Averages and measures of spread — Paper 4 · IGCSE Mathematics - International 0607

2 (a) The heights, x cm, of some plants are shown in the table. Height (x cm) Frequency 0 1 x G 10 7 10 1 x G 20 13 20 1 x G 30 20 30 1 x G 40 32 40 1 x G 50 28 Calculate an estimate of the mean height of the plants. … cm [2] (b) (i) Complete the cumulative frequency table for the plants. Cumulative Height (x cm) Frequency 0 1 x G 10 7 0 1 x G 20 0 1 x G 30 0 1 x G 40 0 1 x G 50 [1] (ii) On the grid below, draw the cumulative frequency curve. 100 90 80 70 60 Cumulative frequency 50 40 30 20 10 x 0 10 20 30 40 50 Height (cm) [3] (c) Use your graph in part (b)(ii) to find estimates for (i) the median height, … cm [1] (ii) the interquartile range, … cm [2] (iii) the range of heights of plants that are between the 45th and the 55th percentile. … cm [3]

12 marks

Mark scheme: 2(a) 31.1 2 M1 for evidence of at least 3 correct midpoints 2(b)(i) [7], 20, 40, 72, 100 1 2(b)(ii) Correct Graph 3 B1 for plotting their points at upper group limit (but points must be increasing vertically) B1 for 4 or 5 correct FT vertical plots (must be increasing) 2(c)(i) 32.5 to 34.5 1 FT their graph, dependent on increasing curve 2(c)(ii) 16.5 to 20 2 FT their graph, dependent on increasing curve B1 for UQ = 40.5 to 42 or LQ = 22 to 24 or M1 for their UQ – their LQ 2(c)(iii) 3 to 4 3 FT their graph, dependent on increasing curve M2 for their 55 th percentile (34 to 36) and their 45 th percentile (31 to 33) or M1 for their 45th percentile (31 to 33) or their 55th percentile (34 to 36) or SC3 for e.g. 32 to 35

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11 A farmer sorts the grapefruit he grows into sizes, according to their diameter. The diameters, d cm, of 170 grapefruit are shown in the table. Size Small Medium Large Very Large Diameter (d cm) 9 1 d G 10 10 1 d G 12 12 1 d G 14 14 1 d G 17 Frequency 10 50 65 45 (a) Calculate an estimate of the mean diameter of the grapefruit. … cm [2] (b) On the grid, draw a histogram to represent this information. Complete the scale on the frequency density axis. Frequency density d 8 9 10 11 12 13 14 15 16 17 18 Diameter (cm) [4] (c) Two of the 170 grapefruit are chosen at random. Calculate the probability that (i) they are both Very Large, … [2] (ii) one is Small and the other is Medium. … [3]

11 marks

Mark scheme: 11(a) 12.9 or 12.86 to 12.87 2 M1 for evidence of at least three mid-interval values 9.5, 11, 13, 15.5 soi by 95, 550, 845, 697.5 or 2187.5 11(b) Correct Histogram 4 B1 for correct bar widths no gaps B3 for 4 correct heights and corresponding scale from 0 or B2 for 3 correct heights and corresponding scale from 0 or B1 for 2 correct heights and corresponding scale from 0 or B1 for 3 correct frequency densities soi 11(c)(i) 198 2 45 44 oe M1 for × 2873 170 169 11(c)(ii) 100 3 10 50 50 10 oe M2 for × + × oe 2873 170 169 170 169 10 50 or M1 for × 170 169

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3 (a) 12 students take part in a quiz. The table shows the number of correct answers given by each student. Student A B C D E F G H I J K L Number of 7 6 9 5 6 4 7 8 4 10 9 3 correct answers Find (i) the median, … [1] (ii) the lower quartile, … [1] (iii) the number of students with a smaller number of correct answers than the lower quartile. … [1] (b) The table shows the average monthly temperature and the average monthly rainfall in Maseru, Lesotho. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Temperature 21 21 19 15 11 8 8 11 15 17 19 21 (t ˚C) Rainfall (r mm) 113 102 99 59 28 12 12 14 27 62 83 88 (i) What type of correlation is there between the monthly temperature and the monthly rainfall? … [1] (ii) Find the range of these temperatures. … ˚C [1] (iii) Find the mean of these temperatures. … ˚C [1] (iv) Find the equation of the line of regression, giving r in terms of t. r = … [2] (v) On the diagram, sketch the graph of the regression line for 8 G t G 21. r 100 0 t 8 21 [2]

10 marks

Mark scheme: 3(a)(i) 6.5 1 3(a)(ii) 4.5 1 3(a)(iii) 3 1 3(b)(i) Positive 1 3(b)(ii) 13 1 3(b)(iii) 15.5 1 3(b)(iv) 7.32t – 55.3 2 (7.322 to 7.323)t – (55.25…) B1 for 7.32t + k or kt – 55.3 or SC1 for 7.3t − 55 3(b)(v) Correct line (positive gradient and not 2 B1 for positive gradient below the x-axis)

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10 (a) The time, t hours, taken by each of 200 cars to complete a journey of 200 km is recorded. The results are shown in the table. Time (t hours) 2.5 1 t G 3 3 1 t G 3.25 3.25 1 t G 3.75 Frequency 60 100 40 (i) Calculate an estimate of the mean. … h [2] (ii) On the grid, draw the histogram to show the information in the table. 450 400 350 300 Frequency 250 density 200 150 100 50 0 t 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Time (hours) [3] (b) One car completes the 200 km journey at an average speed of x km/h. Another car completes the 200 km journey at an average speed of (x + 10) km/h. The difference between the times taken by the two cars is 20 minutes. (i) Show that x 2 + 10x - 6000 = 0 . [4] (ii) Find the time taken for the slower journey. Give your answer in hours and minutes correct to the nearest minute. … h … min [4] Question 11 is printed on the next page.

13 marks

Mark scheme: 10(a)(i) 3.0875 2 M1 for 2.75, 3.125, 3.5 soi 10(a)(ii) Correct histogram 3 B1 correct widths B1 for two correct heights 10(b)(i) 200 200 20 B2 200 200 − = oe B1 for or x x + 10 60 x x + 10 60 × 200( x + 10) − 60 × 200 x = 20 x ( x + 10) M1 i.e. correctly clearing fractions or all over oe common denominator x 2 + 10 x − 6000 = 0 A1 completion with at least one interim line and without any errors or omissions 10(b)(ii) 2 h 45 min 4 B2 for 72.6 or 72.62… or M1 for correct use of formula or correct sketch M1 for 200 ÷ their positive x, implied by 2.75 …

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6 (a) A factory tests the lifetime, t hours, of each of 200 batteries. The table shows the results. Lifetime (t hours) 20 1 t G 30 30 1 t G 40 40 1 t G 50 50 1 t G 60 60 1 t G 70 70 1 t G 80 Frequency 9 17 39 97 29 9 (i) Write down the modal interval. … [1] (ii) Complete the cumulative frequency curve. 200 180 160 140 120 Cumulative 100 frequency 80 60 40 20 0 t 20 30 40 50 60 70 80 Lifetime (hours) [4] (iii) Use your curve to find (a) the median, … hours [1] (b) the number of batteries with a lifetime greater than 65 hours. … [2] (b) This table shows the lifetimes of the same batteries but the time intervals are different. Lifetime (t hours) 20 1 t G 40 40 1 t G 50 50 1 t G 55 55 1 t G 60 60 1 t G 80 Frequency 26 39 55 42 38 (i) Calculate an estimate of the mean. … hours [2] (ii) Complete the table to show the frequency densities. Lifetime (t hours) 20 1 t G 40 40 1 t G 50 50 1 t G 55 55 1 t G 60 60 1 t G 80 Frequency 26 39 55 42 38 Frequency density 3.9 [2] (iii) Complete the histogram. 12 11 10 9 8 7 Frequency density 6 5 4 3 2 1 0 t 20 30 40 50 60 70 80 Lifetime (hours) [3]

15 marks

Mark scheme: 6(a)(i) 50 < t ≤ 60 1 6(a)(ii) Correct curve 4 B2 for 3 or 4 correct heights or B1 for 2 correct heights or correct cumulative frequencies seen B1 for plotting correct t co-ordinates, dependent on increasing curve 6(a)(iii)(a) 52 to 55 1 FT their curve, dependent on increasing 6(a)(iii)(b) Strict follow through 2 FT their curve, dependent on increasing B1FT for their cum freq value soi 6(b)(i) 52.5 or 52.48 to 52.49 2 M1 for evidence of at least three correct mid-values 30, 45, 52.5, 57.5, 70 soi by 10497.5 6(b)(ii) 1.3, … , 11, 8.4, 1.9 2 B1 for 3 correct 6(b)(iii) Correct histogram 3 FT their (ii) B1 for correct widths B2 for correct heights or B1 for three correct heights

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3 Pepe wants to find out if there is a correlation between the hours of sunshine, x hours, and the rainfall, y cm, in Phuket. Pepe recorded the following results. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Daily sunshine 8 9.2 7.9 9.4 8 7.4 7.9 8 7.3 7.4 7.5 8 (x hours) Monthly rainfall 4 3 4 15 20 24 30 26 40 28 20 6 (y cm) (a) (i) Complete the scatter diagram. The first eight points have been plotted for you. y 45 40 35 30 25 Monthly rainfall (cm) 20 15 10 5 0 x 7 8 9 10 Daily sunshine (hours) [2] (ii) What type of correlation is shown by the scatter diagram? … [1] (b) (i) Find the mean number of hours of sunshine. … hours [1] (ii) Find the mean rainfall. … cm [1] (c) (i) Find the equation of the regression line for y in terms of x. y = … [2] (ii) Estimate the rainfall when the number of hours of sunshine is 7.7 . … cm [1]

8 marks

Mark scheme: 3(a)(i) Points correctly plotted 2 B1 for 2 or 3 correct points 3(a)(ii) Negative 1 3(b)(i) 8 1 3(b)(ii) 1 1 18.3 or 18.33 or 183 3(c)(i) y = 97 [.0 ] − 9.84 x 2 or 97.02... and –9.836... B1 for 97[.0] + kx, or a – 9.84x, If 0 scored SC1 for 97 – 9.8x 3(c)(ii) 21.2 to 21.3 or 21 1 Strict FT their (c)(i) provided a linear expression

