Averages and measures of spread — Paper 2 · IGCSE Mathematics - International 0607

2 These are the number of points The Storm have scored in their last 20 basketball matches. 28 33 49 37 26 54 46 48 53 34 26 17 46 41 52 48 37 30 45 53 (a) Construct an ordered stem and leaf diagram to show these scores and complete the key. … … … … … Key … │ … = 53 [3] (b) Find the median score. … [1]

4 marks

Mark scheme: 2(a) 1 7 3 B2 for all elements correct 2 6 6 8 or B1 for all 'correct' but unordered or 1 or 2 3 0 3 4 7 7 missing or wrongly placed or extra element(s) 4 1 5 6 6 8 8 9 5 2 3 3 4 Key 5│3 = 53 B1 for key 2(b) 43 1

This question in 0607/22 May/June 2017

9 The mean of five numbers is 16. When two extra numbers are included the mean of the seven numbers is 20. Find the mean of the two extra numbers. … [2]

2 marks

Mark scheme: 9 30 2 M1 for 7 × 20 −×5 16

This question in 0607/22 Oct/Nov 2019

7 The mean of 10 numbers is 15. When an 11th number is included, the mean is 16. Find the 11th number. … [2]

2 marks

Mark scheme: 7 26 2 B1 for 150 or 176 seen

This question in 0607/23 Oct/Nov 2019

12 The table shows the marks of 80 students in an examination. Mark (x) Frequency 0 1 x G 10 8 10 1 x G 15 16 15 1 x G 20 25 20 1 x G 30 17 30 1 x G 50 14 (a) On the grid, draw a cumulative frequency curve to show this information. 80 70 60 50 Cumulative 40 frequency 30 20 10 0 x 0 10 20 30 40 50 Mark [4] (b) Use your graph to estimate the median mark of the students. … [1]

5 marks

Mark scheme: 12(a) Correct graph passing through 4 B2 for correct vertical plots (0, 0) (10, 8) (15, 24) (20, 49) or B1 for 3 or 4 correct vertical plots or (30, 66) (50, 80) all cf’s seen correct B1 for plotting points at upper group limit B1 for smooth curve 12(b) 17 to 19 1 FT their curve 13 1 11 7 − 1 y = x + 5 M1 for gradient = oe 2 4 1 − 4 − 1 M1 for gradient perp = their gradient B1 for midpoint (2.5, 4) seen M1 for subst their gradient (perp) and their mid-point into y = mx + c

This question in 0607/21 Oct/Nov 2020

1 These are the test results for 14 students. 27 19 22 25 18 23 24 17 16 25 17 27 23 26 (a) Construct an ordered stem-and-leaf diagram to show this information, including a key. Key: … | … = … [3] (b) Find the median. … [1]

4 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1 6 7 7 8 9 3 B1 for one row correct or for all numbers in 2 2 3 3 4 5 5 6 7 7 correct rows but unordered B1 for a correct key key e.g. 1 | 6 = 16 1(b) 23 1

This question in 0607/22 Feb/March 2021

10 Aisha picks three number cards from a pack. 1 The mean of the three numbers is 6 3. She picks another card from the pack. The mean of the four numbers is 6 1. 2 Work out the number on the fourth card. … [3]

3 marks

Mark scheme: 10 7 3 1 1 M2 for 6 × 4 − 6 × 3 2 3 or M1 for either correct OR M2 for 2 (19 + x ) = 13 × 4 oe 1 6 × 3 + x 3 1 or M1 for = 6 oe 4 2

This question in 0607/22 Feb/March 2021

13 The heights, h cm, of 100 plants are measured. The table shows the results. Height, h cm Frequency 0 1 h G 40 15 40 1 h G 80 40 80 1 h G 120 45 Calculate an estimate for the mean height of the plants. … cm [3]

