Averages and range — Paper 1 · IGCSE Mathematics 0580

16 Yousef asked 24 students to choose their favourite sport. He recorded the information in the table below so that he could draw a pie chart. (a) Complete the table. Sport Volleyball Football Hockey Cricket Number of students 6 9 7 2 Angle on pie chart 90o 135o [2] (b) Complete the pie chart accurately to show this data. Volleyball Football [1] (c) Which is the modal sport? Answer(c) [1]

4 marks

Mark scheme: 16 (a) (hockey) 105, (cricket) 30 2 1 mark each correct entry. (b) Correct line on pie chart to divide 1ft ft only if the angles in (a) total hockey and cricket. (30 ± 2) degrees 135° to left of vertical oe. (c) Football 1 19 IGCSE – May/June 2006 0580 and 0581 01

This question in 0580/11 May/June 2006

21 For 0 0 0 1 2 2 4 4 5 9 Examiner's Use The list shows the number of days absent in a school term for each of 10 students. Find the mode, the median and the mean for the number of days absent. Answer Mode = Median = Mean = [4]

4 marks

Mark scheme: 21 (Mode =) 0 1 (Median =) 2 1 (Mean =) 2.7 2 M1 (0 + 0 + 0) + 1 + 2 + 2 + 4 + 4 + 5 + 9 IGCSE – October/November 2010 0580 13

This question in 0580/13 Oct/Nov 2010

19 At a ski resort the temperature, in °C, was measured every 4 hours during one day. The results were –12°, –13°, –10°, 4°, 4°, –6°. (a) Find the difference between the highest and the lowest of these temperatures. Answer(a) °C [1] (b) Find (i) the mean, Answer(b)(i) °C [2] (ii) the median, Answer(b)(ii) °C [2] (iii) the mode. Answer(b)(iii) °C [1] Question 20 is printed on the next page.

6 marks

Mark scheme: 19 (a) 17 1 Allow −17 (b) (i) −5.5 2 M1 for (−12 + −13 + −10 + 4 + 4 + −6) soi ÷ 6 (ii) −8 2 M1 for method of finding mid-value (iii) 4 1

This question in 0580/13 May/June 2011

5 10 8 6 Frequency 4 2 0 Black Silver Red Green Blue Favourite colour The bar chart shows the favourite colours of students in a class. (a) How many students are in the class? Answer(a) [1] (b) Write down the modal colour. Answer(b) [1]

2 marks

Mark scheme: 5 (a) 25 1 (b) Green cao 1 258 75

This question in 0580/11 Oct/Nov 2011

9 For Examiner's 30 Use 25 20 Temperature 15 (°C) 10 5 0 6 am 9 am Noon 3 pm 6 pm Time The graph shows the temperature in Paris from 6 am to 6 pm one day. (a) What was the temperature at 9 am? Answer(a) °C [1] (b) Between which two times was the temperature decreasing? Answer(b) and [1] (c) Work out the difference between the maximum and minimum temperatures shown. Answer(c) °C [1]

3 marks

Mark scheme: 9 (a) 15 1 (b) 2 (pm), 6 (pm) 1 (c) 15 1 Allow −15

This question in 0580/11 Oct/Nov 2011

15 For Examiner's 50 Use 40 30mark test 20English 10 0 10 20 30 40 50 60 70 80 Mathematics test mark The scatter diagram shows the marks obtained in a Mathematics test and the marks obtained in an English test by 15 students. (a) Describe the correlation. Answer(a) [1] (b) The mean for the Mathematics test is 47.3 . The mean for the English test is 30.3 . Plot the mean point (47.3, 30.3) on the scatter diagram above. [1] (c) (i) Draw the line of best fit on the diagram above. [1] (ii) One student missed the English test. She received 45 marks in the Mathematics test. Use your line to estimate the mark she might have gained in the English test. Answer(c)(ii) [1]

4 marks

Mark scheme: 15 (a) Negative 1 Ignore embellishments (b) Correct point 1 (c) (i) Accurate ruled line 1 (ii) English mark 1ft Follow through their (c)(i)

This question in 0580/11 Oct/Nov 2011

19 In Vienna, the mid-day temperatures, in °C, are recorded during a week in December. For This information is shown below. Examiner's Use –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: 19 (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 2