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4 The masses of 120 peaches are recorded in the table. Mass (m grams) Frequency 0 1 m G 120 12 120 1 m G 150 27 150 1 m G 180 33 180 1 m G 210 15 210 1 m G 250 28 250 1 m G 300 5 (a) Calculate an estimate of the mean mass of a peach. Give your answer correct to the nearest gram. … g [3] (b) Two peaches are chosen at random. Find the probability that they both have a mass of more than 210 g. Give your answer as a fraction in its simplest form. … [3] (c) (i) Complete the frequency density column in this table. Frequency Mass (m grams) Frequency density 0 1 m G 120 12 120 1 m G 150 27 150 1 m G 180 33 180 1 m G 210 15 210 1 m G 250 28 250 1 m G 300 5 0.1 [2] (ii) On the grid, draw an accurate histogram to show this information. Frequency density 0 m 0 50 100 150 200 250 300 Mass (grams) [4]

12 marks

Mark scheme: 4(a) 171 cao nfww 3 B2 for 171.25 or 171.3 or M2 for complete method with 1 numerical error or M1 for at least 3 mid-pts (60, 135, 165, 195, 230, 275) soi 4(b) 44 3 1056 cao B2 for oe accept 0.0739 or 0.07394 to 595 14280 0.07395 33 32 or M1 for × 120 119 4(c)(i) 0.1, 0.9, 1.1, 0.5, 0.7, [0.1] 2 B1 for 3 or 4 correct 4(c)(ii) Correct histogram 4 B1 for suitable scale B1 for correct column widths B1FT for 4 or more correct heights

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4 (a) The list shows the temperature, in degrees Celsius, at noon in Paris on each of 14 days. 19 18 21 21 23 21 22 20 24 25 22 21 19 17 (i) Construct an ordered stem and leaf diagram to show this information, including the key. Key … … = … [3] (ii) Find the median and the lower quartile. median = … lower quartile = … [2] (iii) Find the angle on a pie chart that represents the number of days the temperature was less than 20 °C. … [2] (b) 200 students estimated the capacity, x litres, of a container. The results are shown in the cumulative frequency curve. 200 150 Cumulative frequency 100 50 0 x 0 1 2 3 4 5 Capacity (litres) Find (i) the median, … litres [1] (ii) the inter-quartile range, … litres [2] (iii) the number of students who estimated more than 3.5 litres. … [2] (c) 200 students estimated the area, y m2, of a field. The table shows the results. Area (y m2) 100 1 y G 200 200 1 y G 250 250 1 y G 400 Frequency 25 100 75 (i) Calculate an estimate of the mean. … m2 [2] (ii) Complete the histogram to show the information in the table. 2 1.5 Frequency density 1 0.5 y 0 100 200 300 400 Area (m2) [4]

18 marks

Mark scheme: 4(a)(i) 1 7 8 9 9 3 B1for each row 2 0 1 1 1 1 2 2 3 4 5 B1 for key e.g. 2|3 = 23 4(a)(ii) 21 2 B1 for each 19 4(a)(iii) 102.8 to 102.9 2 4 360 M1 for oe or oe 14 14 4(b)(i) 2.4 1 4(b)(ii) 0.9 2 B1 for 3 or 2.1 seen 4(b)(iii) 20 2 M1 for 180 seen 4(c)(i) 253.125 2 M1 for evidence of at least two mid-values or 253.13 or 253.1 or 253 150, 225, 325 soi by e.g. 50625 4(c)(ii) Correct histogram 4 B1 for bars with correct widths B1 for first bar with height 0.25 B1 for second bar with height 2 B1 for third bar with height 0.5 If 0 scored SC1 for three correct frequency densities seen

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4 (a) The mass, x grams, of each of 100 oranges is found. The results are shown in the table. Mass (x grams) Frequency 0 1 x G 100 4 100 1 x G 140 14 140 1 x G 180 22 180 1 x G 250 35 250 1 x G 300 25 (i) Calculate an estimate of the mean mass of the oranges. … g [2] (ii) Two of these oranges are chosen at random. Calculate the probability that they both have a mass of 140 g or less. … [2] (iii) The oranges with a mass of 140 g or less are removed. From the remaining oranges, two are chosen at random. Calculate the probability that one orange has a mass of 250 g or less and the other has a mass of more than 250 g. … [3] (b) (i) Complete the frequency density column in this table. Mass (x grams) Frequency Frequency density 0 1 x G 100 4 100 1 x G 140 14 140 1 x G 180 22 180 1 x G 250 35 250 1 x G 300 25 [2] (ii) On the grid, draw a histogram to show this information. Frequency density 0 x 0 50 100 150 200 250 300 Mass (grams) [4]

13 marks

Mark scheme: 4(a)(i) 198 2 M1 for 3 or more 50, 120, 160, 215, 275 soi 4(a)(ii) 306 2 18 17 oe or 0.0309 M1 for × 9900 100 99 or 0.030 90 to 0.030 91 4(a)(iii) 2850 3 57 25 25 57 oe or 0.429 M2 for × + × oe 6642 82 81 82 81 or 0.4290 to 0.4291 57 25 25 57 or M1 for × or × 82 81 82 81 4(b)(i) 0.04, 0.35, 0.55, 0.5, 0.5 2 B1 for 3 correct 4(b)(ii) Correct histogram 4 FT their fully completed table in (b)(i) with linear scale B1 for suitable scale (must include all heights) B1 for correct column widths B2FT for columns with all heights correct or B1FT for 3 or 4 columns with correct heights

This question in 0607/42 May/June 2018

10 Wasim sprays different amounts of fertiliser on some seedlings. He measures the amount, x millilitres, sprayed on each seedling. A week later he measures the height, y centimetres, of each seedling. His results are shown in the table. Amount of 1 3 5 7 10 14 18 25 30 35 40 fertiliser (x ml) Height (y cm) 15.1 15.6 16.5 16.6 17 19.8 21 25.1 28.8 28.6 29.1 (a) (i) Complete the scatter diagram. The first four points have been plotted for you. y 30 28 26 24 Height (cm) 22 20 18 16 14 x 0 10 20 30 40 Amount of fertiliser (ml) [3] (ii) What type of correlation is shown by the scatter diagram? … [1] (b) Find (i) the mean amount of fertiliser, … ml [1] (ii) the mean height. … cm [1] (c) (i) Find the equation of the regression line in the form y = mx + c . y = … [2] (ii) Use your answer to part (c)(i) to estimate the height of a seedling when the amount of fertiliser is 20 ml. … cm [1] (iii) Write down the units of m in the equation of the regression line, y = mx + c . … [1] Question 11 is printed on the next page.

10 marks

Mark scheme: 10(a)(i) Points correctly plotted 3 B2 for 5 or 6 correct points B1 for 3 or 4 correct points 10(a)(ii) Positive 1 10(b)(i) 17.1 or 17.09… 1 10(b)(ii) 21.2 1 10(c)(i) y = 14.2 + 0.411x 2 B1 for 14.2 + kx or a + 0.411x If 0 scored, SC1 for 14 + 0.41x 10(c)(ii) 22.4 or 22.39 to 22.42 1 FT their (c)(i) 10(c)(iii) cm/ml oe 1

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1 Gunter keeps chickens. He records the number of eggs he collects each day for 31 days. These are the results. Number 10 11 12 13 14 15 16 17 18 19 20 of eggs Number 5 3 2 3 2 3 2 4 4 1 2 of days (a) Write down the range of the numbers of eggs. … [1] (b) Find the inter-quartile range. … [2] (c) Write down the mode. … [1] (d) Find the median. … [1] (e) Find the mean. … [2] (f) Explain why the mode is not the best measure of average to represent these results. … [1]

8 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 10 1 1(b) 6 nfww 2 B1 for 17 or 11 seen 1(c) 10 1 1(d) 15 1 1(e) 14.5 or 14.51 to 14.52 2 M1 for Σxf soi by e.g. 450 1(f) It is the smallest oe 1

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2 The table shows the marks for 75 students in a test. Mark 0 1 2 3 4 5, 6 or 7 8 Number of students 6 18 16 8 15 5 7 (a) Write down the mode. … [1] (b) Find the range. … [1] (c) Find the median. … [1] (d) Find the inter-quartile range. … [2] (e) Calculate an estimate of the mean. … [2] (f) Give a reason why your answer to part (e) is an estimate. … … [1] (g) Two of these students are chosen at random. Find the probability that the highest mark of these students is 2. … [3]

11 marks

Mark scheme: 2(a) 1 1 2(b) 8 1 2(c) 2 1 2(d) 3 2 B1 for either [LQ =] 1, or [UQ =] 4 2(e) 2.93 or 2.933… 2 M1 for ‘ ∑ fx ’ values 2(f) Assumed all scored 6 oe 1 2(g) 1008 3 M2 for 0.182 or 0.1816... or oe 16 15 16 24 24 16 5550 × + × + × oe 75 74 75 74 75 74 or M1 for one correct product 1560 52 SC1 for = = 0.28108... 5550 185

This question in 0607/41 Oct/Nov 2018

2 Here are 12 numbers. 15 9 6 14 6 8 12 21 11 19 6 12 (a) For these numbers find (i) the range, … [1] (ii) the mode, … [1] (iii) the median, … [1] (iv) the mean, … [1] (v) the inter-quartile range. … [2] (b) Dee chooses a number at random from these numbers. Find the probability that it is a prime number. … [1]

7 marks

Mark scheme: 2(a)(i) 15 1 2(a)(ii) 6 1 2(a)(iii) 11.5 1 2(a)(iv) 11.6 or 11.58... 1 2(a)(v) 7.5 2 B1 for 7 or 14.5 seen 2(b) 2 1 oe 12

This question in 0607/42 Oct/Nov 2018

4 Rani planted some seeds in her garden. After two months she measured the heights, h cm, of each of 120 plants. The results are shown in the table. Height (h cm) 0 1 h G 10 10 1 h G 20 20 1 h G 25 25 1 h G 30 30 1 h G 35 35 1 h G 40 40 1 h G 50 Frequency 0 16 28 32 24 14 6 (a) Calculate an estimate of the mean height. … cm [2] (b) Draw a cumulative frequency curve for this information. 120 100 80 Cumulative frequency 60 40 20 0 h 0 10 20 30 40 50 Height (cm) [5] (c) Use your cumulative frequency curve to estimate (i) the median height, … cm [1] (ii) the interquartile range, … cm [2] (iii) the number of plants with a height of more than 37 cm. … [2] (d) (i) Complete this table of frequency densities for the 120 plants. Height 0 1 h G 10 10 1 h G 20 20 1 h G 25 25 1 h G 30 30 1 h G 35 35 1 h G 40 40 1 h G 50(h cm) Frequency 0 1.6density [2] (ii) Draw a histogram to show this information. 7 6 5 Frequency 4 density 3 2 1 0 h 0 10 20 30 40 50 Height (cm) [3]

