 cm. Calculate the heights of the remaining three blocks. Height of block for 2600 1 m G 3500 … cm Height of block for 3500 1 m G 5000 … cm Height of block for 5000 1 m G 5700 … cm [3]

15 marks

Mark scheme: 6(a)(i) Correct curve 3 B1 for correct horizontal placement for 6 plots B1 for correct vertical placement for 6 plots B1 dep on at least B1 for reasonable increasing curve through their 6 points If 0 scored, SC1 for 4 out of 6 points correctly plotted 6(a)(ii)(a) 87 to 89.5 1 6(a)(ii)(b) 12.5 to 14 2 B1 for [LQ =] 80.5 to 81.5 or [UQ =] 94 to 94.5 6(a)(ii)(c) Strict FT, 200 – their cumul freq reading 2 B1FT for correct cumul freq at 110 seen from their graph at 110 given to nearest or for non-integer answer integer 6(b)(i) 3576 4 M1 for midpoints soi M1 for use of fx where x is in the  correct interval including boundaries M1 (dep on 2nd M1) for fx ÷ 50  6(b)(ii) 5 3.2 3 3 B1 for each If 0 scored, SC1 for 3 frequency densities 12 15 16 7 , , , seen oe to 3sf 600 900 1500 700 or better or multiplier 3 or 300

This question in 0580/43 May/June 2023

7 The frequency table shows the time of each of 42 athletes in a race. Time (t seconds) Number of athletes 216 1 t G 219 9 219 1 t G 224 14 224 1 t G 234 14 234 1 t G 244 2 244 1 t G 264 3 (a) Calculate an estimate of the mean time. … seconds [4] (b) Complete the histogram to show the information in the frequency table. Two of the blocks have been drawn for you. 4 3 Frequency density 2 1 0 t 210 220 230 240 250 260 270 Time (seconds) [3]

7 marks

Mark scheme: 7(a) 226 nfww or 226.2 to 226.3[0] 4 M1 for mid-points soi nfww (217.5, 221.5, 229, 239, 254) M1 for use of fm with m in correct interval including both boundaries M1 (dep on 2nd M1) for fm  (9 + 14 + 14 + 2 + 3) 7(b) Blocks with heights 2.8, 1.4, 0.2 3 B1 for each correct block and with correct widths If 0 scored, SC1 for two correct frequency densities soi

This question in 0580/41 Oct/Nov 2023

2 (a) Daisy records her 50 homework marks. The table shows the results. Homework mark 15 16 17 18 19 20 Frequency 1 3 19 11 10 6 (i) Write down the range. … [1] (ii) Write down the mode. … [1] (iii) Find the median. … [1] (iv) Calculate the mean. … [3] (b) 21 33 20 25 21 34 22 21 20 30 18 The list shows Ed’s scores in 11 tests. (i) Complete the stem-and-leaf diagram to show this information. 1 2 3 Key: 2|5 represents 25 [2] (ii) Find the median. … [1] (iii) Find the interquartile range. … [2]

11 marks

Mark scheme: 2(a)(i) 5 1 2(a)(ii) 17 1 2(a)(iii) 18 1 2(a)(iv) 17.88 3 M2 for (1×15 + 3×16 + 19×17 + 11×18 + 10×19 + 6×20) ÷ 50 oe or M1 for 1×15 + 3×16 + 19×17 + 11×18 + 10×19 + 6×20 oe 2(b)(i) 2 1 8 2 0 0 1 1 1 2 5 B1 for two rows correct or for fully correct unordered stem-and- 3 0 3 4 leaf diagram 2(b)(ii) 21 1 2(b)(iii) 10 nfww 2 B1 for [upper qtile] = 30 or [lower qtile] = 20 soi

