Averages and measures of spread — Paper 2 · IGCSE Mathematics 0580

20 The number of hours that a group of 80 students spent using a computer in a week was recorded. For The results are shown by the cumulative frequency curve. Examiner's Use 80 60 Cumulative 40 frequency 20 0 10 20 30 40 50 60 70 Number of hours Use the cumulative frequency curve to find (a) the median, Answer(a) h [1] (b) the upper quartile, Answer(b) h [1] (c) the interquartile range, Answer(c) h [1] (d) the number of students who spent more than 50 hours using a computer in a week. Answer(d) [2]

5 marks

Mark scheme: 20 (a) 38 1 (b) 45 to 46 1 (c) 15 to 16 1 (d) 10 or 11 2 SC1 70 on answer line

This question in 0580/21 Oct/Nov 2009

20 The number of hours that a group of 80 students spent using a computer in a week was recorded. For The results are shown by the cumulative frequency curve. Examiner's Use 80 60 Cumulative 40 frequency 20 0 10 20 30 40 50 60 70 Number of hours Use the cumulative frequency curve to find (a) the median, Answer(a) h [1] (b) the upper quartile, Answer(b) h [1] (c) the interquartile range, Answer(c) h [1] (d) the number of students who spent more than 50 hours using a computer in a week. Answer(d) [2]

5 marks

Mark scheme: 20 (a) 38 1 (b) 45 to 46 1 (c) 15 to 16 1 (d) 10 or 11 2 SC1 70 on answer line

This question in 0580/22 Oct/Nov 2009

1 During one week in April, in Quebec, the daily minimum temperatures were Examiner's Use –5°C, –1°C, 3°C, 2°C, –2°C, 0°C, 6°C. Write down (a) the lowest of these temperatures, Answer(a) °C [1] (b) the range of these temperatures. Answer(b) °C [1]

2 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) –5 1 (b) 11 1 53

This question in 0580/23 May/June 2010

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

9 In Vienna, the mid-day temperatures, in °C, are recorded during a week in December. This information is shown below. –2 2 1 –3 –1 –2 0 Calculate (a) the difference between the highest temperature and the lowest temperature, Answer(a) °C [1] (b) the mean temperature. Answer(b) °C [2]

3 marks

Mark scheme: 9 (a) 5 or −5 1 5 (b) −0.714 (−0.7143 to −0.7142) or −7 2 M1 for −2 + 2 + 1 − 3 − 1 − 2 and ÷ 7

This question in 0580/23 Oct/Nov 2011

6 Leon scores the following marks in 5 tests. 8 4 8 y 9 His mean mark is 7.2. Calculate the value of y. Answer y = [2]

2 marks

Mark scheme: 8 + 4 + 8 + 9 + y 6 7 2 M1 = 7 .2 oe 5

This question in 0580/21 May/June 2012

18 Lauris records the mass and grade of 300 eggs. The table shows the results. For Examiner's Use Mass 30 I x Y 40 40 I x Y 50 50 I x Y 60 60 I x Y 70 70 I x Y 80 80 I x Y 90 (x grams) Frequency 15 48 72 81 54 30 Grade small medium large very large (a) Find the probability that an egg chosen at random is graded very large. Answer(a) [1] (b) The cumulative frequency diagram shows the results from the table. 300 250 200 Cumulative 150 frequency 100 50 0 30 40 50 60 70 80 90 Mass (x grams) Use the cumulative frequency diagram to find (i) the median, Answer(b)(i) g [1] (ii) the lower quartile, Answer(b)(ii) g [1] (iii) the inter-quartile range, Answer(b)(iii) g [1] (iv) the number of eggs with a mass greater than 65 grams. Answer(b)(iv) [2]

6 marks

Mark scheme: 7 84 18 (a) or oe 1 25 300 (b) (i) 62 1 (ii) 52 1 (iii) 19 to 20 1 (iv) 125 2 B1 for 175 seen

This question in 0580/21 Oct/Nov 2012

20 The heights, in metres, of 200 trees in a park are measured. For Examiner′s Use Height (h m) 2 < h Ğ 6 6 < h Ğ 10 10 < h Ğ 13 13 < h Ğ 17 17 < h Ğ 19 19 < h Ğ 20 Frequency 23 47 45 38 32 15 (a) Find the interval which contains the median height. Answer(a) … [1] (b) Calculate an estimate of the mean height. Answer(b) … m [4] (c) Complete the cumulative frequency table for the information given in the table above. Height (h m) 2 < h Ğ 6 h Ğ 10 h Ğ 13 h Ğ 17 h Ğ 19 h Ğ 20 Cumulative 23 frequency [2] _____________________________________________________________________________________ Question 21 is printed on the next page.