This question in 0580/13 Oct/Nov 2011

21 For 13 17 13 17 19 13 31 21 29 Examiner'sUse (a) For the numbers above, find (i) the range, Answer(a)(i) [1] (ii) the median. Answer(a)(ii) [2] (b) Write down the only number in the list which is not a prime number. Answer(b) [1]

4 marks

Mark scheme: (b) 21 1

This question in 0580/11 May/June 2012

14 7 3 8 2 5 1 5 3 4 6 2 3 For the numbers above work out the (a) mode, Answer(a) [1] (b) median, Answer(b) [2] (c) range. Answer(c) [1]

4 marks

Mark scheme: 14 (a) 3 1 (b) 3.5 2 M1 for at least 7 numbers in order and an attempt to find the middle number (c) 7 1

This question in 0580/13 May/June 2012

12 In a traffic survey of 125 cars the number of people in each car was recorded. Number of people in each car 1 2 3 4 5 Frequency 50 40 10 20 5 Find (a) the range, Answer(a) [1] (b) the median, Answer(b) [1] (c) the mode. Answer(c) [1]

3 marks

Mark scheme: 12 (a) 4 1 (b) 2 1 (c) 1 cao 1

This question in 0580/12 Oct/Nov 2012

20 Marco throws a six-sided dice 27 times. For Examiner's The bar chart shows his results. Use 8 7 6 5 Frequency 4 3 2 1 0 1 2 3 4 5 6 Score on dice (a) Write down the mode. Answer(a) … [1] (b) Work out the probability that Marco throws a number less than 5. Answer(b) … [2] (c) Calculate the mean. Answer(c) … [3]

6 marks

Mark scheme: 20 (a) 4 cao 1 (b) 21 2 M1 for 3 + 6 + 5 + 7 + 4 or 21 seen 27 oe isw (c) 3.33(3…) 3 M1 for 3 × 1 + 6 × 2 + 5 × 3 + 7 × 4 + 4 × 5 + 2 × 6, allow one incorrect product or 90 seen and M1 dep for ‘their 90’ ÷ 27

This question in 0580/11 May/June 2013

16 8 15 7 8 7 15 4 13 4 3 10 2 9 4 5 (a) Write down the mode. Answer(a) … [1] (b) Work out the median. Answer(b) … [2] _____________________________________________________________________________________

3 marks

Mark scheme: 16 (a) 4 1 (b) 7 nfww 2 M1 for a correctly ordered list of at least 8 numbers 3 M1 f 800 6

This question in 0580/11 Oct/Nov 2013

19 The table shows the average monthly temperature (°C) for Fairbanks, Alaska. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Temperature (°C) –23.4 –19.8 –11.7 –0.8 9.2 15.4 16.9 13.8 7.5 –5.8 –21.4 –21.8 (a) Find (i) the difference between the highest and the lowest temperatures, Answer(a)(i) … °C [1] (ii) the median. Answer(a)(ii) … °C [2] (b) A month is chosen at random from the table. Find the probability that its average temperature is below zero. Answer(b) … [1] __________________________________________________________________________________________

4 marks

Mark scheme: 19 (a) (i) 40.3 1 (ii) −3.3 2 M1 for attempt at ordering seen 7 (b) oe isw 1 12 IGCSE – May/June 2014 0580 11

This question in 0580/11 May/June 2014

7 Find three numbers which have a mode of 4 and a mean of 6. Answer … , … , … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 7 4 4 10 2 B1 for answer of 4 4 k or 4 p q where p + q = 14

This question in 0580/12 May/June 2014

13 The mean of fi ve numbers is 6. Four of the numbers are 3, 4, 5, and 10. Work out the number that is missing from the list. Answer … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 13 8 2 B1 for 6 × 5 or better

This question in 0580/13 May/June 2014

5 These are the heights, correct to the nearest centimetre, of 12 children. 132 114 151 130 132 145 163 142 153 170 132 125 Find the median height. Answer … cm [2] __________________________________________________________________________________________

2 marks

Mark scheme: 5 137 2 M1 for attempt at ordering to at least 7th term or 132 and 142 indicated 22