This question in 0580/42 Oct/Nov 2023

5 Indira records the time taken for workers in her company to travel to work. The table and the histogram each show part of this information. Time (t minutes) 0 1 t G 10 10 1 t G 25 25 1 t G 40 40 1 t G 60 60 1 t G 80 Frequency 57 38 12 4 3 Frequency 2 density 1 0 t 0 10 20 30 40 50 60 70 80 Time (minutes) (a) Complete the table and the histogram. [5] (b) Calculate an estimate of the mean time. … min [4] (c) Rashid says: ‘The longest time that any of these workers take to travel to work is 80 minutes.’ Give a reason why Rashid may be wrong. … … [1] (d) Indira picks three workers at random from those who take longer than 25 minutes to travel to work. Calculate the probability that one worker takes 60 minutes or less and the other two each take more than 60 minutes. … [4]

14 marks

Mark scheme: 5(a) 28 and 45 on table B2 B1 for each Histogram correctly completed B3 B1 for each correct bar If 0 scored, SC1 for two of FD’s 3.8, 1.9 or 0.6 oe soi 5(b) 30.7 or 30.66 to 30.67 4 M1 for midpoints soi M1 for use of ∑fh with h in correct interval including both boundaries M1 (dep on 2nd M1) for ∑fh ÷ (their 28 + their 45 + 57 + 38 + 12) 5(c) Exact values are not known oe 1 5(d) 1254 4 M3 for oe 39 697  38 + 57 12 11  N     oe  57 + 38 + 12 56 + 38 + 12 56 + 38 + 11  where N = 1, 2 or 3 38 + 57 12 or M2 for and 57 + 38 + 12 56 + 38 + 12 12 11 or and oe seen 57 + 38 + 12 57 + 38 + 11 38 + 57 12 or M1 for or oe seen 57 + 38 + 12 57 + 38 + 12 41040 If 0 scored SC1 for answer or 0.0335… 1225043

This question in 0580/43 Oct/Nov 2023

3 (a) The table shows information about the marks gained by each of 10 students in a test. Mark 15 16 17 18 19 20 Frequency 4 1 2 1 0 2 (i) Calculate the range. … [1] (ii) Calculate the mean. … [3] (iii) Find the median. … [1] (iv) Write down the mode. … [1] (b) Paulo’s mean mark for 7 homework tasks is 17. After completing the 8th task, his mean mark is 17.5 . Calculate Paulo’s mark for the 8th task. … [3] (c) The table shows the percentage scored by each of 100 students in their final exam. Percentage ( p) 0 1 p G 30 30 1 p G 50 50 1 p G 60 60 1 p G 70 70 1 p G 100 Frequency 12 18 35 20 15 On the grid, draw a histogram to show this information. 4 3 Frequency density 2 1 0 p 0 20 40 60 80 100 Percentage [4]

13 marks

Mark scheme: 3(a)(i) 5 1 3(a)(ii) 16.8 3 M1 for 15 × 4 + 16 [× 1] + 17 × 2 + 18 [× 1 ] [+ 19 × 0] + 20 × 2 oe M1 dep on previous M1 for their Σfx ÷10 3(a)(iii) 16.5 1 3(a)(iv) 15 1 3(b) 21 3 M2 for 8  17.5 and 7  17 oe or M1 for 7  17 or 8  17.5 oe seen 3(c) 5 correct blocks, with correct widths, 4 B3 for 4 correct blocks heights 0.8cm, 1.8cm 7cm, 4cm, 1cm or B2 for 3 correct blocks or B1 for 2 correct blocks If 0 scored SC1 for correct frequency densities (0.4 0.9 3.5 2 0.5) soi