17 marks

Mark scheme: 4(a) 27.7 or 27.70 to 27.71 2 M1 for at least 3 midpoints soi 4(b) Correct cf curve 5 Curve/polygon through (10, 0), (20, 16), (25, 44), (30, 76), (35, 100), (40, 114), (50, 120) or B4 for curve through 5 or 6 points or 7 points with no curve or B3 for 'correct curve' through all other consistent points in interval or B2 for all correct cfs or B1 for 4 or 5 correct cfs. If 0 scored SC1 for any cumulative frequency diagram. 4(c)(i) 26 to 28 1 Dep on increasing curve FT 4(c)(ii) 9 to 11.5 2 Dep on increasing curve FT B1 for lq = 22 to 23.5 or uq = 32.5 to 33.5 4(c)(iii) 10 to 15 2 Dep on increasing curve FT B1 for 105 to 110 seen 4(d)(i) 5.6, 6.4, 4.8, 2.8, 0.6 2 B1 for 3 or 4 correct 4(d)(ii) Correct histogram 3 B2 FT for bars with their heights or B1FT for 3 or 4 bars with their heights or bars with all correct widths

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9 240 students take part in a charity run. The table shows information about the times, t minutes, taken to complete the run. Time (t minutes) 20 1 t G 40 40 1 t G 50 50 1 t G 55 55 1 t G 75 Number of students 20 70 120 30 (a) Write down the time interval that contains the median. … 1 t G … [1] (b) Calculate an estimate of the mean. … min [2] (c) Complete the histogram to show the information in the table. 25 20 Frequency 15 density 10 5 0 t 20 30 40 50 60 70 80 Time (minutes) [4] (d) (i) One of the 240 students is chosen at random. Find the probability that this student took more than 55 minutes to complete the run. … [1] (ii) Two students are chosen at random from the 240 students. Calculate the probability that they both took more than 50 minutes. … [2] (iii) Two students are chosen at random from the 240 students. Complete the statement. 161 The probability that they both had times in the interval … 1 t G … is . 1912 [2]

12 marks

Mark scheme: 9(a) 50 < t ⩽ 55 1 Allow e.g. 50 to 55 9(b) 50 2 M1 for at least three of 30, 45, 52.5, 65 soi 9(c) Correct histogram 4 B1 for each correct column height. B1 for all widths correct If 0 scored, SC1 for 7, 24, 1.5 seen 9(d)(i) 30 1 oe 240 9(d)(ii) 22350 2 150 149 oe M1 for × 57360 240 239 9(d)(iii) 40 ... 50 2 k k − 1 M1 for × attempted 240 239

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2 The table shows the marks of 10 students in a physics examination and a chemistry examination. Physics mark (x) 17 29 34 46 57 66 73 84 92 96 Chemistry mark (y) 26 42 41 56 52 61 76 65 73 80 (a) Find (i) the mean physics mark, … [1] (ii) the mean chemistry mark. … [1] (b) Find the equation of the regression line for y in terms of x. y = … [2] (c) Use your regression line to estimate the chemistry mark when (i) the physics mark is 60, … [1] (ii) the physics mark is 5. … [1] (d) Which physics mark, 60 or 5, is likely to give the most reliable chemistry mark? Give a reason for your answer. … … [1]

7 marks

Mark scheme: 2(a)(i) 59.4 1 2(a)(ii) 57.2 1 2(b) [ y = ] 21.8 + 0.596 x 2 B1 for [ y = ] 21.8 + kx or [ y = ] k + 0.596 x or 22 + 0.6[0]x 2(c)(i) 58 or 57.5 to 57.8 1 FT their (b) 2(c)(ii) 25 or 24.8 or 24.75 to 24.78 1 FT their (b) 2(d) 60 1 Both needed Data within range oe

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1 12 students are each given a spelling test. Here is a list of the scores. 9 5 10 9 11 7 7 6 6 7 8 11 Find (a) the range, … [1] (b) the mode, … [1] (c) the median, … [1] (d) the upper quartile, … [1] (e) the inter-quartile range, … [1] (f) the mean. … [1]

6 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6 1 1(b) 7 1 1(c) 7.5 1 1(d) 9.5 1 1(e) 3 1 1(f) 8 1

This question in 0607/41 Oct/Nov 2019

8 (a) 200 people took part in a charity walk. They each recorded how far, d metres, they walked in one hour. The table shows the results. Distance (d metres) 1000 1 d G 2000 2000 1 d G 2500 2500 1 d G 3000 3000 1 d G 4000 Number of people 40 60 80 20 200 150 Cumulative 100 frequency 50 0 d 0 1000 2000 3000 4000 Distance (metres) (i) Complete the cumulative frequency curve. [3] (ii) Use your curve to find the inter-quartile range. … m [2] (iii) Use your curve to estimate the number of people who walked further than 3500 m. … [2] (b) 2000 people took part in a “NO FOOD FOR 6 HOURS” day. They each recorded the reduction in their mass, m grams, at the end of the day. The histogram shows their results. 15 10 Frequency density 5 0 m 0 50 100 150 200 250 300 350 400 Mass (grams) (i) Complete the frequency table. Reduction in mass 0 1 m G 50 50 1 m G 100 100 1 m G 200 200 1 m G 400 (m grams) Number of people 500 [2] (ii) Calculate an estimate of the mean. … g [2]

11 marks

Mark scheme: 8(a)(i) Correct curve 3 B2 for two of (2500, 100), (3000, 180), (4000, 200) plotted or B1 for 100, 180, 200 soi 8(a)(ii) 600 to 700 2 B1 for [u.q.=] 2750 to 2800 or [l.q. = ] 2100 to 2150 not as final answer 8(a)(iii) 5 to 15 2 B1 for 185 to 195 seen 8(b)(i) 600, 600, 300 2 B1 for two correct 8(b)(ii) 118.75 2 M1 for at least two of 25 × 500 + 75 × their 600 + 150 × their 600 + 300 × their 300

This question in 0607/41 Oct/Nov 2019

10 The mass of each of 80 apples is shown in the table. Mass (m grams) Frequency 0 1 m G 100 6 100 1 m G 120 22 120 1 m G 140 31 140 1 m G 160 13 160 1 m G 250 8 (a) Calculate an estimate of the mean mass of an apple. … g [2] (b) Find the interval which contains the upper quartile. … 1 m G … [1] (c) Two of these apples are chosen at random. Find the probability that they both have a mass of 120 g or less. Give your answer as a fraction in its simplest form. … [3] (d) (i) Complete the frequency density column in this table. Mass (m grams) Frequency Frequency density 0 1 m G 100 6 100 1 m G 120 22 120 1 m G 140 31 140 1 m G 160 13 160 1 m G 250 8 [2] (ii) On the grid, draw a histogram to show this information. 2.0 1.8 1.6 1.4 1.2 Frequency 1.0 density 0.8 0.6 0.4 0.2 0 m 0 50 100 150 200 250 Mass (grams) [3]

11 marks

Mark scheme: 10(a) 129.25 2 M1 for at least 3 of 50, 110, 130, 150, 205 seen 10(b) 140[ < m ⩽] 160 1 10(c) 189 3 756 B2 for 0.12[0] or 0.1196... or oe 1580 6320 28 27 or M1 for × 80 79 10(d)(i) 0.06, 1.1, 1.55, 0.65, 0.0889 or 2 B1 for 3 or 4 correct 0.08888 to 0.08889 10(d)(ii) Correct histogram 3 B1 for correct widths B2 FT for all heights correct or B1 FT for 3 or 4 correct heights

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2 The table shows the number of goals scored in 100 matches. Number 0 1 2 3 4 5 6 7 of goals Frequency 17 23 20 18 11 6 4 1 Find (a) the mode, … [1] (b) the range, … [1] (c) the median, … [1] (d) the inter-quartile range, … [2] (e) the mean. … [2]

7 marks

Mark scheme: 2(a) 1 1 2(b) 7 1 2(c) 2 1 2(d) 2 2 B1 for 1 or 3 seen but not final answer 2(e) 2.22 2 M1 for (0 × 17 + 1 × 23 + 2 × 20 + ...) ÷ 100

This question in 0607/43 Oct/Nov 2019

2 (a) These are Tom’s ten homework marks. 8 7 10 8 9 5 8 10 6 8 Find (i) the range, … [1] (ii) the mean, … [1] (iii) the median, … [1] (iv) the upper quartile. … [1] (b) The mass, m kg, of each of 120 parcels is recorded. The cumulative frequency curve shows the results. 120 100 80 Cumulative 60 frequency 40 20 0 m 0 0.5 1 1.5 2 2.5 3 3.5 4 Mass (kg) (i) Find the median. … kg [1] (ii) Find the lower quartile. … kg [1] (iii) Find the interquartile range. … kg [1] (iv) Find the number of parcels with a mass of more than 3 kg. … [2] (v) (a) Use the cumulative frequency curve to complete the frequency table. Mass (m kg) 0 1 m G 1 1 1 m G 1. 5 1.5 1 m G 2 2 1 m G 3 3 1 m G 4 Frequency 30 30 [3] (b) Use the frequency table to calculate an estimate of the mean. … kg [2]

14 marks

This question in 0607/41 May/June 2020

1 A class of 40 students complete a science test. The table shows the marks of the 40 students. Mark 0 1 2 3 4 5 6 7 8 9 10 Number of students 1 1 2 5 5 5 6 3 9 2 1 (a) Write down the mode. … [1] (b) Work out the range. … [1] (c) Find the median. … [1] (d) Find the interquartile range. … [2] (e) Calculate the mean. … [2] (f) Two of the students are chosen at random. Find the probability that the difference in their marks is 8. … [3]