7 marks

Mark scheme: 20 (a) 10 < h ≤ 13 1 (b) 12.1[2] www 4 M1 for at least 5 correct mid-values seen M1 for ∑ fx where x is in the correct interval (c) 70, 115, 153, 185, 200 2 M1 for their ∑ fx ÷ 200 B1 for 3 or 4 correct

This question in 0580/22 May/June 2013

4 Cheryl recorded the midday temperatures in Seoul for one week in January. Day Mon Tue Wed Thu Fri Sat Sun Temperature (°C) –4 –5 –3 –11 –8 –3 –1 (a) Write down the mode. Answer(a) … °C [1] (b) On how many days was the temperature lower than the mode? Answer(b) … [1] __________________________________________________________________________________________

2 marks

Mark scheme: 4 (a) –3 1 (b) 4 1FT FT their numerical mode 3 2

This question in 0580/21 Oct/Nov 2014

18 72 students are given homework one evening. They are told to spend no more than 100 minutes completing their homework. The cumulative frequency diagram shows the number of minutes they spend. 80 60 Cumulative 40 frequency 20 0 30 40 50 60 70 80 90 100 Minutes (a) How many students spent more than 48 minutes completing their homework? Answer(a) … [2] (b) Find (i) the median, Answer(b)(i) … [1] (ii) the inter-quartile range. Answer(b)(ii) … [2] __________________________________________________________________________________________

5 marks

Mark scheme: 18 (a) 56 2 B1 for 16 soi or M1 for 72 – their 16 (b) (i) 63 or 63 to 63.5 1 (ii) 22 or 21.6 to 23 nfww 2 B1 for 49.8 to 50.2 seen or 71.8 to 72.8

This question in 0580/22 Oct/Nov 2014

5 Jim scores the following marks in 8 tests. 7 8 8 y 6 9 10 5 His mean mark is 7.5 . Calculate the value of y. Answer y = … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 5 7 nfww 2 M1 for 5.7 × 8 or for ( 7 + 8 + 8 + y + 6 + 9 + 10 + 5) ÷ 8 = 5.7 or better oe 4 × 30

This question in 0580/21 Oct/Nov 2015

22 The table shows information about the numbers of pets owned by 24 students. Number of pets 0 1 2 3 4 5 6 Frequency 1 2 3 5 7 3 3 (a) Calculate the mean number of pets. Answer(a) … [3] (b) Jennifer joins the group of 24 students. When the information for Jennifer is added to the table, the new mean is 3.44 . Calculate the number of pets that Jennifer has. Answer(b) … [3]

6 marks

Mark scheme: 22 (a) 3.5 nfww 3 M1 for Σfx soi M1 (dep) for ÷ 24 their 84 + x (b) 2 nfww 3 M2FT for = .344 or better 25 or M1 for 25 × 3.44 8 5

This question in 0580/22 Oct/Nov 2015

16 Raj measures the height, h cm, of 70 plants. The table shows the information. Height (h cm) 10  h  20 20  h  40 40  h  50 50  h  60 60  h  90 Frequency 7 15 27 13 8 Calculate an estimate of the mean height of the plants. … cm [4]

4 marks

Mark scheme: 16 44.1 or 44.07... 4 M1 for 4 of mid-values 15 30 45 55 75 soi M1 for ∑fx for any x in intervals including boundaries M1 dep for ∑fx ÷ 70 Dep on 2nd M mark earned

