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

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

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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

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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

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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

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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

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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

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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

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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

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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

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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.

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

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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

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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

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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

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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 )

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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

(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

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

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