3 marks

Mark scheme: 13 72 3 15 × 20 + 40 × 60 + 45 × 100 M2 for 100 or M1 for their (20) × 15 + their (60) × 40 + their (100) × 45 100 or use correct mid-points but not totalled

This question in 0607/22 May/June 2021

8 The mean of eight numbers is 25. When two extra numbers are included the mean of the ten numbers is 24. Find the mean of the two extra numbers. … [2]

2 marks

Mark scheme: 8 20 2 M1 for 10  24 or 8  25

This question in 0607/22 May/June 2022

2 This is a list of 8 numbers. 11 7 8 13 7 14 15 5 (a) Find the median. … [2] (b) An extra number is added to the list. The mean of the nine numbers is 1 more than the mean of the eight numbers. Find the ninth number. … [3]

5 marks

Mark scheme: 2(a) 9.5 oe 2 M1 for 5 7 7 8 11 ... or (8 + 11) ÷ 2 2(b) 19 3 M1 for attempt at mean (5 + 7 + 7 + 8 ..+ 15) / 8 M1 for 9 × (their 10 + 1)

This question in 0607/23 May/June 2022

7 These are the scores of 10 students in a test. 15 5 20 25 7 13 15 11 17 12 Find (a) the range, … [1] (b) the mean. … [2]

3 marks

Mark scheme: 7(a) 20 1 7(b) 14 2 M1 for (15 + 5 + 20 + 25 +….)/10

This question in 0607/21 Oct/Nov 2022

1 These are the scores of 10 students in a test. 7 15 9 4 16 6 8 11 12 10 Find (a) the median, … [2] (b) the mean. … [2]

4 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 9.5 2 M1 for 4, 6, 7, 8, 9, 10, 11, 12, 15, 16 Ordered as far as 10 forwards or 9 backwards 1(b) 9.8 2 M1 for (7 + 15 + 16 + 4 ...) ÷ 10

This question in 0607/22 Oct/Nov 2022

4 Aklima records the masses, m kg, of 120 parcels. The results are shown in the table. Mass, m kg 0 1 m G 2 2 1 m G 4 4 1 m G 6 6 1 m G 8 8 1 m G 10 Frequency 35 30 40 12 3 Find (a) the modal class … 1 m G … [1] (b) the class which contains the median. … 1 m G … [1]

2 marks

Mark scheme: 4(a) 4 [< m ⩽] 6 1 4(b) 2 [< m ⩽] 4 1

This question in 0607/22 May/June 2023

11 (a) The range of ten numbers is 30. The range of eight other numbers is 13. Find the smallest possible value of the range of all eighteen numbers. … [1] (b) The mean of twelve numbers is 25. The mean of ten of these numbers is 16. Find the mean of the other two numbers. … [2]

3 marks

Mark scheme: 11(a) 30 1 11(b) 70 2 M1 for 12  25 or 10  16

This question in 0607/23 May/June 2023

2 Priya rolls a die 10 times. The table shows the results. Score 1 2 3 4 5 6 Frequency 2 1 0 2 0 5 (a) Find the mode. … [1] (b) Find the interquartile range. … [2]

3 marks

Mark scheme: 2(a) 6 1 2(b) 4 2 M1 for [u.q. =] 6 or [l.q. =] 2 identified

This question in 0607/21 Oct/Nov 2023

3 This is a list of ten numbers. 19 24 16 17 22 14 28 34 20 18 (a) Find the range. … [1] (b) Find the median. … [2]

3 marks

Mark scheme: 3(a) 20 1 3(b) 19.5 oe 2 M1 for ordering first or last 6 or identifying 19 and 20

This question in 0607/21 Oct/Nov 2024

10 The mean of five numbers is 7. The five numbers are 3, 5, 10, 11 and x. Find the value of x. x = … [2] 2

2 marks

Mark scheme: 10 6 2 M1 for 3 + 5 + 10 + 11 + x = 5 × 7 oe

This question in 0607/22 Oct/Nov 2024