Statistical charts and diagrams — Paper 2 · IGCSE Mathematics 0580

19 ForFor 15 Examiner'sExaminer's UseUse 10 Speed (metres per second) 5 0 2 4 6 8 10 12 14 Time (minutes) The diagram shows the speed-time graph of a train journey between two stations. The train accelerates for two minutes, travels at a constant maximum speed, then slows to a stop. (a) Write down the number of seconds that the train travels at its constant maximum speed. Answer(a) s [1] (b) Calculate the distance between the two stations in metres. Answer(b) m [3] (c) Find the acceleration of the train in the first two minutes. Give your answer in m/s2. Answer(c) m/s2 [2] Question 20 is printed on the next page.

6 marks

Mark scheme: p p 19 (a) 480 1 (b) 9900 3 M1 for attempt at area under graph M1 for 0.5 × 15 × (their (a) + 14 × 60) oe or 0.5 × 15 × (8 + 14) oe 1 2 M1 for numerical vertical/horizontal or numerical (c) 0.125 or 8 use of v = u + at but t ≤ 120 or t ≤ 2

This question in 0580/21 May/June 2011

16 In a survey of 60 cars, the type of fuel that they use is recorded in the table below. For Examiner's Each car only uses one type of fuel. Use Petrol Diesel Liquid Hydrogen Electricity 40 12 2 6 (a) Write down the mode. Answer(a) [1] (b) Olav drew a pie chart to illustrate these figures. Calculate the angle of the sector for Diesel. Answer(b) [2] (c) Calculate the probability that a car chosen at random uses Electricity. Write your answer as a fraction in its simplest form. Answer(c) [2]

5 marks

Mark scheme: 16 (a) Petrol cao 1 (b) 72 2 M1 for 360 × 12 ÷ 60 1 6 3 2 (c) 2 B1 or or or 0.1 or 10% 10 60 30 20

This question in 0580/22 Oct/Nov 2011

7 For Examiner's Height (h cm) 0 < h Y 10 10 < h Y 15 15 < h Y 30 Use Frequency 25 u 9 Frequency density 2.5 4.8 v The table shows information about the heights of some flowers. Calculate the values of u and v. Answer u = v = [2]

2 marks

Mark scheme: 7 u = 24(.0), v = 0.6 2 B1 each

This question in 0580/23 May/June 2012

4 The four sector angles in a pie chart are 2x°, 3x°, 4x° and 90°. Find the value of x. Answer x = … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 4 30 2 M1 for 2x + 3x + 4x + 90 = 360 oe

This question in 0580/23 Oct/Nov 2014

17 The mass, m grams, of cornfl akes in each of 200 boxes is recorded. The cumulative frequency diagram shows the results. 200 180 160 140 120 Cumulative frequency 100 80 60 40 20 0 m 494 496 498 500 502 504 506 508 510 Mass (grams) (a) Use the diagram to estimate the inter-quartile range. Answer(a) … g [2] (b) Find the probability that a box chosen at random has a mass of 500 grams or less. Answer(b) … [2] (c) Mass (m grams) 496 < m Y 500 500 < m Y 504 504 < m Y 508 508 < m Y 510 Frequency 16 74 104 6 The data in this frequency table is to be shown in a histogram. Complete the frequency density table below. Mass (m grams) 496 < m Y 500 500 < m Y 504 504 < m Y 508 508 < m Y 510 Frequency density 4 [2] __________________________________________________________________________________________

6 marks

Mark scheme: 17 (a) 3.08 to 3.22 nfww 2 B1 for 502.5 to 502.62 or 505.7 to 505.8 16 (b) oe 2 B1 for 16 soi 200 their 16 or M1 for 200 (c) 18.5 26 3 2 B1 for 18.5 and 26 B1 for 3

This question in 0580/23 Oct/Nov 2014

22 The table shows some information about the mass, m grams, of 200 bananas. Mass (m grams) 90 1 m G 110 110 1 m G 120 120 1 m G 125 125 1 m G 140 Frequency 40 70 60 30 Height of column 6 in histogram (cm) Complete the table. [4]

4 marks

Mark scheme: 22 1 3.5 1 4 B3 for 2 correct B2 for 1 correct or M1 for 2, 7, […] and 2 seen [FDs]