This question in 0580/11 Oct/Nov 2014

10 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: 10 (a) –3 1 (b) 4 1FT FT their numerical mode

This question in 0580/11 Oct/Nov 2014

4 (a) Write down two whole numbers that have a product of –15. Answer(a) … and … [1] (b) During one year, the temperature in Ulaanbaatar varied from –33 °C to 27 °C. Find the range of the temperatures during that year. Answer(b) … °C [1] __________________________________________________________________________________________

2 marks

Mark scheme: 4 (a) 5 and −3 or −5 and 3 or 1 1 and −15 or −1 and 15 (b) 60 1 1

This question in 0580/12 Oct/Nov 2014

9 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: 9 7 nfww 2 M1 for 7.5 × 8 or for (7 + 8 + 8 + y + 6 + 9 + 10 + 5 ) ÷ 8 = 7.5 or better oe 4 × 30

This question in 0580/11 Oct/Nov 2015

18 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 Calculate the mean number of pets. Answer … [3]

3 marks

Mark scheme: 18 3.5 nfww 3 M1 for Σfx soi M1 (dep) for ÷ 24 2 2

This question in 0580/12 Oct/Nov 2015

21 Write down a set of five numbers that has • a mode of 3 and • a median of 6 and • a range of 5. Answer … , … , … , … , … [3]

3 marks

Mark scheme: 21 3, 3, 6, 7, 8 3 B2 for two of: 5 numbers with mode 3 5 numbers with median 6 5 numbers with range 5 or B1 for one of them

This question in 0580/12 Oct/Nov 2015

23 2 5 6 2 8 2 6 3 9 For the numbers in the list, write down (a) the range, … [1] (b) the mode, … [1] (c) the median. … [2]

4 marks

Mark scheme: 23 (a) 7 1 (b) 2 1 (c) 5 2 M1 for correctly ordering at least first 5 or last 5 numbers from list 41 123 [ ]

This question in 0580/12 Feb/March 2016

21 The table shows the temperature each night for a week. Monday Tuesday Wednesday Thursday Friday Saturday Sunday –3 °C 1 °C – 4 °C –2 °C 5 °C 3 °C –1 °C (a) Which night was the coldest? … [1] (b) Find the difference between the temperature on Monday night and the temperature on Tuesday night. … °C [1] (c) Find the range. … °C [1] (d) Find the median. … °C [1]

4 marks

Mark scheme: 21 (a) Wed[nesday] 1 (b) 4 1 (c) 9 1 (d) –1 nfww 1 1

This question in 0580/12 May/June 2016

13 Eleven children attempt to solve a puzzle. This list shows the number of attempts each child made. 7 6 8 5 6 5 7 8 3 8 1 (a) Write down the mode. … [1] (b) Find the median. … [2]

3 marks

Mark scheme: 13 (a) 8 1 (b) 6 2 M1 for ordered list of at least the first 6 or last 6 values provided any following work is an attempt at the median

This question in 0580/11 Oct/Nov 2016

13 Here are the heights, in centimetres, of 8 people. 153 175 168 158 161 172 164 172 (a) Write down the mode. … cm [1] (b) Find the median. … cm [2]

3 marks

Mark scheme: 13 (a) 172 1 (b) 166 2 M1 for an ordered list of at least 5 numbers or B1 for 164 and 168 identified

This question in 0580/13 Oct/Nov 2016

5 34 38 10 87 45 28 19 23 Calculate the mean of these 8 numbers. … [2]

2 marks

Mark scheme: 5 35.5 2 M1 for (34 + 38 + 10 + 87 + 45 + 28 + 19 + 23) ÷ 8

This question in 0580/12 Feb/March 2017

11 7 2 3 5 1 2 6 9 7 2 6 4 2 3 6 For these numbers (a) find the range, … [1] (b) write down the mode. … [1]

2 marks

Mark scheme: 11 (a) 8 1 (b) 2 1

This question in 0580/12 Feb/March 2017

14 These are the weights, in kilograms, of 10 babies. 3.7 2.7 3.5 3.8 3.1 3.0 3.8 2.8 4.1 3.7 (a) Find the range. … kg [1] (b) Calculate the mean. … kg [2]