This question in 0580/22 Feb/March 2016

20 The diagram shows a fair spinner. 1 6 3 4 3 Anna spins it twice and adds the scores. (a) Complete the table for the total scores. Score on first spin 1 3 3 4 6 1 2 4 4 5 7 3 4 6 6 7 9 Score on 3 4 6 6 7 9 second spin 4 6 [1] (b) Write down the most likely total score. … [1] (c) Find the probability that Anna scores (i) a total less than 6, … [2] (ii) a total of 3. … [1]

5 marks

Mark scheme: 20(a) 5 7 7 8 10 1 7 9 9 10 12 20(b) 7 1 20(c)(i) 7 2FT their 7 or 0.28 or 28% FT 25 25 k B1 for 25 2 6 If zero scored, then SC1 for or if no 5 15 values in the bottom two rows of the table. 20(c)(ii) 0 1FT their 0 FT 25

This question in 0580/21 May/June 2017

4 Amber’s mean mark on five tests is 80. Her marks on four of these tests are 68, 81, 74 and 89. Work out her mark on the fifth test. … [2]

2 marks

Mark scheme: 4 88 2 68 + 81 + 74 + 89 + x M1 for = 80 oe 5 or B1 for 400

This question in 0580/21 Oct/Nov 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

18 The cumulative frequency diagram shows information about the time, m minutes, taken by 120 students to complete some homework. 120 100 80 Cumulative 60 frequency 40 20 0 m 0 10 20 30 40 50 60 Time (minutes) Use the cumulative frequency diagram to find an estimate of (a) the interquartile range, … min [2] (b) the number of students who took more than 50 minutes to complete the homework. … [2]

4 marks

Mark scheme: 18(a) 10 nfww 2 B1 for UQ = 30 or LQ = 20 clearly identified 18(b) 4 2 B1 for 116 indicated

This question in 0580/21 May/June 2018

23 40 people were asked how many times they visited the cinema in one month. The table shows the results. Number of cinema visits 0 1 2 3 4 5 6 7 Frequency 5 5 6 6 7 3 6 2 (a) (i) Find the mode. … [1] (ii) Calculate the mean. … [3] (b) Omar wants to show the information from the table in a pie chart. Calculate the sector angle for the people who visited the cinema 5 times. … [2] Question 24 is printed on the next page.

6 marks

Mark scheme: 23(a)(i) 4 1 23(a)(ii) 3.2 3 M1 for Σ fx , allow one error or omission their 128 and M1dep for 40 23(b) 27 2 3 360 M1 for or 40 40

This question in 0580/21 May/June 2018

24 The time, t minutes, 80 students each spend completing their homework is recorded. The cumulative frequency diagram shows the results. 80 70 60 50 Cumulative 40 frequency 30 20 10 0 t 0 10 20 30 40 50 60 Time (minutes) Use the cumulative frequency diagram to find an estimate of (a) the median, … min [1] (b) the interquartile range, … min [2] (c) the number of students who spend more than 40 minutes completing their homework. … [2] Question 25 is printed on the next page.

5 marks

Mark scheme: 24(a) 25 1 24(b) 12 2 B1 for 16 or 28 24(c) 5 2 B1 for 75

This question in 0580/22 Oct/Nov 2018

4 The table shows the different methods of travel for 20 people going to work. Method of travel Frequency Car 10 Walk 5 Bike 3 Bus 2 Which type of average, mean, median or mode, can be used for this information? … [1]

1 marks

Mark scheme: 4 Mode 1

This question in 0580/23 May/June 2019

23 160 students record the amount of time, t hours, they each spend playing computer games in a week. This information is shown in the cumulative frequency diagram. 160 140 120 100 Cumulative 80 frequency 60 40 20 0 0 2 4 6 8 10 12 t Time (hours) (a) Use the diagram to find an estimate of (i) the median, … hours [1] (ii) the interquartile range. … hours [2] (b) Use the diagram to complete this frequency table. Time (t hours) 0 1 t G 2 2 1 t G 4 4 1 t G 6 6 1 t G 8 8 1 t G 10 10 1 t G 12 Frequency 20 24 12 4 [2]

5 marks

Mark scheme: 23(a)(i) 5 1 23(a)(ii) 2.4 to 2.6 2 B1 for [LQ=] 3.4 to 3.6 or [UQ=] 6 23(b) 26, 74 2 B1 for each