This question in 0580/42 Feb/March 2024

4 (a) Jianyu records the time, in seconds, that some cars take to travel 195 m. The box and whisker plot shows this information. 5 6 7 8 9 10 11 12 13 14 Time (s) (i) Find the median time. … s [1] (ii) Find the interquartile range. … s [1] (iii) Find the difference between the average speed of the fastest car and the average speed of the slowest car. Give your answer in kilometres per hour. … km/h [5] (b) Matilda records the distances that 80 different cars can travel with a full tank of fuel. The table shows this information. Distance (d km) 250 1 d G 300 300 1 d G 400 400 1 d G 420 420 1 d G 450 450 1 d G 500 Frequency 7 13 19 21 20 (i) Write down the class interval that contains the median. … 1 d G … [1] (ii) Calculate an estimate of the mean. … km [4] (iii) A histogram is drawn to show the information in the table. The height of the bar for the interval 250 1 d G 300 is 2.8 cm. Calculate the height of the bar for each of the following intervals. 300 1 d G 400 … cm 400 1 d G 420 … cm 420 1 d G 450 … cm [3] (iv) Two of the 80 cars are chosen at random. Find the probability that, with a full tank of fuel, one of the cars can travel more than 450 km and the other car can travel not more than 300 km. … [3]

18 marks

Mark scheme: 4(a)(i) 9.3 1 4(a)(ii) 3.4 1 4(a)(iii) 63 5 195 3600 195 3600 M4 for    oe 6 1000 13 1000 195 3600 195 3600 or M3 for  oe or  6 1000 13 1000 oe 195 or for (  195) k  oe 6 13 OR 195 195 M1 for or or their speed 6 13 3600  seen 1000 M1 for selecting 6 and 13 4(b)(i) 420 < d ⩽ 450 1 4(b)(ii) 411.25 4 M1 for 275, 350, 410, 435, 475 soi M1 for fx M1 dep for their fx ÷ 80 4(b)(iii) 2.6 3 B1 for each 19 If 0 scored, SC1 for 3 of 0.14, 0.13, 0.95 14 or 0.7 oe 4(b)(iv) 7 3 oe 158 7 M2 for  2  20  oe 80 79 20 7 7 20 or M1 for or or or oe 80 79 80 79 seen 7 After 0 scored, SC1 for oe 160

This question in 0580/41 May/June 2024

3 (a) The table shows the time that each of 40 students takes to travel to school. Time (m minutes) 0 1 m G 10 10 1 m G 25 25 1 m G 40 40 1 m G 60 Frequency 3 18 15 4 (i) Calculate an estimate of the mean. … min [4] (ii) On the grid, draw a histogram to show the information in the table. 2 Frequency 1 density 0 m 0 10 20 30 40 50 60 Time (minutes) [3] (iii) Two students are selected at random from the 40 students. Calculate the probability that one student takes more than 25 minutes and the other student takes 10 minutes or less to travel to school. … [3] (b) This is some information about the time that 200 people took to fill in a questionnaire: • The longest time taken was 30 minutes. • The median time was 22 minutes. • The lower quartile was 8 minutes. • The interquartile range was 19 minutes. • The range was 25 minutes. (i) Write down the shortest time taken. … minutes [1] (ii) On the grid, draw a box-and-whisker plot to show this information. 0 10 20 30 40 Time (minutes) [3] (iii) George says that 101 of the 200 people took more than 22 minutes to fill in the questionnaire. Explain why he is wrong. … [1]

15 marks

Mark scheme: 3(a)(i) 25.4375 4 M1 for mid-points soi (5, 17.5, 32.5, 50) M1 for use of fm with m in correct interval including both boundaries M1 for (dep on 2nd M1) for fm  40 3(a)(ii) correct histogram 3 B2 for 3 correct blocks or B1 for 2 correct blocks If 0 scored SC1 for 4 correct frequency densities 0.3, 1.2, 1, 0.2 oe soi 3(a)(iii) 19 3 oe 260 19 3 M2 for   2  oe 40 39 19 3 19 3 or M1 for any of , , , oe 40 40 39 39 seen 57 If 0 scored, SC1 for oe 800 3(b)(i) 5 1 3(b)(ii) 3 5 30 B2 for with LQ at 8 and median at 22 and 8 22 27 UQ at 27 and boxed or M1 for LQ at 8 and median at 22 Correct box plot or for UQ at 27 B1 for lowest = 5 and highest = 30 Max B1 if not box and whisker diagram 3(b)(iii) Correct explanation which states the 1 median is 22 and correct reference to 100 or 101 e.g.  Median is 22 which is 50% of the people and 101 is more than 50% oe  The median is 22 which is the 100th number (accept 100.5th number)

