Here are the shoe sizes of 9 pupils in a class: 5, 6, 5, 7, 8, 5, 9, 6, 4. State the modal shoe size.
(Total for Question 1 is 1 mark)
2
The table shows the lowest temperature (in degrees C) recorded overnight in five UK cities in January: London 2, Aberdeen -5, Cardiff -1, Belfast -3, Newcastle -6. Calculate the range of these temperatures.
(Total for Question 2 is 2 marks)
3
Find the median of these numbers: 14, 7, 20, 9, 12.
(Total for Question 3 is 2 marks)
4
Calculate the mean of 8, 12, 10, 6 and 14.
(Total for Question 4 is 2 marks)
5
A netball team scored the following number of goals in 6 matches: 9, 4, 15, 7, 11, 13. Find the median number of goals scored.
(Total for Question 5 is 2 marks)
6
Five numbers have a mean of 8. Four of the numbers are 5, 9, 10 and 6. Work out the fifth number.
(Total for Question 6 is 3 marks)
7
The table shows the number of brothers and sisters (siblings) for 10 children in a class. Number of siblings (x): 0, 1, 2, 3. Frequency (f): 2, 4, 3, 1.
(a)Write down the modal number of siblings.(1)
(b)Calculate the mean number of siblings per child.(3)
(Total for Question 7 is 4 marks)
8
Six pupils sat a test. Their scores out of 100 were: 42, 58, 65, 71, 39, 61.
(a)Calculate the mean test score.(2)
(b)Calculate the range of the scores.(2)
(Total for Question 8 is 4 marks)
9
Show that the mean of 4, 9, 14, 19 and 24 is 14.
(Total for Question 9 is 2 marks)
10
In a school, Class A has 12 pupils with a mean test mark of 65. Class B has 8 pupils with a mean test mark of 70. Calculate the mean test mark for all 20 pupils in the two classes combined.
(Total for Question 10 is 4 marks)
11
A list of five numbers has a mean of 9. One of the numbers, 21, is removed from the list. Calculate the mean of the remaining four numbers.
(Total for Question 11 is 3 marks)
12
Priya wants her mean weekly saving over 6 weeks to be £14.50. In the first five weeks she saves £12, £15, £18, £9 and £16. How much must she save in week 6 to reach her target mean?
(Total for Question 12 is 3 marks)
13
The table shows the number of pets owned by 20 pupils. Number of pets (x): 0, 1, 2, 3, 4. Frequency (f): 5, 8, 4, 2, 1.
(a)State the modal number of pets.(1)
(b)Calculate the mean number of pets per pupil.(3)
(Total for Question 13 is 4 marks)
14
Six people are in a lift. Their ages are 21, 24, 26, 29, 31 and 73.
(a)Calculate the mean age.(2)
(b)Find the median age.(2)
(c)Explain why the median is a better measure of the average age of this group than the mean.(2)
(Total for Question 14 is 6 marks)
15
A coach travels 150 km in 3 hours for the first part of a journey, then a further 90 km in 2 hours. Calculate the average speed for the whole journey, in km/h.
(Total for Question 15 is 3 marks)
16
The mean of four numbers is (x + 7). The four numbers are x, x+3, 2x-1 and 4x+6. Form an equation and solve it to find the value of x.
(Total for Question 16 is 4 marks)
17
Over 5 days, Tom reads pages of a book. On the first four days he reads 24, 31, 18 and 27 pages. If the mean number of pages read per day over the 5 days is 25, calculate how many pages he read on day 5.
(Total for Question 17 is 3 marks)
18
Which of these is the median of the numbers 3, 8, 5, 12, 7, 9, 4?
A) 5
B) 7
C) 8
D) 9
(Total for Question 18 is 1 mark)
19
A data set has the values 2, 2, 2, 5, 9. Which statement about this data set is true?
A) mode > mean
B) range = mean
C) median = mode
D) mean = median
(Total for Question 19 is 1 mark)
20
A set of five whole numbers has mean 8, median 8, mode 6 and range 5. Find a set of five numbers that satisfies all four conditions.
(Total for Question 20 is 4 marks)
Mark scheme · EP.M7 Averages
Question 1
B1 modal shoe size = 5 (cao)
Answer: 5
Question 2
M1 identifies highest value (2) and lowest value (-6)
M1 combined total (1340) divided by combined number of pupils (20)
A1 combined mean = 67, cao
Answer: 67
Question 11
M1 total of the original five numbers = 9 x 5 = 45
M1 remaining total after removing 21: 45 - 21 = 24
A1 new mean = 24 / 4 = 6, cao
Answer: 6
Question 12
M1 total needed over 6 weeks = 14.50 x 6 = 87 (pounds sterling)
M1 sum of first five weeks' savings = 70 (pounds sterling)
A1 week 6 saving = £17, cao
Answer: £17
Question 13
(a) B1 mode = 1, cao
(a) Answer: 1
(b) M1 correct values of fx: 0, 8, 8, 6, 4 summed to give 26
(b) M1 divides total fx by total frequency (20)
(b) A1 mean = 1.3 (oe 13/10), cao
(b) Answer: 1.3
Question 14
(a) M1 sum of the six ages = 204
(a) A1 mean = 34, cao
(a) Answer: 34
(b) M1 list already ordered, middle pair identified (26, 29)
(b) A1 median = 27.5, cao
(b) Answer: 27.5
(c) B1 identifies that 73 is an extreme value / outlier compared with the rest of the data
(c) B1 explains that the outlier pulls the mean up so it does not represent most of the group, whereas the median is not affected by extreme values (oe)
(c) Answer: The median (27.5) is not affected by the extreme value 73, so it better represents the typical age; the mean (34) is pulled upward by this one large value.
Question 15
M1 total distance = 150 + 90 = 240 km
M1 total time = 3 + 2 = 5 hours
A1 average speed = 48 km/h, cao (units required)
Answer: 48 km/h
Question 16
M1 sum of the four expressions = 8x + 8 (oe, unsimplified acceptable)
M1 forms the equation (8x+8)/4 = x+7, oe
M1 correct simplification 2x+2 = x+7 and rearranges to isolate x
A1 x = 5, cao
Answer: x = 5
Question 17
M1 total pages needed over 5 days = 25 x 5 = 125
M1 sum of first four days = 24+31+18+27 = 100
A1 day 5 = 25 pages, cao
Answer: 25 pages
Question 18
B1 B) 7, cao
Answer: B) 7
Question 19
B1 C) median = mode, cao
Answer: C) median = mode
Question 20
B1 five whole numbers with a total of 40 (satisfying mean = 8)
B1 middle value (when ordered) equal to 8 (satisfying median = 8)
B1 value 6 appearing more often than any other value (satisfying mode = 6)
B1 difference between highest and lowest value equal to 5 (satisfying range = 5); ft any other valid set meeting all four conditions
Answer: 6, 6, 8, 9, 11 (or any other valid set satisfying all four conditions)