10 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6 1 1(b) 10 1 1(c) 6 1 1(d) 4 2 B1 for LQ = 4 or UQ = 8 1(e) 5.55 2 M1 for attempt at  fx (3 or more terms correct) 1(f) 1 13 3 M2 for two of = or 0.0083 recurring or 120 1560  1 2   2 1   9 1   ×  +  ×  +  ×  0.008333...  40 39   40 39   40 39  or M1 for any one of above products

This question in 0607/42 May/June 2020

3 Petra is a singer. She wants to estimate how much to spend on advertising. The table shows the amount spent on advertising, $x, and the number of tickets sold, y, for 10 performances. Amount spent ($x) 80 60 50 120 90 40 100 110 70 150 Number of tickets sold ( y) 100 90 60 150 100 75 120 120 100 150 (a) (i) Complete the scatter diagram. The first six points have been plotted for you. y 150 100 Number of tickets sold 50 0 x 0 20 40 60 80 100 120 140 160 Amount spent (dollars) [2] (ii) What type of correlation is shown by the scatter diagram? … [1] (b) Find the mean amount of money spent on advertising. $ … [1] (c) (i) Find the equation of the regression line for y in terms of x. y = … [2] (ii) Use your regression line to estimate the number of tickets sold when Petra spends $130 on advertising. … [1] (iii) Explain why Petra should not rely on this regression line to estimate the number of tickets she will sell if she spends $500 on advertising. … … [1]

8 marks

Mark scheme: 3(a)(i) All four points correct 2 B1 for two or three correct points 3(a)(ii) positive 1 3(b) 87 1 3(c)(i) [ y = ] 35.9 + 0.811x 2 B1 for 35.9 + kx, or for a + 0.811x, If 0 scored SC1 for 36 + 0.81x 3(c)(ii) 141 1 FT their (i) 3(c)(iii) Outside data range oe 1

This question in 0607/42 May/June 2020

8 The number of people living in each house in a street of 100 houses is recorded. The results are shown in the table. Number of people Frequency 1 5 2 16 3 28 4 32 5 17 6 2 (a) Find (i) the range, … [1] (ii) the median, … [1] (iii) the mean. … [2] (b) Two of the houses are selected at random. Find the probability that (i) both had exactly one person living in them, … [2] (ii) one had exactly 2 people living in it and the other had exactly 3 people living in it, … [3] (iii) at least one house had fewer than 5 people living in it. … [2]

11 marks

Mark scheme: 8(a)(i) 5 1 8(a)(ii) 4 1 fx8(a)(iii) 3.46 2  M1 for 100 8(b)(i) 20 2 5 4 oe M1 for × oe 9900 100 99 8(b)(ii) 896 3 16 28 28 16 M2 for × + × oe 9900 100 99 100 99 or M1 for one of the above products 8(b)(iii) 9558 2 19 18 M1 for 1 – × oe 9900 100 99

This question in 0607/43 May/June 2020

1 Ten students at a school each study chemistry and physics. Their marks in an examination in each subject are recorded. Chemistry mark (x) 27 36 48 52 53 62 75 80 86 93 Physics mark (y) 45 68 36 55 62 73 66 81 94 80 (a) What type of correlation is there between the chemistry mark and the physics mark? … [1] (b) Find (i) the mean chemistry mark, … [1] (ii) the mean physics mark. … [1] (c) (i) Find the equation of the regression line for y in terms of x. y = … [2] (ii) Another student scored 40 in the chemistry examination but was absent for the physics examination. Estimate a physics mark for this student. … [1]

6 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) positive 1 1(b)(i) 61.2 1 1(b)(ii) 66 1 1(c)(i) [ y = ] 28.7 + 0.61[0] x 2 B1 for [ y = ] 28.7 + kx or [ y = ] k + 0.61[0] x or 29 + 0.6[1]x 1(c)(ii) 53 or 53.1 1 FT their (i)

This question in 0607/41 Oct/Nov 2020

3 (a) Eva records her science homework marks during the school year. The table shows the results. Homework mark 5 6 7 8 9 10 Frequency 2 7 11 13 5 2 Find (i) the range, … [1] (ii) the mode, … [1] (iii) the median, … [1] (iv) the lower quartile, … [1] (v) the mean. … [2] (b) Frank compares the science marks, x, with the mathematics marks, y, of ten students. The table shows the results. Science mark (x) 14 18 15 20 17 17 18 15 18 15 Mathematics mark (y) 13 19 16 19 17 14 17 15 15 12 (i) Complete the scatter diagram. The first six points have been plotted for you. y 20 19 18 17 16 Mathematics mark 15 14 13 12 11 10 x 10 11 12 13 14 15 16 17 18 19 20 Science mark [2] (ii) What type of correlation is shown on the scatter diagram? … [1] (iii) Find the equation of the line of regression, giving y in terms of x. y = … [2] (iv) Another student’s science mark is 16. Use your answer to part (b)(iii) to find an expected mathematics mark for this student. … [1] (c) Georgio records the time, t minutes, he takes to complete each of 40 pieces of mathematics homework. The table shows his results. Time (t minutes) 0 1 t G 10 10 1 t G 15 15 1 t G 20 20 1 t G 40 Frequency 9 20 6 5 Calculate an estimate of the mean. … min [2]

14 marks

Mark scheme: 3(a)(i) 5 1 3(a)(ii) 8 1 3(a)(iii) 7.5 1 3(a)(iv) 7 1 3(a)(v) 7.45 2 M1 for at least three of the products 2 × 5, 7 × 6, 11 × 7, 13 × 8, 5 × 9, 2 × 10 soi by 298 3(b)(i) Four points correctly plotted 2 B1 for 2 or 3 correct 3(b(ii) Positive 1 3(b)(iii) 0.938x + 0.0405 2 B1 for 0.938x + k 0.9376 to 0.9377 or for kx + 0.0405 0.04049 to 0.04050 or for 0.94x + 0.04[0] 3(b)(iv) 15 or to 15.0 to 15.1 1 FT 3(c) 13.75 2 M1 for at least 3 mid-values seen 5, 12.5, 17.5, 30 implied by 45, 250, 105, 150 or 550

This question in 0607/43 Oct/Nov 2020

4 (a) The mass, m grams, of each of 50 apples is found. The results are shown in the table. Mass (m grams) Frequency 70 1 m G 90 2 90 1 m G 110 7 110 1 m G 130 14 130 1 m G 150 10 150 1 m G 170 12 170 1 m G 190 5 (i) Write down the modal class. … 1 m G … [1] (ii) Calculate an estimate of the mean. … g [2] (b) The mass, x grams, of each of 120 different apples is found. The results are shown in Table 1. (i) Complete the cumulative frequency column in Table 2. Mass (x grams) Frequency Mass (x grams) Cumulative Frequency 70 1 x G 90 8 x G 90 8 90 1 x G 110 8 x G 110 110 1 x G 120 22 x G 120 120 1 x G 130 39 x G 130 130 1 x G 140 27 x G 140 140 1 x G 150 9 x G 150 150 1 x G 170 7 x G 170 Table 1 Table 2 [2] (ii) On the grid, draw the cumulative frequency curve to show the results in Table 2. 120 100 80 Cumulative 60frequency 40 20 0 70 80 90 100 110 120 130 140 150 160 170 180 Mass (grams) [3] (iii) Use your cumulative frequency curve to estimate (a) the median, … g [1] (b) the interquartile range. … g [2]

11 marks

Mark scheme: 4(a)(i) 110 < m ≤ 130 1 4(a)(ii) 135.2 2 M1 for mid-values seen or implied 4(b)(i) (8) 16 38 77 104 113 120 2 B1 for 4 or 5 correct FT one error 4(b)(ii) Correct cumulative frequency 3 B2 for 6 points correct curve OR B1FT for 7 heights correct B1 for plotting at upper boundary of interval 4(b)(iii)(a) 124 to 127 nfww 1 4(b)(iii)(b) 14 to 21 2 B1 for [LQ =] 115 to 118 or [UQ =] 132 to 136

This question in 0607/42 Feb/March 2021

1 A stadium sells tickets at 10 different prices for a sporting event. The table shows the number of tickets sold at each price. Ticket price ($x) 22 23 35 40 53 55 58 61 69 73 Number of tickets sold (y) 8600 9100 7000 7600 5200 6000 4800 4500 2600 3000 (a) What type of correlation is shown by the data? … [1] (b) Find the mean of the 10 ticket prices. $ … [1] (c) (i) Find the equation of the regression line for y in terms of x. y = … [2] (ii) The stadium decides to sell some tickets at a price of $45. Use your answer to part (i) to estimate the number of tickets it will sell at this price. … [1]

5 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Negative 1 1(b) 48.9[0] 1 1(c)(i) –120x + 11 700 2 B1 for –120x + k or –kx + 11 700 1(c)(ii) 6300 or 6294 to 6320 1 FT their (i)

This question in 0607/41 May/June 2021

4 The marks, x, of 300 students in a chemistry test are shown in the table. Mark (x) Frequency 0 1 x G 10 41 10 1 x G 20 32 20 1 x G 3 0 44 30 1 x G 40 50 40 1 x G 60 65 60 1 x G 8 0 48 80 1 x G 100 20 (a) Calculate an estimate of the mean mark. … [2] (b) Complete the cumulative frequency table. Cumulative Mark (x) frequency x G 10 41 x G 20 x G 30 x G 40 x G 60 x G 80 x G 100 300 [1] (c) On the grid, draw a cumulative frequency curve. 300 250 200 Cumulative frequency 150 100 50 0 0 10 20 30 40 50 60 70 80 90 100 Mark [3] (d) Use your curve in part (c) to find an estimate for (i) the median mark, … [1] (ii) the interquartile range. … [2] (e) 35% of the students pass the test. Use your curve in part (c) to find an estimate of the minimum mark needed to pass. … [2]

11 marks

Mark scheme: 4(a) 39.8 or 39.81 to 39.82 2 M1 for at least 5 correct mid-points soi 4(b) [41], 73, 117, 167, 232, 280, [300] 1 In parts (c), (d) and (e), marks can only be earned with an increasing curve 4(c) Correct curve 3 M1 for horizontal plot correct (10, 41) (20, 73) (30, 117) (40, 167) M1 for at least 6 vertical plots from their (60, 232) (80, 280) (100, 300) table correct 4(d)(i) 35 to 38 1 4(d)(ii) 35 to 39 2 B1 for [UQ =] 56 to 59 or [LQ =] 20 to 21 4(e) 46 to 50 2 B1 for 195 or 105 seen

This question in 0607/41 May/June 2021

3 The table shows the masses of 30 sheep. Mass, m kg 60 1 m G 80 80 1 m G 100 100 1 m G 120 120 1 m G 140 Frequency 8 3 12 7 (a) Write down the modal group. … [1] (b) Write down the class which contains the lower quartile. … [1] (c) Maria says that the range of masses is 80 kg. Explain why she is incorrect. … … [1] (d) Draw an accurate pie chart to show this information. [4]

7 marks

Mark scheme: 3(a) 100 < m ⩽ 120 1 3(b) 60 < m ⩽ 80 1 3(c) Any correct statement 1 3(d) Correct labelled pie chart (labels 4 B3 for pie chart with all angles correct indicating masses) or B2 for pie chart with two angles correct or B1 for 2 correct angles calculated B1 for correct labels on sectors.