3 marks

Mark scheme: 14(a) 1.4 1 14(b) 3.42 2 M1 for (sum of the 10 numbers) ÷ 10

This question in 0580/13 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 0580/11 Oct/Nov 2017

14 The mass, correct to the nearest gram, of each of 20 potatoes is shown below. 85 97 125 100 90 102 116 89 96 104 89 107 106 93 84 118 120 98 112 109 (a) Complete the frequency table. You may use the tally column to help you. Mass (g) Tally Frequency 80 to 89 90 to 99 100 to 109 110 to 119 120 to 129 [2] (b) Write down the modal group. … [1]

3 marks

Mark scheme: 14(a) Frequencies 4, 5, 6, 3, 2 cao 2 B1 for 3 or 4 correct in frequency column or for fully correct tally if no frequencies 14(b) 100 to 109 1 FT their frequency table

This question in 0580/13 Oct/Nov 2017

25 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]

6 marks

Mark scheme: 25(a)(i) 4 1 25(a)(ii) 3.2 3 M1 for Σfx , allow one error or omission their128 and M1dep for 40 25(b) 27 2 3 360 M1 for or 40 40

This question in 0580/11 May/June 2018

22 Monday Tuesday Wednesday Thursday Friday Saturday 67 75 53 68 94 87 The table shows the number of customers in a restaurant on each day it is open during one week. (a) Write down the day most customers came into the restaurant. … [1] (b) Calculate the mean number of customers per day. … [2] (c) Find the range of the number of customers. … [1]

4 marks

Mark scheme: 22(a) Friday 1 22(b) 74 2 M1 for (67 + 75 + 53 + 68 + 94 + 87) ÷ 6 22(c) 41 1

This question in 0580/12 May/June 2018

18 16 7 23 18 73 20 95 17 89 54 For this list of numbers, find (a) the median, … [2] (b) the range. … [1]

3 marks

Mark scheme: 18(a) 21.5 2 M1 for at least the first or last 6 values listed in order or 20 and 23 identified 18(b) 88 1

This question in 0580/13 Oct/Nov 2018

21 The table shows the number of pets owned by each of the 95 students in a school. Number of pets Frequency 0 5 1 14 2 39 3 14 4 23 Calculate the mean number of pets. … [3]

3 marks

Mark scheme: 21 2.38 or 2.378 to 2.379 3 M1 ∑(pets × frequency) M1 dep their 226 ÷ 95

This question in 0580/13 Oct/Nov 2018

24 Five numbers have a mean of 9.4 . Four of the numbers are 3, 5, 10 and 12. Work out the range of the five numbers. … [4]

4 marks

Mark scheme: 24 14 4 M1 for 5 × 9.4 M1 for their ( 5 × 9.4 ) − ( 3 + 5 + 10 + 12 ) M1dep for their greatest number − 3

This question in 0580/12 Feb/March 2019

7 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: 7 Mode 1

This question in 0580/13 May/June 2019

19 27 14 8 93 32 55 14 38 73 47 From this list of numbers find (a) the median, … [2] (b) the range. … [1]

3 marks

Mark scheme: 19(a) 35 2 M1 for first 6 or last 6 values listed in order or for 32 and 38 identified 19(b) 85 1

This question in 0580/11 Oct/Nov 2019

15 These are the number of texts sent one day by each of 10 students. 18 13 15 8 9 17 12 8 6 14 (a) Write down the mode. … [1] (b) Calculate the mean. … [2]

3 marks

Mark scheme: 15(a) 8 1 15(b) 12 nfww 2 M1 for (18 + 13 + 15 + 8 + 9 + 17 + 12 + 8 + 6 + 14) ÷ 10 or for 120 ÷ 10

This question in 0580/12 Oct/Nov 2019

15 Davina records the colour of each car passing her house one morning. red grey black red grey white white black black white grey red grey white grey black grey black white grey (a) Complete the frequency table. You may use the tally column to help you. Colour of car Tally Frequency Black Grey Red White [2] (b) Write down the mode. … [1]

3 marks

Mark scheme: 15(a) 5 2 B1 for 2 correct frequencies in frequency 7 column 3 or for all correct tallies if frequency column 5 blank or for 5, 7, 3, 5 seen in tally column with frequency column blank or incorrect 15(b) grey cao 1 FT their table