This question in 0580/42 May/June 2024

3 (a) The table shows the waiting times for 120 patients at a medical centre. Waiting time 0 1 t G 10 10 1 t G 20 20 1 t G 40 40 1 t G 50 50 1 t G 80 (t minutes) Frequency 2 46 33 26 13 Calculate an estimate of the mean waiting time. … min [4] (b) The histogram shows some information about the waiting times at a different medical centre. 2 1.5 Frequency density 1 0.5 0 t 0 10 20 30 40 50 60 70 80 Waiting time (minutes) The total number of patients is 90 and no patient waits for more than 80 minutes. Complete the histogram for the patients that have a waiting time between 10 and 30 minutes. [4]

8 marks

Mark scheme: 3(a) 30.875 4 M1 for 5, 15, 30, 45, 65 soi M1 for fx M1 dep for their fx ÷ 120 dep on 2nd M1 3(b) Draws correct bar to height 1.75 4 B3 for [height = ] 1.75 OR M2 for [90 – ](10 × 1.3 + 20 × 1.5 + 30 × 0.4) oe or M1 for 10 × 1.3 or 20 × 1.5 or 30 × 0.4 M1dep for their frequency ÷ 20 dep on at least M1 After 0 scored SC1 for bar of correct width and height between 1.7 and 1.8

This question in 0580/41 Oct/Nov 2024

8 Guillaume measures the speed of each of 100 cars. The results are shown in the table. Speed (v km/h) 30 1 v G 4 0 40 1 v G 45 45 1 v G 50 50 1 v G 70 Frequency 15 20 35 30 (a) Guillaume draws a pie chart for this data. Calculate the angle for the interval 45 1 v G 50 . … [2] (b) Calculate an estimate of the mean speed. … km/h [4] (c) Complete the histogram to show the data in the table. 8 7 6 5 Frequency density 4 3 2 1 030 40 50 60 70 v Speed (km / h) [3]

9 marks

Mark scheme: 8(a) 126 2 35 M1 for  360 100 8(b) 48.375 4 M1 for mid-values 35, 42.5, 47.5, 60 soi M1 for 15 × 35 + 20 × 42.5 + 35 × 47.5 + 30 × 60 fx M1 dep dep on second M1 100 8(c) Correct histogram with correct widths 3 B1 for each column and heights 1.5, … 7, 1.5 If 0 scored, SC1 for freq. densities 1.5, ...7, 1.5 seen 15 35 30 or , , 10 5 20

This question in 0580/43 Oct/Nov 2024

15 Virat records the height of each of 80 sunflowers. The results are shown in the table. Height (h m) 1.2 1 h # 1 .5 1.5 1 h # 1 .6 1 .6 1 h # 1 .7 1.7 1 h # 1.9 Frequency 12 20 34 14 (a) Calculate an estimate of the mean height. … m [4] (b) Draw a histogram to show the information in the table. 400 300 Frequency density 200 100 0 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 h Height (m) [3]

7 marks

Mark scheme: 15(a) 1.606 25 4 M1 for mid-points soi (1.35, 1.55, 1.65, 1.8 ) M1 for use of fm with m in correct interval including both boundaries M1 dep (dep on 2nd M1) for fm  80 15(b) Correct histogram 3 B2 for 3 correct blocks or B1 for 2 correct blocks If 0 scored, SC1 for 3 correct freq densities soi (40, 200, 340, 70)

This question in 0580/42 Feb/March 2025

1 Find the median of these numbers. 5 11 11 13 17 21 … [1]

1 marks

Mark scheme: Question Answer Marks Partial Marks 1 12 1

This question in 0580/43 May/June 2025

16 The table shows some information about the heights of 50 plants. Height (h cm) 5 1 h G 10 10 1 h G 12 12 1 h G 20 Frequency 3 24 23 Calculate an estimate of the mean height. … cm [4]