This question in 0607/42 May/June 2021

5 (a) There are 200 students in a school. The table shows information about their heights, h cm. Height, h cm 150 1 h G 165 165 1 h G 170 170 1 h G 17 5 175 1 h G 1 80 180 1 h G 190 190 1 h G 200 Frequency 7 17 43 64 49 20 Calculate an estimate of the mean height. … cm [2] (b) A biased die in the shape of a cube is numbered 0, 1, 1, 2, 3 and 3. It is rolled 100 times. The table shows the results. Score 0 1 2 3 Frequency x y 30 45 The mean score is 2.13 . Find the value of x and the value of y. x = … y = … [3]

5 marks

Mark scheme: 5(a) 178 or 178.4 to 178.5 2 M1 for evidence of mid-values 5(b) [x =] 7 3 B2 for y = 18 [y =] 18 or M1 for ([x × 0] + y [× 1] + 30 × 2 + 45 × 3) ÷ 100 = 2.13 oe If 0 scored SC1 for their x + their y = 25

This question in 0607/43 May/June 2021

6 (a) Ten students compare their test marks in Physics (x) and Chemistry (y). The table shows the results. Student A B C D E F G H I J Physics (x) 50 48 31 80 65 85 27 30 45 53 Chemistry (y) 55 56 30 83 63 90 30 32 45 55 (i) Write down the type of correlation between the Physics and Chemistry marks. … [1] (ii) Find the equation of the line of regression, giving y in terms of x. y = … [2] (iii) Student K scores 70 in the Physics test. Use your answer to part (a)(ii) to estimate this student’s mark in Chemistry. … [1] (b) The stem-and-leaf diagram shows information about the speeds of cars passing a school. 4 2 2 3 4 5 8 5 1 3 3 4 4 5 7 9 6 0 0 1 1 2 5 Key : 4 | 5 = 45 km/h Find (i) the range, … km/h [1] (ii) the median, … km/h [1] (iii) the lower quartile. … km/h [1]

7 marks

Mark scheme: 6(a)(i) Positive 1 6(a)(ii) 1.03x + 1.1[0] or 2 B1 for 1.03x + k or kx + 1.1[0] 1.027...x + 1.095... or 1.027...x + k or kx + 1.095... 6(a)(iii) 73 1 FT their (a)(ii) 6(b)(i) 23 1 6(b)(ii) 54 1 6(b)(iii) 46.5 1

This question in 0607/43 May/June 2021

1 The table shows the marks scored by 180 students in an examination. Mark 0 1 2 3 4 5 6 7 8 9 10 Number of 3 7 16 11 7 32 20 26 28 19 11 students (a) (i) Write down the mode. … [1] (ii) Write down the range. … [1] (iii) Find the median. … [1] (iv) Find the interquartile range. … [2] (v) Calculate the mean. … [2] (b) A different group of 140 students take the same examination. The marks of the two groups are combined and the mean mark of the 320 students is 6.5 . Find the mean mark of the 140 students. … [2]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 5 1 1(a)(ii) 10 1 1(a)(iii) 6 1 1(a)(iv) 3 2 B1 for LQ = 5 or UQ = 8 1(a)(v) 5.93 or 5.927 to 5.928 2 M1 for attempt at xf 1(b) 7.23 or 7.24 or 7.232 to 7.237 2 M1 for (320 × 6.5 – 180 × their (a)(v))[/140] oe

This question in 0607/43 Oct/Nov 2021

3 (a) The table shows the coursework grades for 20 students. Grade 3 4 5 6 7 Frequency 1 3 6 2 8 Find (i) the mode, … [1] (ii) the range, … [1] (iii) the median, … [1] (iv) the lower quartile. … [1] (b) The table shows some information about the heights, h cm, of 100 bushes. Height (h cm) 100 1 h G 110 110 1 h G 115 115 1 h G 130 Frequency 18 37 45 Calculate an estimate of the mean height. … cm [2] (c) The table shows some information about the times, t minutes, taken by some students to read a magazine. Time (t minutes) 0 1 t G 10 10 1 t G 20 20 1 t G 30 30 1 t G 40 Frequency 3 11 n 19 When using mid-interval values, an estimate of the mean value of t is 25.4 . Find the value of n. n = … [4]

10 marks

Mark scheme: 3(a)(i) 7 1 3(a)(ii) 4 1 3(a)(iii) 5.5 1 3(a)(iv) 5 1 3(b) 115.65 2 M1 for mid-values soi 3(c) 17 4 B3 for 25n + 845 = 25.4n + 838.2 oe or better or M2 for 3 × 5 + 11 × 15 + n × 25 + 19 × 35 = 25.4( n + 3 + 11 + 19) oe or M1 for 3 × 5 + 11 × 15 + n × 25 + 19 × 35 oe or25.4( n + 3 + 11 + 19) or for correct trial with integer value of n

This question in 0607/42 Feb/March 2022

2 (a) The cumulative frequency curve shows the marks for 300 students in a history test. 300 250 200 Cumulative 150 frequency 100 50 0 0 10 20 30 40 50 History mark (i) Find an estimate for the median. … [1] (ii) Estimate the number of students with a mark of more than 20. … [2] (iii) 70% of the students pass the test. Find the pass mark. … [2] (b) The table shows the marks for 100 students in a geography test. Mark m 10 1 m G 20 20 1 m G 30 30 1 m G 40 40 1 m G 50 Frequency 2 28 57 13 Calculate an estimate of the mean. … [2] (c) The table shows the marks for 9 students in chemistry and in physics. Chemistry 33 28 39 40 22 25 38 43 36mark (x) Physics 45 32 26 49 18 36 29 40 35mark (y) (i) Find the equation of the regression line for y in terms of x. y = … [2] (ii) What type of correlation is seen in this data? … [1] (iii) Use your answer to part (c)(i) to estimate the physics mark for a student with a mark of 30 in chemistry. … [1]

11 marks

Mark scheme: 2(a)(i) 31 1 2(a)(ii) 260 2 B1 for 40 seen 2(a)(iii) 27 2 70 30 M1 for  300 soi or  300 100 100 2(b) 33.1 2 M1 for at least three mid-values soi 2(c)(i) y  0.618 x  13.6 2 B1 for 0.618x + k or kx + 13.6 or 0.62x + 14 2(c)(ii) positive 1 2(c)(iii) 32 or 32.0 to 32.6 1 FT their (c)(i) if linear eqn

This question in 0607/41 May/June 2022

2 The number of hours, x, spent revising and the mark scored, y, in an examination for each of 10 students are shown in the table. Time, x hours 1 3 4.5 4 6 4 5.5 6 12 8 Mark, y 15 18 28 24 28 30 38 40 43 48 (a) (i) Complete the scatter diagram. The first four points have been plotted for you. y 50 40 30 Mark 20 10 0 x 0 1 2 3 4 5 6 7 8 9 10 11 12 Time (hours) [2] (ii) Write down the type of correlation shown by the scatter diagram. … [1] (b) Find the mean mark. … [1] (c) (i) Find the equation of the regression line for y in terms of x. Give your answer in the form y = mx + c. y = … [2] (ii) The value for m represents a connection between time and mark. Write down the units of m. … [1] (d) Use your answer to part (c)(i) to estimate (i) the mark scored for a student who revised for 10 hours, … [1] (ii) the number of hours spent revising for a student to score a mark of 36. … [1]

9 marks

Mark scheme: 2(a)(i) Correct points 2 B1 for 4 or 5 points correct 2(a)(ii) Positive 1 2(b) 31.2 1 2(c)(i) y = 3.01x + 15[.0] 2 B1 for y = 3x + 15 or y = 3.01x + k or y = kx + 15[.0] 2(c)(ii) Marks per hour oe 1 2(d)(i) 45 1 FT their (c)(i) if linear and answer is positive 2(d)(ii) 7 1 FT their (c)(i) if linear and answer is positive

This question in 0607/42 May/June 2022

6 The lifetimes, x hours, of 80 electric light bulbs are shown in the table. Lifetime (x hours) Frequency 850 1 x G 870 4 870 1 x G 890 6 890 1 x G 900 12 900 1 x G 920 18 920 1 x G 940 16 940 1 x G 950 20 950 1 x G 1000 4 (a) Calculate an estimate of the mean lifetime. … h [2] (b) Complete the cumulative frequency table. Lifetime (x hours) Cumulative frequency x G 870 4 x G 890 x G 900 x G 920 x G 940 x G 950 x G 1000 80 [1] (c) On the grid below, draw a cumulative frequency curve. 80 70 60 50 Cumulative 40frequency 30 20 10 0 x 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 Lifetime (hours) [3] (d) Use your graph in part (c) to find an estimate for (i) the median lifetime, … h [1] (ii) the interquartile range. … h [2] (e) Find the percentage of bulbs that have a lifetime of more than 900 hours. … % [2]

11 marks

Mark scheme: 6(a) 919 2 M1 for at least 5 correct midpoints soi 6(b) [ 4], 10, 22, 40, 56, 76, [80] 1 6(c) Correct curve or polygon and correct points 3 M1 for at least 6 horizontal plots correct plotted M1FT for at least 6 vertical plots correct (870, 4) (890, 10) (900, 22) (920, 40) (940, 56) (950, 76) (1000, 80) 6(d)(i) 920 1 6(d)(ii) 42 to 47 2 M1FT for [UQ =] 941 to 944 or [LQ =] 897 to 899 6(e) 72.5 2 B1 for 18+16+20+4 or 80 – 22 soi (58) or M1 for (80 – their 22)/80 × 100