This question in 0580/13 Oct/Nov 2019

19 The mean of three numbers is 150. The numbers are 361, 2n and (n - 1) . Find the value of n. n = … [3]

3 marks

Mark scheme: 19 30 3 M2 for 3 × 150 = 361 + 2n + n − 1 oe or B1 for 361 + 2n + n − 1

This question in 0580/13 Oct/Nov 2019

11 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: 11(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 11(b) 27 1

This question in 0580/12 Feb/March 2020

2 The table shows the temperature, in °C, at midday on the first day of each month during one year in a city. Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 9 11 15 19 23.5 27.5 29 28 25 19.5 14.5 10 Calculate the mean of these temperatures. … °C [2]

2 marks

Mark scheme: 2 19.25 2 M1 for sum of 12 numbers ÷ 12

This question in 0580/11 May/June 2020

5 The mean of seven numbers is 16. Six of these numbers are 12, 20, 19, 10, 21 and 13. Find the seventh number. … [2]

2 marks

Mark scheme: 5 17 2 M1 for 7 × 16

This question in 0580/13 Oct/Nov 2020

6 These are the heights of four sisters. 1.61 m 1.65 m 1.53 m 1.58 m (a) Work out the range of these heights. Give your answer in centimetres. … cm [2] (b) The four sisters have a brother. The range of the five heights is 18 cm. Work out the two possible heights of the brother. … m or … m [2]

4 marks

Mark scheme: 6(a) 12 2 M1 for 1.65−1.53 soi by figs 12 or B1 for a clear subtraction seen of any 2 heights correctly converted to cm 6(b) 1.47 1.71 2 B1 for each or M1 for 1.65 − 0.18 or 1.53 + 0.18

This question in 0580/12 Feb/March 2021

11 The mean of nine numbers is 17. Seven of these numbers add to 132. The other two numbers have a difference of 5. Find the two numbers with a difference of 5. … , … [3]

3 marks

Mark scheme: 11 8 13 3 9 × 17 − 132 M2 for 2 or M1 for 9 × 17

This question in 0580/12 Feb/March 2021

4 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: 4(a) 28 1 4(b) 21 1 4(c) 35 1

This question in 0580/11 May/June 2021

4 253 306 185 270 386 Calculate the mean of these numbers. … [2]

2 marks

Mark scheme: 4 280 2 M1 for (253 + 306 + 185 + 270 + 386) ÷ 5

This question in 0580/12 May/June 2021

12 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 q0 = 20 minutes Complete the table. Mode … min Median … min Range … min [3]

3 marks

Mark scheme: 12 3 B1 for each Mode 16 Median 11 Range 17

This question in 0580/12 May/June 2021

6 18 28 7 15 41 19 31 53 Calculate the mean of these numbers. … [2]

2 marks

Mark scheme: 6 26.5 2 M1 for (18 + 28 + 7 + 15 + 41 + 19 + 31 + 53) ÷ 8

This question in 0580/13 May/June 2021

11 125 people taste a new drink. Each person gives a score out of 5. The bar chart shows the results. 40 30 Number of people 20 10 0 0 1 2 3 4 5 Score Calculate the mean score. … [3]

3 marks

Mark scheme: 11 3.08 3 M1 for [4 × 0 +] 15 × 1 + 23 × 2 + 36 × 3 + 19 × 4 + 28 × 5  fx M1 dep for 125

This question in 0580/11 Oct/Nov 2021

12 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: 12 41 3 B1 for each 43 20

This question in 0580/12 Oct/Nov 2021

6 62 43 16 21 73 16 33 16 35 For this list of numbers find (a) the mode, … [1] (b) the median. … [2]

3 marks

Mark scheme: 6(a) 16 1 6(b) 33 2 M1 for listing first 5, or last 5 numbers in order

This question in 0580/13 Oct/Nov 2021

15 Sara takes 5 tests. Her mean score is 62. She takes another test and her mean score is now 68. Work out her score in the sixth test. … [3]

3 marks

Mark scheme: 15 98 3 M2 for 68 × 6 – 62 × 5 or M1 for 68 × 6 or 62 × 5

This question in 0580/13 Oct/Nov 2021

8 Here is some information about six numbers: • The lowest number is 37. • The range is 24. • The mode is 43. • The median is 46. • One number is a multiple of 11. Find the other five numbers. 37, … , … , … , … , … [4]