This question in 0580/23 May/June 2019

5 The mass, correct to the nearest kilogram, of each of 11 parcels is shown below. 24 23 23 26 25 27 18 96 16 17 32 (a) Find the mode. … kg [1] (b) Give a reason why the mean would be an unsuitable average to use. … [1]

2 marks

Mark scheme: 5(a) 23 1 5(b) One extreme value oe 1

This question in 0580/22 Oct/Nov 2019

10 5n is the mean of the three numbers 391, n and n - 1. Find the value of n. n = … [3]

3 marks

Mark scheme: 10 30 3 391 + n + n 1 M1 for −= 5 n oe 3 M1 for correct first step for solving their equation 390 + 2 n e.g. 391 + n + n −=1 3 × 5n , = 5 n 3

This question in 0580/23 Oct/Nov 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

6 The table shows the marks scored by 40 students in a test. Mark 5 6 7 8 9 10 Frequency 8 5 11 7 5 4 Calculate the mean mark. … [3]

3 marks

Mark scheme: 6 7.2 3 M1 for 5 × 8 + 6 × 5 + 7 × 11 + 8 × 7 + 9 × 5 + 10 × 4 M1dep for ÷ 40

This question in 0580/22 Feb/March 2020

14 The box-and-whisker plot gives information about the heights, in centimetres, of some plants. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Height (cm) (a) Write down the median. … cm [1] (b) Find (i) the range, … cm [1] (ii) the interquartile range. … cm [1]

3 marks

Mark scheme: 14(a) 11.5 1 14(b)(i) 12 1 14(b)(ii) 8.5 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

15 The table shows the amount of money, $x, given to a charity by each of 60 people. Amount ($x) 0 1 x G 20 20 1 x G 25 25 1 x G 35 35 1 x G 50 50 1 x G 100 Frequency 21 16 6 10 7 Calculate an estimate of the mean. $ … [4]

4 marks

Mark scheme: 15 28.33 or 28.3 or 28.33… 4 M1 for midpoints soi M1 for use of ∑fx M1 dep for ∑fx ÷ 60

This question in 0580/23 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

3 The number of passengers on a bus is recorded each day for 14 days. 15 18 22 17 35 38 24 19 19 24 25 31 36 29 (a) Complete the stem-and-leaf diagram. 1 2 3 Key: 1| 5 represents 15 passengers [2] (b) Find the median. … [1]

3 marks

Mark scheme: 3(a) 2 B1 for two rows correct or for a fully correct 1 5 7 8 9 9 unordered stem-and-leaf diagram or for a correct diagram with one leaf incorrect or 2 2 4 4 5 9 omitted 3 1 5 6 8 3(b) 24 1

This question in 0580/22 Feb/March 2021

17 Some students were asked how many books they each had in their school bags. The table shows some of this information. Number of books 5 6 7 8 9 10 Frequency 4 5 x 11 7 5 The mean number of books is 7.6 . Calculate the value of x. x = … [3]

3 marks

Mark scheme: 17 13 nfww 3 M2 for 251 + 7 x = 7.6 ( 32 + x ) or better or M1 for 5 × 4 + 6 × 5 + 7 x + 8 × 11 + 9 × 7 + 10 × 5 = 7.6 32 + x oe

This question in 0580/22 Feb/March 2021

3 The stem-and-leaf diagram shows the number of hours that each of 16 students studied last week. 1 2 5 6 8 2 0 1 1 7 9 3 2 3 4 5 4 4 5 7 Key: 1q2 represents 12 hours Find (a) the median, … h [1] (b) the mode, … h [1] (c) the range. … h [1]

3 marks

Mark scheme: 3(a) 28 1 3(b) 21 1 3(c) 35 1

This question in 0580/21 May/June 2021

3 Emma has 15 mathematics questions to complete. The stem‑and‑leaf diagram shows the time, in minutes, it takes her to complete each question. 0 3 5 6 7 7 8 8 1 1 2 2 3 6 6 6 2 0 Key: 2 | 0 = 20 minutes Complete the table. Mode … min Median … min Range … min [3]