This question in 0580/23 Oct/Nov 2016

16 Six students revise for a test. The scatter diagram shows the time, in hours, each student spent revising and their mark in the test. 50 45 40 Mark 35 30 25 0 1 2 3 4 5 6 7 8 9 10 Time (hours) (a) The data for two more students is shown in the table. Time (hours) 4.5 6.5 Mark 33 35 Plot these two points on the scatter diagram. [1] (b) What type of correlation is shown on the scatter diagram? … [1] (c) Draw a line of best fit on the scatter diagram. [1] (d) Another student spent 5.5 hours revising. Estimate a mark for this student. … [1]

4 marks

Mark scheme: 16(b) Positive 1 16(c) Correct ruled line 1 16(d) 33.5 to 37.5 1FT FT from their line providing positive gradient

This question in 0580/21 May/June 2017

22 Simon records the heights, h cm, of 200 sunflowers in his garden. The cumulative frequency diagram shows this information. 200 180 160 140 120 Cumulative frequency 100 80 60 40 20 0 h 100 120 140 160 180 200 220 Height (cm) (a) Find the number of these sunflowers that have a height of more than 160 cm. … [2] (b) Sue records the heights, h cm, of 200 sunflowers in her garden. The cumulative frequency table shows this information. Height (h cm) Cumulative frequency h G 100 0 h G 110 20 h G 120 48 h G 130 100 h G 140 140 h G 150 172 h G 160 188 h G 170 200 On the grid above, draw another cumulative frequency diagram to show this information. [3] (c) Work out the difference between the median heights of Simon’s sunflowers and Sue’s sunflowers. … cm [2] Question 23 is printed on the next page.

7 marks

Mark scheme: 22(a) 80 to 84 2 M1 for 116 to 120 22(b) Correct curve or ruled lines 3 B2 for 7 or 8 correct points B1 for 5 or 6 correct points 22(c) 26 2 B1 for 156 or 130 or for their 130 from their increasing curve (or lines)

This question in 0580/21 Oct/Nov 2017

13 The histogram shows information about the time, t minutes, spent in a shop by each of 80 people. 2 Frequency density 1 0 t 0 10 20 30 40 50 60 70 Time (minutes) Complete the frequency table. Time (t minutes) 0 1 t G 5 5 1 t G 15 15 1 t G 30 30 1 t G 50 50 1 t G 70 Number of people 6 27 10 [2]

2 marks

Mark scheme: 13 15 and 22 2 M1 for 1.5 × 10 or 1.1 × 20

This question in 0580/22 May/June 2018

18 120 students choose what they want to do when they leave school. Their choices are shown in the table. Choice Number of students University 57 Training 45 Work 18 Complete the pie chart to show this information. Label each sector clearly. [4]

4 marks

Mark scheme: 18 Correct pie chart e.g. 4 B3B for correcct chart no laabels oro for 2 correect sectors wwith or withouut labels oro B2 for 3 correctc angless seen (171°, 135° and 54°)5 oro 3 correct percentagesp ((47.5%, 37.55% and 15%)) oro M1 for method 57 57 e.g.e × 360,3 57 × 33 or ×× 100 oe 120 120 or one correctc sectorr on the pie chartc

This question in 0580/22 Oct/Nov 2018

18 The table shows the number of people in different age groups at a cinema. Age ( y years) 15 1 y G 25 25 1 y G 30 30 1 y G 50 50 1 y G 80 Number of people 35 32 44 12 Dexter draws a histogram to show this information. The height of the bar he draws for the group 15 1 y G 25 is 7 cm. Calculate the height of each of the remaining bars. 25 1 y G 30 … cm 30 1 y G 50 … cm 50 1 y G 80 … cm [3]

3 marks

Mark scheme: 18 12.8 3 B2 for 2 correct heights or 3 correct freq 4.4 densities 0.8 or B1 for 1 correct height or 2 correct freq densities

This question in 0580/22 May/June 2019

23 The time, t minutes, it takes each of 50 students to travel to school is recorded. The table shows the 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 7 19 16 8 (a) Write down the modal class. … 1 t G … min [1] (b) On the grid, complete the histogram to show the information in the table. 4 3 Frequency 2 density 1 0 0 10 20 30 40 t Time (minutes) [3]