4 marks

Mark scheme: 8 [37] 43 43 49 55 61 in any order 4 B1 for 43 43 B1 for 49 B1 for 55 B1 for 61

This question in 0580/11 May/June 2022

17 Kim has a 6-sided spinner numbered 1 to 6. She spins it 63 times and her scores are shown in the table. Score on spinner 1 2 3 4 5 6 Frequency 12 7 15 11 8 10 (a) Find the relative frequency of scoring a 5 with this spinner. … [1] (b) Work out the mean score. … [3]

4 marks

Mark scheme: 17(a) 8 1 or [0].127 or 12.7% 63 17(b) 3.41 or 3.412 to 3.413 3 M1 for 1×12 + 2×7 + 3×15 + 4×11 + 5×8 + 6×10 M1 dep for their 215 ÷ 63 18 7y(2x – y) final answer 2 2 B1 for 7 2 xy  y or y 14 x  7 y    or 7 y  2 x  y  seen then spoilt

This question in 0580/11 May/June 2022

4 The stem-and-leaf diagram shows the journey time to school of some students. 1 3 5 7 9 9 2 3 4 5 3 0 3 4 6 7 4 2 4 5 8 Key: 1 3 represents 13 minutes Find (a) the number of students with a journey time of more than 35 minutes, … [1] (b) the mode. … min [1]

2 marks

Mark scheme: 4(a) 6 1 4(b) 19 1

This question in 0580/12 May/June 2022

10 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: 10(a) 2 B1 for two rows correct or for fully 0 (3 4) 7 8 correct unordered stem-and-leaf diagram 1 1 1 2 2 7 8 or for a correct diagram with one error or omission 2 1 3 10(b) 1.15 1

This question in 0580/13 May/June 2022

10 The birth weights, in kg, of 11 babies are recorded. 2.1 1.6 2.7 4.2 4.0 2.2 3.1 1.7 2.6 3.3 3.7 (a) Complete the stem-and-leaf diagram to show this information. 1 2 3 4 Key: 2 1 represents 2.1 kg [2] (b) Find the median. … kg [1]

3 marks

Mark scheme: 10(a) 6 7 2 B1 for 2 rows correctly ordered 1 2 6 7 or fully correct unordered 1 3 7 0 2 10(b) 2.7 cao 1

This question in 0580/11 Oct/Nov 2022

13 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: 13(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 13(b) One extreme value oe 1

This question in 0580/12 Oct/Nov 2022

5 The stem-and-leaf diagram shows the marks scored by each of 35 students in a science test. 2 7 8 8 9 3 0 2 2 4 5 7 8 9 4 1 1 2 3 4 5 7 8 9 9 5 0 2 3 5 5 5 6 7 7 8 6 1 2 4 Key: 2 7 represents 27 (a) Find the range. … [1] (b) Find the mode. … [1] (c) Find the median. … [1]

3 marks

Mark scheme: 5(a) 37 1 5(b) 55 1 5(c) 45 1

This question in 0580/13 Oct/Nov 2022

11 The median of six numbers is 61. Five of the numbers are 24, 43, 58, 71 and 85. Work out the sixth number. … [1]

1 marks

Mark scheme: 11 64 1

This question in 0580/12 Feb/March 2023

17 A school records how many calculators it sells each week for 40 weeks. The results are shown in the table. Number of Frequency calculators 0 14 1 12 2 6 3 5 4 0 5 2 6 1 Work out the mean number of calculators the school sells each week. … [3]

3 marks

Mark scheme: 17 1.375 3 M1 for [0 ×14] +(1 × 12) + (2 × 6) + (3 × 5) +[4 × 0] + (5 × 2) + (6 × 1) oe fx  M1 dep for 40

This question in 0580/12 Feb/March 2023

5 21 8 15 32 3 29 19 45 8 Calculate the mean of these numbers. … [2]