4 marks

Mark scheme: 16 13.09 4 M1 for mid-values 7.5, 11 and 16 soi M1 for fx where x-values in correct interval (including boundaries) fx M1dep on second M1 for 50

This question in 0580/41 Oct/Nov 2025

6 One morning, a dentist has appointments for 10 patients. The stem-and-leaf diagram shows the waiting time for 8 of these patients. 0 1 4 1 0 2 9 2 1 5 5 Key: 1 | 0 represents 10 minutes The times for the two other patients, P and Q, are not shown in the stem-and-leaf diagram. The mean waiting time of all 10 patients that morning is 16 minutes. The range of waiting times is 26 minutes. Patient P waits longer than patient Q. Find the waiting time for each of patient P and patient Q. Patient P … min Patient Q … min [4]

4 marks

Mark scheme: 6 [Patient P =] 27 4 B1 for answer P = 27 [Patient Q =] 16 M2 for 10 × 16 – (1 + 4 + 10 + 12 + 19 + 21 + 25 + 25 + their 27) oe isw or M1 for 10 × 16 oe 1 + 4 + 10 + 12 + 19 + 21 + 25 + 25 + P + Q or for = 16 oe 10

This question in 0580/42 Oct/Nov 2025

16 The histogram shows information about the masses of some coconuts. The masses are classified into four categories A, B, C and D. 200 150 Frequency density 100 C 50 B D A 0 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Mass (kg) (a) Show that there are 10 coconuts in category D. [1] (b) Two of the coconuts from those in category C and category D are chosen at random. Find the probability that both are from category D. … [3] (c) Calculate an estimate of the mean mass of the coconuts. … kg [4]

8 marks

Mark scheme: 16(a) (1.6 – 1.35) oe × 40 [= 10] 1 16(b) 5 3 10 9 oe M2 for  oe 39 10 + 170  0.1 9 + 170  0.1 10 9 9 10 or M1 for or or or oe 10 + 17 10 + 16 10 + 17 10 + 16 seen 10 9 or  oe with k > 10 and an integer k k − 1 m m − 1 or  oe with 0 < m < 27 and an integer 10 + 17 10 + 16 16(c) 1.26 or 1.259… nfww 4 M1 for frequencies 6, 15, 17 soi M1 for midpoints soi (1, 1.175, 1.3, 1.475) M1 for use of their fm  their f with m in correct interval including both boundaries

This question in 0580/42 Oct/Nov 2025

2 The stem-and-leaf diagram shows the age of each of 16 adults. 3 2 3 3 5 6 7 4 0 1 5 5 6 8 9 5 1 1 1 Key: 3 | 2 represents age 32 years (a) Find the mode. … years [1] (b) Find the median. … years [1] (c) Find the percentage of the 16 adults with an age of less than 38 years. … % [2]

4 marks

Mark scheme: 2(a) 51 1 2(b) 43 1 2(c) 37.5 2 6 M1 for oe 16

This question in 0580/43 Oct/Nov 2025

23 The table shows some information about the mass of each of 200 oranges. Mass (m grams) 180 1 m G 200 200 1 m G 2 10 210 1 m G 215 215 1 m G 230 Frequency 32 64 74 30 (a) Calculate an estimate of the mean mass of an orange. … g [4] (b) Sarah draws a histogram to show this information. The table shows the height of one of the bars for this histogram. Complete the table. Mass (m grams) 180 1 m G 200 200 1 m G 2 10 210 1 m G 215 215 1 m G 230 Height of bar (cm) 7.4 [3]

7 marks

Mark scheme: 23(a) 208 4 M1 for midpoints soi 190, 205, 212.5, 222.5 M1 for use of Σfx where x is in the correct interval including boundaries 190 × 32 + 205 × 64 + 212.5 × 74 + 222.5 × 30 M1 (dep on second M1) for Σfx ÷ 200 23(b) 0.8 3.2 1 3 B2 for two correct or B1 for one correct or M1 for three of 1.6, 6.4, 14.8 and 2 seen

This question in 0580/43 Oct/Nov 2025