4 marks

Mark scheme: 23(a) 10 [< t ⩽] 15 1 23(b) Correct histogram 3 B1 for each correct block 4 If 0 scored, SC1 for correct frequency densities 3.8, 3.2, 0.4 soi by correct heights 3 2 1 0 t Time (minutes)

This question in 0580/23 Oct/Nov 2019

2 The number of people swimming in a pool is recorded each day for 12 days. 24 28 13 38 15 26 45 21 48 36 18 38 (a) Complete the stem-and-leaf diagram. 1 2 3 4 Key: 1 3 represents 13 swimmers [2] (b) Find the median number of swimmers. … [1]

3 marks

Mark scheme: 2(a) 1 3 5 8 2 M1 for correct but not ordered or for two 2 1 4 6 8 correct rows ordered 3 6 8 8 4 5 8 2(b) 27 1

This question in 0580/22 Feb/March 2020

12 Gemma records the times, in seconds, taken for a group of children and a group of adults to complete a puzzle. The box-and-whisker plot shows information about the times taken for the children to complete the puzzle. Children Adults 20 40 60 80 100 Time (seconds) (a) Find the interquartile range of the times taken for the children to complete the puzzle. … seconds [2] (b) The table shows some information about the times, in seconds, taken for the adults to complete the puzzle. Minimum Lower quartile Median Upper quartile Maximum 28 42 58 70 75 On the grid above, draw the box-and-whisker plot for the adults. [2]

4 marks

Mark scheme: 12(a) 22 2 B1 for 48 and 70 12(b) 2 M1 for a box with two whiskers and at least two correct from Min 28, LQ 42, Med 58, UQ 70, Max 75

This question in 0580/21 May/June 2020

22 The table shows information about the times, t seconds, taken by each of 100 students to solve a puzzle. Time (t seconds) 0 1 t G 10 10 1 t G 15 15 1 t G 20 20 1 t G 40 40 1 t G 75 Frequency 9 18 22 30 21 (a) Calculate an estimate of the mean time. … s [4] (b) Emmanuel draws a histogram to show this information. The table shows the heights, in cm, of some of the bars for this histogram. Complete the table. Time (t seconds) 0 1 t G 10 10 1 t G 15 15 1 t G 20 20 1 t G 40 40 1 t G 75 Height of bar (cm) 3.6 14.4 17.6 [3]

7 marks

Mark scheme: 22(a) 27.625 4 M1 for 5, 12.5, 17.5, 30, 57.5 M1 for where x is in correct fx interval including boundaries Σfx M1 dep on second M1 for 100 22(b) 6 and 2.4 3 B2 for either correct or M1 for [fd =] 1.5 or 0.6 oe or B1 for [multiplier] 4

This question in 0580/23 Oct/Nov 2020

2 Thibault records the number of cars of each colour in a car park. Colour Black White Silver Red Number of cars 8 5 4 3 He draws a pie chart to show this information. Calculate the sector angle for the red cars. … [2]

2 marks

Mark scheme: 2 54 2 360 3 M1 for  3 or  360  oe 8  5  4  3 8  5  4  3

This question in 0580/22 May/June 2022

13 The table shows information about the mass of each of 50 children. Cumulative Mass (k kg) Frequency k G 20 0 k G 22 7 k G 24 23 k G 28 35 k G 32 43 k G 36 47 k G 42 50 (a) Draw a cumulative frequency diagram to show this information. 50 40 30 Cumulative frequency 20 10 0 k 20 24 28 32 36 40 44 Mass (kg) [3] (b) Use your graph to find an estimate of the 90th percentile. … [1]

4 marks

Mark scheme: 13(a) A correct cumulative frequency diagram 3 B1 for correct horizontal placement for 7 plots B1 for correct vertical placement for 7 plots B1FT dep on at least B1 for reasonable increasing curve or polygon through their 7 points If 0 scored SC1 FT for 6 out of 7 points correctly plotted 13(b) 33 to 34.5 1 FT their increasing cumulative frequency graph

This question in 0580/22 Oct/Nov 2022

23 Some students record their reaction times. The table shows the results. Reaction time 0 1 t G 6 6 1 t G 10 (t seconds) Frequency 18 16 On a histogram, the height of the block for the 0 1 t G 6 interval is 7.5 cm. Calculate the height of the block for the 6 1 t G 10 interval. … cm [2]