3 marks

Mark scheme: 3 3 B1 for each Mode 16 Median 11 Range 17

This question in 0580/22 May/June 2021

4 The number of items that each of 22 people buy in a supermarket is shown in the stem-and-leaf diagram. 1 1 3 6 6 2 0 2 2 2 4 8 9 3 1 1 5 8 9 9 4 2 4 6 7 8 Key: 1 | 1 represents 11 items (a) Find the mode. … [1] (b) Find the median. … [1]

2 marks

Mark scheme: 4(a) 22 1 4(b) 30 1

This question in 0580/21 Oct/Nov 2021

2 The stem-and-leaf diagram shows the age, in years, of each of 15 women. 3 1 5 8 9 4 1 1 2 3 5 6 9 5 0 2 3 8 Key: 3 | 1 represents 31 years Complete these statements. The modal age is … The median age is … The percentage of women that are older than 51 years is … %. [3]

3 marks

Mark scheme: 2 41 3 B1 for each 43 20

This question in 0580/22 Oct/Nov 2021

4 These are the masses, in kg, of 12 parcels. 0.3 0.4 1.2 0.8 1.1 2.1 1.7 1.8 1.2 2.3 0.7 1.1 (a) Complete the stem-and-leaf diagram for the 12 parcels. 0 3 4 1 2 Key: 0 q3 represents 0.3 kg [2] (b) Find the median. … kg [1]

3 marks

Mark scheme: 4(a) 2 B1 for two rows correct or for fully correct 0 (3 4) 7 8 unordered stem-and-leaf diagram or for a correct diagram with one error or omission 1 1 1 2 2 7 8 2 1 3 4(b) 1.15 1

This question in 0580/23 May/June 2022

8 Daryl records the number of hours in a week 8 people spend exercising. 5 2 1.5 3 18 4.5 2 4 (a) Find the median. … h [2] (b) Explain why the mean may not be a suitable average to use. … [1]

3 marks

Mark scheme: 8(a) 3.5 2 M1 for values in correct order 1.5 2 2 3 4 4.5 5 18 or 3 and 4 identified as middle numbers 8(b) One extreme value oe 1

This question in 0580/22 Oct/Nov 2022

4 The mean mass of four men in a rowing team is 97.5 kg. The modal mass is 101 kg. The range of the masses is 8 kg. Find the mass of each of the four men. … kg , … kg , … kg, … kg [3]

3 marks

Mark scheme: 4 93 95 101 101 3 M1 for 4  97.5 implied by 390 or for four numbers which add to 390 B1 for four numbers with a range of 8 B1 for four numbers with mode of 101 to a maximum of 2 marks

This question in 0580/23 Oct/Nov 2022

3 On ten days, Stefan records the number of minutes he has to wait for a train. 1 3 12 5 4 23 5 24 11 8 (a) Complete the stem-and-leaf diagram to show this information. 0 1 3 1 2 Key: 0 q1 represents 1 minute [2] (b) Find the median. … min [1]

3 marks

Mark scheme: 3(a) 2 B1 for a correct diagram with one error or omission or for a fully correct unordered stem-and-leaf 0 (1 3) 4 5 5 8 diagram 1 1 2 2 3 4 3(b) 6.5 1

This question in 0580/22 May/June 2023

2 The stem‑and‑leaf diagram shows the time, in minutes, it takes each of 15 people to complete a race. 1 6 6 7 2 1 3 3 4 5 6 7 7 7 3 0 1 1 Key: 1 6 represents 16 minutes Find (a) the mode … min [1] (b) the range … min [1] (c) the median. … min [1]

3 marks

Mark scheme: 2(a) 27 1 2(b) 15 1 2(c) 25 1

This question in 0580/21 Oct/Nov 2023

3 The stem-and-leaf diagram shows the heights, in centimetres, of some plants. 10 4 8 11 1 3 4 6 12 2 3 6 9 13 2 6 9 Key: 10 4 represents 10.4 cm (a) Find the median height. … cm [1] (b) Work out the mean height. … cm [2]