This question in 0607/42 May/June 2022

2 The heights, h cm, of 100 seedlings are shown in the table. h cm Frequency 4.5 1 h G 5.5 9 5.5 1 h G 6.5 18 6.5 1 h G 7 .5 27 7.5 1 h G 8.5 19 8.5 1 h G 9.5 16 9.5 1 h G 10.5 11 Total 100 (a) Calculate an estimate for the mean. … cm [2] (b) Write down the modal group. … 1 h G … [1] (c) (i) Draw a cumulative frequency curve for the heights of the seedlings. 100 90 80 70 60Cumulative frequency 50 40 30 20 10 0 4 5 6 7 8 9 10 11 h Height (cm) [4] (ii) Use your curve to estimate the median. … cm [1] (iii) Use your curve to estimate the interquartile range. … cm [2] (iv) Find an estimate of the percentage of the seedlings that were more than 8 cm in height. … % [2]

12 marks

Mark scheme: 2(a) 7.48 2 M1 for evidence of mid-values 2(b) 6.5 7.5 1 2(c)(i) Correct cf curve through 6 points 4 B3 for curve through 5 correct points or B2 for curve through 4 correct points or correct cfs [9], 27, 54, 73, 89, 100 or B1 for curve through 4 correct points or 3, 4 or 5 cfs 2(c)(ii) 7.2 to 7.4 1 FT Only from increasing diagram 2(c)(iii) 2.0 to 2.4 2 B1FT for lq = 6.3 to 6.5 or uq = 8.5 to 8.7 FT only from increasing diagram 2(c)(iv) 34 to 38 2 B1 FT for 62 to 66 seen

This question in 0607/43 May/June 2022

2 The number of barrels of oil produced and the price of one barrel of oil on ten consecutive Mondays are shown in the table. Number of barrels, x million 100 97 94 95 86 84 77 76 82 83 Price, $y 48 43 35 36 44 48 54 58 58 62 (a) (i) Complete the scatter diagram. The first four points have been plotted for you. y 70 60 50 Price ($) 40 30 20 x 60 70 80 90 100 110 120 Number of barrels (million) [2] (ii) What type of correlation is shown by the scatter diagram? … [1] (b) Find the mean price of one barrel of oil. $ … [1] (c) Find the equation of the regression line for y in terms of x. y = … [2] (d) Use your answer to part (c) to estimate (i) the price of one barrel of oil when the number of barrels produced is 90 million, $ … [1] (ii) the price of one barrel of oil when the number of barrels produced is 120 million. $ … [1] (e) Which of your two answers to part (d) is likely to be more reliable? Give a reason for your answer. Part … because … … [1]

9 marks

Mark scheme: 2(a)(i) Correct points plotted 2 B1 for 4 or 5 points correct 2(a)(ii) Negative 1 2(b) 48.6 [0] 1 2(c) y = 117 − 0.784 x 2 B1 for y = 120 − 0.78 x or y = 117 + kx or y = k − 0.784 x 2(d)(i) 46.4 to 46.9 1 FT (c)(i) if linear equation and positive answer 2(d)(ii) 22.9 to 23.5 1 FT (c)(i) if linear equation and positive answer 2(e) Part (i) [because] part (ii) is outside data 1 oe

This question in 0607/41 Oct/Nov 2022

8 The cumulative frequency table shows the masses, in grams, of 1200 potatoes. Cumulative Mass (x grams) frequency x G 150 22 x G 180 160 x G 200 480 x G 250 860 x G 300 1120 x G 400 1200 (a) On the grid below, draw a cumulative frequency curve. 1200 1100 1000 900 800 700Cumulative frequency 600 500 400 300 200 100 0 x 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 Mass [3] (b) Use your curve to estimate (i) the median mass, … g [1] (ii) the interquartile range. … g [2] (c) Find the percentage of potatoes that have a mass of at least 280 grams. … % [2] (d) Complete the table to show the masses of the 1200 potatoes. Mass (x grams) Frequency 100 1 x G 150 22 150 1 x G 180 180 1 x G 200 200 1 x G 250 250 1 x G 300 300 1 x G 400 80 [1] (e) Calculate an estimate of the mean mass of a potato. … g [2]

11 marks

Mark scheme: 8(a) Correct curve 3 M1 for at least 5 horizontal plots correct (150, 22) (180, 160) (200, 480) M1 for at least 5 vertical plots correct (250, 860) (300, 1120) (400, 1200) 8(b)(i) 208 to 218 1 FT their curve 8(b)(ii) 55 to 75 2 M1FT for [UQ =] 250 to 260 or [LQ =] 185 to 195 seen 8(c) 12 to 17 2 1200 − their 1020 M1 for [100] 1200 their 1020 or  100 1200 8(d) [22], 138, 320, 380, 260, [80] 1 8(e) 226.1 or 226 2 M1 for at least four of 125, 165, 190, 225, 275, 350 soi

This question in 0607/41 Oct/Nov 2022

5 The distance, d km, cycled by each of 120 cyclists was recorded. The results are shown in the cumulative frequency curve. 120 100 80 Cumulative frequency 60 40 20 0 d 0 10 20 30 40 50 60 Distance (km) (a) Use the curve to estimate (i) the median, … km [1] (ii) the interquartile range. … km [2] (b) Use the curve to complete the frequency table. Distance (d km) 0 1 d G 10 10 1 d G 20 20 1 d G 30 30 1 d G 40 40 1 d G 50 50 1 d G 60 Frequency 6 18 [2] (c) Write down the modal class. … 1 d G … [1] (d) Calculate an estimate for the mean. … km [2]

8 marks

Mark scheme: 5(a)(i) 31 cao 1 5(a)(ii) 17 cao 2 B1 for [l.q. =] 22 or [u.q. =] 39 seen 5(b) 32, 38, 20, 6 2 B1 for 2 correct 5(c) 30 < d ⩽ 40 1 FT their table 5(d) 30.5 2 M1 for mid-points 5, 15, 25, ... soi

This question in 0607/42 Oct/Nov 2022

7 (a) The time, t hours, spent watching television in one week by each of 100 students is shown in the table. Time, t hours 0 1 t G 10 10 1 t G 20 20 1 t G 25 25 1 t G 30 30 1 t G 60 Frequency 3 11 42 40 4 (i) A pie chart is drawn to show the results. Calculate the sector angle for the number of students who spend more than 30 hours watching television. … [2] (ii) Calculate an estimate of the mean. … h [2] (b) A shopkeeper records the midday temperature, t °C, and the number of ice creams, n, sold each day in one week. The table shows the results. Midday 20 24 20 17 18 20 25 temperature, t °C Number of ice 103 106 95 91 93 98 114 creams, n (i) Write down the type of correlation shown in the table. … [1] (ii) Find the equation of the regression line, giving n in terms of t. n = … [2] (iii) Use your answer to part(b)(ii) to find the number of ice creams expected to be sold when the midday temperature is 22 °C. … [1] (iv) During this week, the shopkeeper sells 700 ice creams. She estimates that she will sell a total of 9800 ice creams during the next 14 weeks. Give a reason why this may not be a good estimate. … [1] (c) When the weather is fine, the probability that Lance goes cycling is 7. 9 When the weather is not fine, the probability that Lance goes cycling is 1. 5 The probability that the weather is fine is 3. 4 (i) Complete the tree diagram. Weather Cycles Yes 7 9 Fine 3 4 No … Yes … … Not fine … No [2] (ii) Find the probability that Lance goes cycling. … [3]

14 marks

Mark scheme: 7(a)(i) 14.4 2 4 M1 for  360 100 7(a)(ii) 24.05 or 24.1 2 M1 for at least 3 mid-values soi 7(b)(i) positive 1 7(b)(ii) n = 2.61t + 46.3 2 B1 for 2.61t + k or kt + 46.3 or 2.6t + 46 7(b)(iii) 103 or 104 1 FT their (c)(ii) but must be integer answer 7(b)(iv) small sample oe or reference to weather 1 7(c)(i) 1 2 1 4 2 B1 for 2 correct , , , 4 9 5 5 7(c)(ii) 19 3 3 7 1 1 oe M2 FT for  + their  their 30 4 9 4 5 or M1 FT for one of the products only FT probabilities < 1

This question in 0607/43 Oct/Nov 2022

1 The table shows the marks scored by each of 75 students in a test. Mark 0 1 2 3 4 5 6 7 8 9 10 Number of students 1 4 5 6 9 10 11 7 6 13 3 (a) Write down the mode. … [1] (b) Write down the range. … [1] (c) Find the median. … [1] (d) Find the lower quartile. … [1] (e) Calculate the mean. … [2]

6 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 9 1 1(b) 10 1 1(c) 6 1 1(d) 4 1 1(e) 5.71 or 5.706 to 5.707 2 M1 for attempt at fx/f

This question in 0607/42 Feb/March 2023

4 The heights, x cm, of 500 students in a school are shown in the table. Height (x) Frequency 150 1 x G 155 24 155 1 x G 160 42 160 1 x G 165 84 165 1 x G 170 106 170 1 x G 1 75 112 175 1 x G 180 87 180 1 x G 185 45 (a) Calculate an estimate of the mean height. … cm [2] (b) Complete the cumulative frequency table. Height (x) Cumulative frequency x G 155 24 x G 160 x G 165 x G 170 x G 175 x G 180 x G 185 500 [1] (c) On the grid below, draw a cumulative frequency curve. 500 450 400 350 300 250Cumulative frequency 200 150 100 50 0 x 150 155 160 165 170 175 180 185 Height (cm) [3] (d) Use your graph in part (c) to find an estimate for (i) the upper quartile … cm [1] (ii) the percentage of students who are less than 162 cm in height. … % [2]

9 marks

Mark scheme: 4(a) 169.31 or 169 or 169.3 2 M1 for use of mid-points e.g. 24 × 152.5 + 42×157.5 + 84 × 162.5 … 4(b) [24], 66, 150, 256, 368, 455, [500] 1 4(c) Correct curve 3 M1 for horizontal plot correct (155, 24) (160, 66) (165, 150) M1 for at least 5 vertical plots correct (170, 256) (175, 368) (180, 455) (185, 500) 4(d)(i) 175 to 176.5 1 FT their curve 4(d)(ii) 18 to 20 2 B1 for 90 to 100 their 90 or M1 for [ 100] soi 500