2 marks

Mark scheme: 5 20 2 M1 for sum of the nine numbers ÷ 9

This question in 0580/11 May/June 2023

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

This question in 0580/12 May/June 2023

7 The stem-and-leaf diagram shows the ages of 21 people. 1 6 9 2 1 4 4 5 8 3 2 6 7 9 4 0 2 4 6 8 9 5 3 4 5 7 Key : 1q6 represents 16 years (a) Find the fraction of people who are more than 30 years old. … [1] (b) Work out the range. … [1] (c) Find the median. … [1]

3 marks

Mark scheme: 7(a) 2 1 oe fraction 3 7(b) 41 1 7(c) 39 1

This question in 0580/13 May/June 2023

7 For 16 days, Safia records the number of dresses she sells. 24 6 18 14 27 37 9 16 22 17 16 16 24 20 15 32 (a) Complete the stem-and-leaf diagram. 0 1 2 3 Key: 2 4 represents 24 dresses [2] (b) Write down the mode. … [1] (c) Find the median. … [1]

4 marks

Mark scheme: 7(a) 2 B1 for two or three rows correct or for a fully 0 6 9 correct unordered stem-and-leaf diagram or for a correct diagram with one error or 1 4 5 6 6 6 7 8 omission 2 0 2 4 4 7 3 2 7 7(b) 16 1 7(c) 17.5 1

This question in 0580/12 Oct/Nov 2023

6 Jamie records the masses of two samples of oranges, type A and type B. The stem-and-leaf diagram shows the mass, in grams, of each of 30 oranges of type A. 17 6 8 8 9 18 0 1 2 2 4 7 19 1 2 2 3 6 7 8 20 0 2 5 5 5 6 7 7 8 21 1 5 6 8 Key: 17 6 represents 176 grams (a) Complete the table to show the range for type A oranges. Type A Type B Mean (g) 195.7 215.8 Range (g) 35 [1] (b) Use the information in the table to write down two comments comparing the masses of type A oranges with the masses of type B oranges. 1. … … 2. … … [2]

3 marks

Mark scheme: 6(a) 42 1 6(b) Type A [masses] lighter on average 2 B1 for each oe Type A [masses] more varied/less strict FT their range in part (a) consistent oe

This question in 0580/13 Oct/Nov 2023

7 The range of eight numbers is 31. These are seven of the numbers. 28 36 42 24 38 16 21 Find the two possible values of the eighth number. … or … [2]

2 marks

Mark scheme: 7 11, 47 2 B1 for each

This question in 0580/12 Feb/March 2024

11 Sarah records the number of people who play golf on each of 14 days. 28 46 54 71 70 65 49 50 64 77 68 72 45 58 (a) Complete the stem-and-leaf diagram. 2 3 4 5 6 7 Key : 2 8 represents 28 [2] (b) Find the median. … [1]

3 marks

Mark scheme: 11(a) 2 B1 for three rows fully correct 2 8 or for a correct unordered stem-and-leaf diagram 3 4 5 6 9 5 0 4 8 6 4 5 8 7 0 1 2 7 11(b) 61 1

This question in 0580/12 Feb/March 2024

9 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: 9(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 9(b) 46 1

This question in 0580/12 May/June 2024

6 The stem-and-leaf diagram shows the number of cars sold each day by a company. 1 0 3 4 5 6 7 2 1 2 2 4 7 7 7 3 0 0 1 2 2 5 6 8 4 0 1 4 6 5 1 2 4 Key: 3 | 2 represents 32 (a) Find the range. … [1] (b) Find the mode. … [1]

2 marks

Mark scheme: 6(a) 44 1 6(b) 27 1

This question in 0580/11 Oct/Nov 2024

15 A bus stops 25 times on a journey. The table shows the number of people who get on the bus at each stop. Number of people Frequency 0 1 1 6 2 7 3 4 4 5 5 2 Calculate the mean. … [3]

3 marks

Mark scheme: 15 2.48 3 M1 for [0 × 1] + (1 × 6) + (2 × 7) + (3 × 4) + (4 × 5) + (5 × 2) or [0] + 6 +14 + 12 + 20 + 10 soi or 62 soi M1dep for their  fx 25

This question in 0580/11 Oct/Nov 2024

4 7 19 8 12 3 12 9 7 12 Find the mode of these numbers. … [1]