3 marks

Mark scheme: 3(a) 12.2 1 3(b) 12.1 2 B1 for 157.3 oe or M1 for their total ÷ 13

This question in 0580/23 Oct/Nov 2023

14 The box-and-whisker plot shows information about the mass, in kg, of some parcels. 1 1.5 2 2.5 3 3.5 Mass (kg) (a) Find the mass of the heaviest parcel. … kg [1] (b) Find the interquartile range. … kg [1]

2 marks

Mark scheme: 14(a) 3.3 1 14(b) 0.55 1

This question in 0580/23 Oct/Nov 2023

17 The height of each of 200 people is measured. The table shows the results. Height (h cm) 100 1 h G 120 120 1 h G 1 30 130 1 h G 150 150 1 h G 190 Frequency 32 55 64 49 Calculate an estimate of the mean height. … cm [4]

4 marks

Mark scheme: 17 138.425 4 M1 for mid-points soi (110, 125, 140, 170) M1 for use of fh with h in correct interval including both boundaries M1 for (dep on 2nd M1) for fh ¸ 200

This question in 0580/22 Feb/March 2024

3 A delivery driver records the number of pizzas she delivers each month for one year. 48 44 39 28 57 22 36 41 54 57 49 52 (a) Complete the stem-and-leaf diagram. 2 3 4 5 Key: 4 q8 represents 48 pizzas [2] (b) Find the median. … [1]

3 marks

Mark scheme: 3(a) Correct table 2 B1 for two rows correct or for fully correct unordered stem-and-leaf diagram 2 2 8 3 6 9 4 1 4 8 9 5 2 4 7 7 3(b) 46 1

This question in 0580/22 May/June 2024

15 200 180 160 140 120 Cumulative 100 frequency 80 60 40 20 0 0 10 20 30 40 50 Time (seconds) The time taken for each of 200 students to complete a calculation is measured. The cumulative frequency diagram shows the results. Use the diagram to find an estimate for (a) the interquartile range … s [2] (b) the number of students taking more than 40 seconds to complete the calculation. … [2]

4 marks

Mark scheme: 15(a) 11 2 B1 for 16 or 27 seen 15(b) 6 2 M1 for 194 seen

This question in 0580/23 May/June 2024

16 The stem-and-leaf diagram shows the mass of each of 13 packets. 3 1 2 8 4 0 1 2 3 3 8 5 1 2 3 4 Key: 3 q1 represents 31 g (a) Work out the interquartile range. … g [3] (b) Two of these packets are chosen at random. Find the probability that the one packet has a mass of more than 50 g and the other packet has a mass of less than 50 g. … [3]

6 marks

Mark scheme: 16(a) 12.5 3 M2 for 51.5 – 39 oe OR B1 for [UQ =] 51.5 B1 for [LQ =] 39 OR M1 for k – c where 50.25 ⩽ k ⩽ 52 and 38 ⩽ c ⩽ 40 16(b) 6 3  4 9  oe M2 for  2      oe 13  13 12  or B1 for 4 9 9 4 and or and 13 12 13 12 k c or M1 for  13 12 where 0 < k < 13 and 0 < c < 12  4 9  If 0 scored, SC1 for 2     13 13 

This question in 0580/22 Feb/March 2025

9 The table shows some information about the marks scored by a group of students in a test. Test mark 4 5 8 Frequency 2 4 n The mean mark is 6. Work out the value of n. n = … [3]

3 marks

Mark scheme: 9 4 nfww 3 M2 for 8 + 20 + 8n = 6(2 + 4 + n) or better 2 +4 4 +5 n  8 or M1 for [= 6] oe 2 + 4 + n or 8 + 20 + 8n or 6(2 + 4 + n)

This question in 0580/21 May/June 2025

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

13 These are Rahul’s 10 test scores. 9 8 9 10 7 x 9 9 x 7 The mean of these scores is 8. Find the interquartile range. You must show all your working. … [4]

4 marks

Mark scheme: 13 68 + 2 x M1 = 8 or better 10 x = 6 A1 Lower quartile = 6.5 or 6.75 or 7 B1 or upper quartile = 9 2 or 2.25 or 2.5 nfww A1

This question in 0580/21 Oct/Nov 2025