This question in 0607/42 Feb/March 2023

1 25 students each record the number of logic problems they solve in one hour. The table shows the results. Number of logic problems solved 3 4 5 6 7 8 Frequency 1 3 8 7 5 1 (a) Find (i) the range … [1] (ii) the mode … [1] (iii) the median … [1] (iv) the interquartile range … [2] (v) the mean. … [2] (b) Nabile draws a pie chart. Calculate the angle that represents 7 logic problems solved. … [2] (c) Shabana draws a bar chart using these results. The bar that represents 4 logic problems solved has a height of 4.5 cm. Calculate the height of the bar that represents 5 logic problems solved. … cm [2]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 5 1 1(a)(ii) 5 1 1(a)(iii) 6 1 1(a)(iv) 1.5 2 B1 for [u.q. = ] 6.5 or [l.q. = ] 5 1(a)(v) 3 2 M1 for 5.6 or 5 5 (1  3 + 3  4 + 8  5 + 7  6 + 7  5 + 1  8)  25 1(b) 72 2 5 360 M1 for [360] or [5] 25 25 1(c) 12 2 8 4.5 M1 for [4.5] or [8] 3 3

This question in 0607/41 May/June 2023

3 The table shows the marks of 12 students in a French examination and a Spanish examination. French mark (x) 17 23 28 32 37 42 57 61 77 82 94 96 Spanish mark (y) 26 22 33 46 41 53 62 67 66 75 83 95 (a) Find the median Spanish mark. … [1] (b) Find the mean French mark. … [1] (c) Find the equation of the regression line for y in terms of x. y = … [2] (d) Use your equation to estimate the Spanish mark when (i) the French mark is 50 … [1] (ii) the French mark is 6. … [1] (e) Which French mark, 50 or 6, is likely to give the most reliable Spanish mark? Give a reason for your answer. … because … … [1]

7 marks

Mark scheme: 3(a) 57.5 1 3(b) 53.8 or 53.83… 1 3(c) 0.791x + 13.2 2 M1 for 0.791x + k or kx + 13.2 or 0.79x + 13 3(d)(i) 53 or 52.7 to 52.8 1 FT their part (b) 3(d)(ii) 18 or 17.90 to 17.95 1 FT their part (b) 3(e) 50, within range 1 or 50 as 6 is not in range

This question in 0607/43 May/June 2023

3 Each of 200 students records their height, h cm. The results are shown on the cumulative frequency curve. 200 180 160 140 120 Cumulative 100 frequency 80 60 40 20 0 120 130 140 150 160 170 180 190 h Height (cm) (a) Use the cumulative frequency curve to find (i) the median … cm [1] (ii) the interquartile range … cm [2] (iii) the number of students with a height greater than 150 cm. … [2] (b) Use the cumulative frequency curve to complete the frequency table. Height (h cm) 120 1 h G 150 150 1 h G 170 170 1 h G 180 180 1 h G 190 Frequency [2] (c) Use the frequency table to calculate an estimate of the mean height.

9 marks

Mark scheme: 3(a)(i) 170 1 3(a)(ii) 22 2 B1 for 158 or 180 seen 3(a)(iii) 172 2 B1 for 28 seen 3(b) 28, 72, 48 to 52, 52 to 48 2 B1 for two or three correct [total = 200] 3(c) 166.4 to 166.6 2 M1 for 3 or more mid-values soi

This question in 0607/41 Oct/Nov 2023

4 (a) A group of 10 people were asked the time, correct to the nearest minute, they each spent listening to the news and reading the news on Monday. The results are shown in the table. Minutes listening (x) 1 9 3 3 11 8 2 7 1 4 Minutes reading (y) 5 10 9 7 2 1 3 6 11 5 (i) Complete the scatter diagram. The first six points have been plotted for you. y 12 10 8 Minutes 6 reading 4 2 x 0 2 4 6 8 10 12 Minutes listening [2] (ii) Find the median time spent reading the news on Monday. … min [1] (iii) Find the equation of the line of regression. Give your answer in the form y = mx + c . y = … [2] (iv) On Tuesday, each person spends the same time listening to the news as they did on Monday. They each spend 5 minutes longer reading the news than they did on Monday. Write down the equation of the line of regression for Tuesday. y = … [1] (b) In February Sancho read the news for a total of 8 hours. This was a reduction of 36% from January. Work out how long Sancho read the news in January. … hours [2] (c) The bar chart shows the number of news articles read one day by each of 23 people. 5 Number of 4 news articles read 3 2 0 1 2 3 4 5 6 7 8 9 10 Number of people Calculate the mean number of articles read. … [2]

10 marks

Mark scheme: 4(a)(i) 4 correct points plotted 2 B1 for 3 correct 4(a)(ii) 5.5 1 4(a)(iii)  y =  − 0.323 x + 7.48 2 B1 for [ y =] − 0.323 x + k or [y=] kx + 7.48 or [y=] −0.32 x + 7.5 4(a)(iv)  y =  − 0.323 x + 12.48 1 FT their (k) + 5 4(b) 12.5 2  100 − 36 = M1 for x   8 oe  100  4(c) 3.57 or 3.565... 2 M1 for 5 +5 4 +6 3 +9 2  3 implied by 82

This question in 0607/42 Oct/Nov 2023

2 These are Sunni’s last 12 scores in a game. 7 17 4 20 15 12 11 16 6 18 9 20 (a) Find (i) the mode … [1] (ii) the median … [1] (iii) the mean … [1] (iv) the range … [1] (v) the upper quartile. … [1] (b) Explain why the mode is not the best measure of average to represent Sunni’s scores. … … [1]

6 marks

Mark scheme: 2(a)(i) 20 1 2(a)(ii) 13.5 1 2(a)(iii) 12.9 or 12.91 to 12.92 1 2(a)(iv) 16 1 2(a)(v) 17.5 1 2(b) It’s the highest oe 1

This question in 0607/43 Oct/Nov 2023

7 240 people take part in a marathon race. The times, t minutes, they took for the race are shown in the cumulative frequency curve. 240 220 200 180 160 140 Cumulative frequency 120 100 80 60 40 20 0 t 150 160 170 180 190 200 210 220 Time in minutes (a) Use the curve to estimate (i) the median time … min [1] (ii) the interquartile range. … min [2] (b) The fastest 20% of the runners are awarded a medal. Use the curve to estimate the longest time taken by a runner who received a medal. … min [2] (c) Use the curve to complete the frequency table. Time, 150 1 t G 160 160 1 t G 170 170 1 t G 180 180 1 t G 190 190 1 t G 200 200 1 t G 210 210 1 t G 220t minutes Frequency 16 32 [2] (d) Use the table in part (c) to calculate an estimate of the mean time. … min [2]

9 marks

Mark scheme: 7(a)(i) 182 1 7(a)(ii) 16 2 B1 for [uq=]189 or [lq=] 173 7(b) 170 2 B1 for 48 seen 7(c) 56, 84, 36, 12, 4 2 B1 for 3 or 4 correct 7(d) 181 2 M1 for at least 4 mid-points soi

This question in 0607/43 Oct/Nov 2023

8 The table shows the money received in a shop for 120 days. Money received Frequency ($x) 500 1 x G 1000 6 1000 1 x G 1500 16 1500 1 x G 2000 24 2000 1 x G 2500 36 2500 1 x G 3000 20 3000 1 x G 3500 14 3500 1 x G 4000 4 (a) On the grid, draw a cumulative frequency curve to show this information. 120 100 80 Cumulative frequency 60 40 20 0 x 500 1000 1500 2000 2500 3000 3500 4000 Money received ($) [4] (b) Use your curve to estimate (i) the median $ … [1] (ii) the interquartile range. $ … [2] (c) Use your curve to estimate the percentage of these 120 days where the shop received more than $1800. … % [3]

10 marks

Mark scheme: 8(a) Correct graph through 7 points 4 B3 for graph through 5 correct points or B2 for graph through 3 correct points or for all correct heights translated to other point in interval or for correct points plotted not joined or B1 for 6, 22, 46, 82, 102, 116, 120 8(b)(i) 2100 to 2300 1 FT from increasing curve. 8(b)(ii) 950 to 1150 2 B1 for 1650 ⩽ [LQ] ⩽ 1750 or 2600 ⩽ [UQ] < 2750 8(c) 68.3 to 71.7 3 B1FT for 34 to 38 their M1 for (34to38)[100] 120 120 − their or (34to38)[100] 120

This question in 0607/42 Feb/March 2024

2 (a) The heights, x cm, of 100 plants are shown in the table. Height (x cm) 0 1 x G 20 20 1 x G 35 35 1 x G 40 40 1 x G 60 60 1 x G 80 Frequency 7 13 20 32 28 (i) Calculate an estimate of the mean height of the plants. … cm [2] (ii) (a) Complete the cumulative frequency table for the plants. Height (x cm) x G 20 x G 35 x G 40 x G 60 x G 80 Cumulative 7 100 frequency [1] (b) On the grid, draw the cumulative frequency curve. 100 90 80 70 60 Cumulative 50 frequency 40 30 20 10 0 x 0 10 20 30 40 50 60 70 80 Height (cm) [3] (c) Use your cumulative frequency curve to find an estimate for the interquartile range. … cm [2] (b) The heights, h cm, of 50 different plants are shown in the table, where k is an integer. Height (h cm) Frequency 0 1 h G 20 25 20 1 h G k 15 k 1 h G 80 10 An estimate of the mean height of these plants is 27 cm. Find the value of k. k = … [3]

11 marks

Mark scheme: 2(a)(i) 47.4 or 47.375 2 M1 for at least 4 correct mid-points soi 2(a)(ii)(a) [7], 20, 40, 72, [100] 1 In parts (a)(ii)(b) and (a)(ii)(c), marks can only be earned with an increasing curve (a)(ii)(b) Correct curve 3 B1 for horizontal plot correct (20, 7), (35, 20), (40, 40), (60, 72), B1FT for at least 4 vertical plots correct (80, 100) (a)(ii)(c) 24 to 28 2 M1FT for [UQ =] 61 to 63 or [LQ =] 35 to 37 2(b) 44 3 M2 for (20  k ) ( k  80) 10  25   15   10 [  27  50] 2 2 oe (20  k ) ( k  80) or M1 for or 2 2