1 marks

Mark scheme: 4 12 1

This question in 0580/13 Oct/Nov 2024

13 Each student in a class of 20 students records the number of coins in their pockets. The table shows the results. Number of coins 0 1 2 3 4 5 6 Frequency 3 1 7 8 0 0 1 (a) Find the median. … [1] (b) Calculate the mean. … [3]

4 marks

Mark scheme: 13(a) 2 1 13(b) 2.25 3 M1 for [3×0] + 1×1 + 7×2 + 8×3 + [0×4] + [0×5] + 1×6 oe or for 45 their fx M1 dep for dep on first M1 20

This question in 0580/13 Oct/Nov 2024

11 0 2 2 3 4 7 For these six numbers (a) write down the mode … [1] (b) work out the range … [1] . (c) work out the median … [1] (d) work out the mean. … [2]

5 marks

Mark scheme: 11(a) 2 1 11(b) 7 1 11(c) 1 1 2.5 or 2 2 11(d) 3 2  0 +  2 + 2 + 3 + 4 + 7 M1 for 6

This question in 0580/12 May/June 2025

6 These are the lengths of time, in minutes, of seven phone calls. 10 22 5 7 35 8 75 (a) (i) Find the median. … min [2] (ii) Find the range. … min [1] (b) The longest phone call is 75 minutes. Write 75 minutes in hours. … h [1]

4 marks

Mark scheme: 6(a)(i) 10 2 M1 for at least the first four or last four correctly ordered 6(a)(ii) 70 1 6(b) 1 1 1.25 or 14

This question in 0580/13 May/June 2025

10 The bar chart shows the number of books sold in a shop in each of five months. 12 11 10 9 8 Number 7 of books 6 sold 5 4 3 2 1 0 Mar Apr May Jun Jul Aug Months (a) 4 books were sold in August. Complete the bar chart. [1] (b) Calculate the mean number of books sold in the six months. … [2]

3 marks

Mark scheme: 10(a) Correct bar for August 1 10(b) 7 nfww 2 M1 for (3 + 9 + 7 + 11 + 8 + 4) ÷ 6 or better

This question in 0580/11 Oct/Nov 2025

14 These are the ages, in months, of each of 12 children. 11 27 8 10 26 17 28 12 9 13 22 12 (a) Complete the stem-and-leaf diagram to show this information. 0 1 2 Key: 1 | 7 represents 17 months [2] (b) Find the number of children over 2 years old. … [1] (c) Show that the median is 12.5 . [1]

4 marks

Mark scheme: 14(a) 2 B1 for a correct ordered diagram with 0 8 9 one error or omission or for a correct but unordered stem-and- 1 0 1 2 2 3 7 leaf diagram 2 2 6 7 8 14(b) 3 1 14(c) 12 + 13 1 oe leading to 12.5 nfww 2

This question in 0580/11 Oct/Nov 2025

11 The stem-and-leaf diagram shows the number of customers entering a shop each day for 20 days. 3 0 1 5 9 4 1 4 6 8 9 5 1 3 4 4 4 7 8 6 3 6 6 7 2 Key : 3 0 represents 30 customers (a) Find the range. … [1] (b) Find the mode. … [1] (c) Work out the percentage of these 20 days when more than 55 customers enter the shop. … % [2] (d) (i) Find the median. … [1] (ii) On the next day 48 customers enter the shop. Will the median increase or decrease? Give a reason for your answer. … because … … [1]

6 marks

Mark scheme: 11(a) 42 1 11(b) 54 1 11(c) 30 2 6 B1 for oe 20 11(d)(i) 52 1 11(d)(ii) Decrease AND acceptable reason e.g. 48 1 is below the median

This question in 0580/12 Oct/Nov 2025

8 These are the masses, in kg, of each of 11 bags. 23 16 8 10 27 19 4 17 13 4 14 (a) Complete the stem-and-leaf diagram to show this information. 0 1 2 Key: 2 | 7 represents 27 kg [2] (b) Find the median. … kg [1]

3 marks

Mark scheme: 8(a) 2 B1 for a correct diagram with one error 0 4 4 8 or omission or for a fully correct 1 0 3 4 6 7 9 unordered stem-and-leaf diagram 2 3 7 8(b) 14 1

This question in 0580/13 Oct/Nov 2025