2 marks

Mark scheme: 23 10 2 7.5 M1 for oe or better 18  6 or [frequency densities] 3 and 4 or 45 and 4h or 45 and 40

This question in 0580/22 Oct/Nov 2023

15 Students in class P take a test. These statistics show information about their marks. • lower quartile = 38 • median = 53 • interquartile range = 28 • range = 81 • highest mark = 96 (a) Draw a box-and-whisker plot to represent this information. 0 20 40 60 80 100 Test marks [3] (b) Students in class Q take the same test. For class Q, the median is 49 and the interquartile range is 35. Make two comments comparing the distribution of marks for class P with that of class Q. 1. … … 2. … … [2]

5 marks

Mark scheme: 15(a) Correct box-and-whisker plot 3 B1 for UQ = 66 or Lowest = 15 soi L = 15 M1 for at least 3 values correct within box and LQ = 38 whisker plot Median = 53 UQ = 66 H = 96 15(b) Class Q scored fewer marks on 2 B1 for each average [as median is lower] oe Class Q have a larger spread of marks [as IQR is higher] oe

This question in 0580/21 Oct/Nov 2024

13 (a) 100 students solve a puzzle. The table shows information about the time taken by each student to solve the puzzle. Time (t seconds) 20 1 t G 40 40 1 t G 60 60 1 t G 100 Frequency 30 40 30 (i) Work out an estimate of the mean. … s [4] (ii) Complete the histogram to show the information in the table. 4 3 Frequency 2 density 1 0 t 20 30 40 50 60 70 80 90 100 Time (seconds) [2] (b) 80 adults solve the same puzzle as the students. The cumulative frequency table shows information about the time taken by each adult to solve the puzzle. Time (t seconds) t G 20 t G 40 t G 60 t G 80 t G 100 t G 120 Cumulative frequency 0 12 36 60 74 80 (i) On the grid, draw a cumulative frequency diagram. 80 70 60 50 Cumulative 40 frequency 30 20 10 0 t 20 30 40 50 60 70 80 90 100 110 120 Time (seconds) [3] (ii) Use your cumulative frequency diagram to find an estimate for (a) the median … s [1] (b) the lower quartile. … s [1]

11 marks

Mark scheme: 13(a)(i) 53 4 M1 for correct midpoints soi M1 for fx where x is in correct interval including boundaries M1 for fx ÷ 100 dep on second M1 13(a)(ii) Two correct bars with correct widths 2 B1 for one correct bar and heights 2 and 0.75 or M1 for 40/20 oe and 30/40 oe soi 13(b)(i) Correct diagram 3 B1 for correct horizontal placement for 6 plots B1 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, SC1 for 5 out of 6 points correctly plotted 13(b)(ii)(a) 62 to 64 1 FT their increasing curve or polygon reading at 40 13(b)(ii)(b) 46 to 48 1 FT their increasing curve or polygon reading at 20

This question in 0580/22 May/June 2025

6 There are 15 giraffes in a group. The table gives information about the heights of the 15 giraffes. One giraffe has a height of 2.6 m No giraffe is shorter than 2.5 m The range of heights for the 15 giraffes is 2.3 m More than 3 giraffes have the same height The modal height for the giraffes is 3.9 m The stem-and-leaf diagram shows information about the height of 9 of these giraffes. 2 5 3 2 7 7 4 1 1 4 5 7 Key: 4|1 represents a giraffe height of 4.1 m Use the information in the table to complete the stem-and-leaf diagram for the group of 15 giraffes. [3]

3 marks

Mark scheme: 6 3 B1 for each correct row 2 5 6 3 2 7 7 9 9 9 9 4 1 1 4 5 7 8

This question in 0580/23 May/June 2025

5 The pie chart shows some information about the way 600 students travel to school. Walk 60° Bicycle (a) Work out the number of students that walk to school. … [2] (b) 120 of the students travel to school by car. The remaining students travel by bus. Complete the pie chart. [3]

5 marks

Mark scheme: 5(a) 150 2 90 M1 for  600  oe 360 5(b) Correctly completed pie chart including 3 B2 for 72 or 138 labels of car [72] and bus [138] 120 or M1 for  360 oe 600 or B1FT for drawing one correct sector for their angle(s)

This question in 0580/22 Oct/Nov 2025