This question in 0607/41 May/June 2024

4 (a) Erin rolls a biased die a number of times. The table shows the results. Score 1 2 3 4 5 6 Frequency 6 6 3 6 x 4 The mean score is 3.75 . Find the value of x. x = … [3] (b) 70 students each record the time taken to complete their mathematics homework. The table shows the results. Time, t minutes 0 1 t G 5 5 1 t G 10 10 1 t G 15 15 1 t G 25 25 1 t G 50 Frequency 7 21 23 16 3 (i) Calculate an estimate of the mean. … min [2] (ii) (a) Use the information in the table to complete the cumulative frequency table. Time, t minutes t G 5 t G 10 t G 15 t G 25 t G 50 Cumulative frequency [2] (b) 70 60 50 40 Cumulative frequency 30 20 10 0 t 0 10 20 30 40 50 Time (minutes) On the grid, draw the cumulative frequency curve. [3] (c) Use your curve to estimate the median. … min [1] (d) Use your curve to estimate the number of students who took more than 13 minutes to complete their mathematics homework. … [2]

13 marks

Mark scheme: 4(a) 15 3 M2 for 6 1 6 2 3 3 6 4  x 5 4  6 [  3.75] 6  6  3  6  x  4 or better or M1 for 6 1 6 2 3 3 6 4 x 5 4 6 or better or for 3.75 × (6 + 6 + 3 + 6 + x + 4) or better 4(b)(i) 12.8 or 12.78 to 12.79 2 M1 for at least correct four mid-values soi 4(b)(ii)(a) 7, 28, 51, 67, 70 2 B1 for 3 correct In (b), (c) and (d) marks can only be earned with an increasing curve or polygon at least as far as (25, 67 FT) 4(b)(ii)(b) Correct curve 3 B1 FT for 5 points with correct heights B1 for 5 points with correct t values 4(b)(ii)(c) 11 to 12 1 FT 4(b)(ii)(d) 26, 27, 28, 29 or 30 cao 2 B1 for 40 to 44 seen or B1FT for their reading from t = 13

This question in 0607/42 May/June 2024

1 (a) There are 120 houses in a street. The table shows the numbers of letters delivered to the houses one day. Number of letters 0 1 2 3 4 5 6 Frequency 26 20 23 25 14 8 4 Find (i) the mode … [1] (ii) the median … [1] (iii) the range … [1] (iv) the upper quartile … [1] (v) the mean. … [2] (b) This table shows the numbers of letters delivered to the houses in another street one day. Number of letters 0 1 2 3 4 5 6 Frequency 18 31 27 18 n 12 5 The mean number of letters delivered in this street is 2.28 . Find the value of n. n = … [3]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 0 1 1(a)(ii) 2 1 1(a)(iii) 6 1 1(a)(iv) 3 1 1(a)(v) 2.175 2 M1 for [0 × 26] + 1 × 20 + 2 × 23 ... 1(b) 14 3 M2 for  0  18  1 31  2  27  3  18  4  n  5  12  6  5  2.28 18  31  27  18  n  12  5 oe or M1 for  0  18  1 31  2  27 3 18  4  n 5 12  6  5 or for (18 + 31 + 27 + 18 + n + 12 + 5) × 2.28

This question in 0607/43 May/June 2024

3 Paulo compares the fuel consumption of his car and the average speed of his car for ten journeys. The results are shown in the table. Average speed 48 56 64 72 88 96 104 120 128 136 (x kilometres per hour) Fuel consumption 18 16 14 13.3 12.2 11.8 11.4 9.2 8 7 (y kilometres per litre) (a) (i) Complete the scatter diagram. The first six points have been plotted for you. y 20 18 16 14 12 Fuel consumption 10 (km/l) 8 6 4 2 0 x 40 60 80 100 120 140 Average speed (km/h) [2] (ii) What type of correlation is shown by the scatter diagram? … [1] (b) Find the mean fuel consumption. … km/l [1] (c) (i) Find the equation of the regression line for y in terms of x. y = … [2] (ii) Use your regression line to estimate the fuel consumption when the average speed is 80 km/h. … km/l [1] (iii) Paulo drives his next journey at an average speed of 30 km/h. Give a reason why the regression line is unlikely to give a reliable estimate of the fuel consumption for this journey. … [1]

8 marks

Mark scheme: 3(a)(i) Correct points plotted 2 B1 for 3 points correct 3(a)(ii) negative 1 3(b) 12.1 or 12.09 1 3(c)(i) y = −0.109 x + 22.1 2 B1 for y = − kx + 22.1 or y = −0.109 x + k or y = −0.11x + 22 3(c)(ii) 13.4 or 13.38 1 FT their (c)(i) 3(c)(iii) Outside data range oe 1

This question in 0607/41 Oct/Nov 2024

1 The table shows the heights of 100 sunflower plants. Height (h cm) 90 1 h G 11 0 110 1 h G 120 12 0 1 h G 130 130 1 h G 150 150 1 h G 170 170 1 h G 200 Frequency 10 12 22 35 14 7 (a) Calculate an estimate for the mean height of the sunflower plants. … cm [2] (b) Complete the cumulative frequency table for the heights of the sunflower plants. Height (h cm) h G 110 h G 120 h G 130 h G 150 h G 170 h G 200 Cumulative frequency [2] (c) On the grid, draw a cumulative frequency curve to show this information. 100 90 80 70 60 Cumulative 50 frequency 40 30 20 10 0 90 100 110 120 130 140 150 160 170 180 190 200 h Height (cm) [3] (d) Use your cumulative frequency curve to estimate the number of sunflower plants that are more than 180 cm in height. … [2]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 136 or 135.65 or 135.7 2 M1 for midpoints soi 1(b) 10, 22, 44, 79, 93, 100 2 M1 for 4 correct 1(c) Correct cumulative frequency 3 FT their table with increasing values curve B1 for 6 points with correct heights B1 for 6 points with correct h values 1(d) 2, 3, 4 or 5 2 FT their increasing curve or polygon B1 for reading from their curve at 180 soi by 95 or 96 or 97 or 98

This question in 0607/43 Oct/Nov 2024

10 The table shows the number of pens in each room in a school. Number of pens 1 2 3 4 5 6 Frequency 14 5 3 x 2 1 The mean number of pens is 2.3 . Find the value of x. x = … [3]

3 marks

Mark scheme: 10 5 nfww 3 M2 for 49 + 4x = 2.3 × (25 + x) or M1 for numerator 1 × 14 + 2 × 5 + 3 × 3 + 4x + 5 × 2 + 6 × 1 or better or for denominator 14 + 5 + 3 + x + 2 + 1 or better

This question in 0607/42 Feb/March 2025

1 150 students are each asked how many texts they sent the previous day. The results are shown in the table. Number of texts 0 1 2 3 4 5 6 Frequency 18 45 37 24 15 8 3 (a) Find (i) the mode … [1] (ii) the median … [1] (iii) the range … [1] (iv) the upper quartile. … [1] (b) One of the 150 students is selected at random. Find the probability that this student sent fewer than 3 texts. … [1]

5 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 1 1 1(a)(ii) 2 1 1(a)(iii) 6 1 1(a)(iv) 3 1 1(b) 2 1 oe 3

This question in 0607/41 May/June 2025

14 Ahmed records the mass of each of 50 pumpkins. The results are shown in the table. Mass (m kg) 0 1 m G 2 2 1 m G 5 5 1 m G 10 10 1 m G 15 15 1 m G 25 Frequency 13 17 10 7 3 (a) Calculate an estimate of the mean. … kg [2] (b) Ahmed picks two of the 50 pumpkins at random. Find the probability that one of these pumpkins has a mass greater than 10 kg and the other pumpkin has a mass of not more than 2 kg. … [3]

5 marks

Mark scheme: 14(a) 5.9 2 M1 for at least 3 correct midpoints soi 14(b) 26 3 10 13 oe M2 for [2  oe 245 ]50 49 10 13 13 10 or B1 for and oe or and oe 50 49 50 49 13 If 0 scored, SC1 for answer oe 125

This question in 0607/41 May/June 2025

10 The table shows the marks of each of 10 students in a physics exam and in a chemistry exam. Physics mark (x) 9 21 33 41 55 68 75 83 89 96 Chemistry mark (y) 31 46 42 50 50 61 69 68 72 90 (a) Find the mean physics mark. … [1] (b) (i) Find the equation of the regression line for y in terms of x. y = … [2] (ii) Use your answer to part (b)(i) to estimate the chemistry mark when the physics mark is 46. … [1] (c) Two of the students who scored more than 35 in the physics exam are chosen at random. Find the probability that they both scored more than 65 in the chemistry exam. … [3]

7 marks

Mark scheme: 10(a) 57 1 10(b)(i) y = 0.548 x + 26.6 2 B1 for y = kx + 26.6 or y = 0.548x + k or y = 0.55x + 27 10(b)(ii) 52 or 51.8 to 51.9 1 FT their (b)(i) 10(c) 2 3 4 3 oe M2 for  7 7 6 4 or M1 for seen 7 x x − 1 or  where x < y and y < 10 y y − 1

This question in 0607/42 May/June 2025

10 The speed of each of 155 cars passing a school gate is recorded. The results are shown in the table. Speed (v km/h) 10 1 v G 20 20 1 v G 30 30 1 v G 35 35 1 v G 40 40 1 v G 60 Frequency 7 23 36 49 40 Calculate an estimate of the mean speed. … km/h [2]

2 marks

Mark scheme: 10 36.7 or 36.69... 2 M1 for 3 correct mid values soi

This question in 0607/43 May/June 2025

2 The table shows the marks scored by 100 students in a test. Mark 1–10 11–20 21–40 41–60 61–80 81–90 91–100 Number of students 2 8 17 21 14 25 13 (a) One of these students is chosen at random. Find the probability that this student scored more than 90 marks. … [1] (b) Write down the group that contains the median. … [1] (c) Calculate an estimate for the mean. … [2]

4 marks

Mark scheme: 2(a) 0.13 oe 1 2(b) 61 - 80 1 2(c) 60.8 2 M1 for 5 midpoints soi If 0 scored SC1 for 60.3

This question in 0607/42 Oct/Nov 2025