In 8 matches, a school football team scored the following number of goals: 2, 1, 3, 2, 4, 2, 1, 2. Which of these is the mode of this data?
A) 1
B) 2
C) 3
D) 4
E) 8
(Total for Question 1 is 1 mark)
2
Six golfers' scores relative to par were: +2, -3, 0, -5, +4, -1. Calculate the range of these scores.
A) 9
B) 4
C) -9
D) -1
E) 1
(Total for Question 2 is 1 mark)
3
Find the median of these numbers: 21, 8, 15, 4, 19.
(Total for Question 3 is 2 marks)
4
Calculate the mean of 7, 13, 9, 15 and 11.
(Total for Question 4 is 2 marks)
5
Six pupils recorded the number of minutes they spent on homework one evening: 25, 40, 18, 55, 30, 45. Which of these is the median number of minutes?
A) 30
B) 35
C) 40
D) 45
E) 37.5
(Total for Question 5 is 1 mark)
6
Five numbers have a mean of 12. Four of the numbers are 8, 14, 10 and 16. Work out the fifth number.
(Total for Question 6 is 3 marks)
7
A survey asked 10 pupils how many pets they owned. Their answers were: 0, 1, 1, 2, 0, 3, 1, 2, 1, 0. Which of these is the mode of this data?
A) 0
B) 1
C) 2
D) 3
E) 4
(Total for Question 7 is 1 mark)
8
The table shows the number of goals scored by a school hockey team in 10 matches. Goals scored (x): 0, 1, 2, 3, 4. Frequency (f): 2, 4, 2, 1, 1.
(a)State the modal number of goals.(1)
(b)Calculate the mean number of goals per match.(3)
(Total for Question 8 is 4 marks)
9
A running club has two training groups. Group A has 15 members with a mean weekly training time of 40 minutes. Group B has 5 members with a mean weekly training time of 60 minutes. Calculate the mean weekly training time for all 20 members combined.
(Total for Question 9 is 4 marks)
10
Which of these is the median of the numbers 6, 14, 2, 20, 11, 17 and 8?
A) 8
B) 11
C) 14
D) 17
E) 2
(Total for Question 10 is 1 mark)
11
Show that the mean of 15, 22, 8, 19 and 11 is 15.
(Total for Question 11 is 2 marks)
12
A delivery van travels 84 km in 2 hours, then a further 66 km in 1 hour. Calculate the average speed for the whole journey, in km/h.
(Total for Question 12 is 3 marks)
13
A data set has the values 3, 3, 7, 10, 12. Which statement about this data set is true?
A) mode > mean
B) range = mean
C) median = mode
D) mean = median
E) mode = range
(Total for Question 13 is 1 mark)
14
Over 6 days, Aisha practises the piano. On the first five days she practises for 20, 35, 15, 40 and 25 minutes. If the mean practice time per day over the 6 days is 28 minutes, calculate how many minutes she practised on day 6.
(Total for Question 14 is 3 marks)
15
Which of these is the mean of the numbers 9, 14, 7, 18 and 12?
A) 11
B) 12
C) 13
D) 15
E) 18
(Total for Question 15 is 1 mark)
16
Two dice are rolled 10 times and the sums recorded: 7, 9, 5, 8, 7, 10, 6, 7, 4, 7.
(a)State the modal sum.(1)
(b)Calculate the range of the sums.(2)
(Total for Question 16 is 3 marks)
17
Which of these is the range of the numbers 34, 19, 47, 22 and 41?
A) 28
B) 47
C) 19
D) 66
E) 25
(Total for Question 17 is 1 mark)
18
Three data sets are shown below. Set P: 4, 8, 10, 15. Set Q: 2, 6, 9, 20. Set R: 5, 7, 11, 14. Which of these has the largest range?
A) Set P
B) Set Q
C) Set R
D) Sets P and Q have equal range
E) All three sets have the same range
(Total for Question 18 is 1 mark)
19
A tuck shop sold the following number of flapjacks over 5 days: 12, 18, 15, 20, 10. Which of these is the mean number sold per day?
A) 13
B) 14
C) 15
D) 16
E) 20
(Total for Question 19 is 1 mark)
20
A list of four numbers has a mean of 15. A fifth number, 25, is added to the list. Calculate the new mean of all five numbers.
(Total for Question 20 is 3 marks)
21
The mean of four numbers is (x + 9). The four numbers are x, x+5, 2x-3 and 3x+10. Form an equation and solve it to find the value of x.
(Total for Question 21 is 4 marks)
22
Six cousins each saved some pocket money over half term. Their savings were: £10, £20, £30, £40, £50 and £150 (the £150 included a birthday gift from a grandparent).
(a)Calculate the mean amount saved.(2)
(b)Find the median amount saved.(2)
(c)Explain why the median is a better measure of the typical amount saved by this group than the mean.(2)
(Total for Question 22 is 6 marks)
23
A cricketer's mean score after 9 innings is 30 runs. In her 10th innings she scores 70 runs. Which of these is her new mean score after 10 innings?
A) 30
B) 34
C) 32
D) 38
E) 50
(Total for Question 23 is 1 mark)
24
A set of six whole numbers has mean 11, median 11, mode 9 and range 12. Find a set of six numbers that satisfies all four conditions.
(Total for Question 24 is 4 marks)
Mark scheme · EP.M7B Averages: Practice Set 2
Question 1
B1 B) 2, cao
Answer: B) 2
Question 2
B1 A) 9, cao
Answer: A) 9
Question 3
M1 numbers ordered correctly: 4, 8, 15, 19, 21
A1 median = 15 (cao)
Answer: 15
Question 4
M1 sum of the five numbers = 55
A1 mean = 11 (cao)
Answer: 11
Question 5
B1 B) 35, cao
Answer: B) 35
Question 6
M1 total of all five numbers = 12 x 5 = 60
M1 sum of the four known numbers = 8 + 14 + 10 + 16 = 48
A1 fifth number = 60 - 48 = 12, cao
Answer: 12
Question 7
B1 B) 1, cao
Answer: B) 1
Question 8
(a) B1 mode = 1, cao
(a) Answer: 1
(b) M1 correct values of fx: 0, 4, 4, 3, 4 summed to give 15
(b) M1 divides total fx by total frequency (10)
(b) A1 mean = 1.5 (oe 15/10), cao
(b) Answer: 1.5
Question 9
M1 total training time for Group A = 15 x 40 = 600 minutes
M1 total training time for Group B = 5 x 60 = 300 minutes
M1 combined total (900) divided by combined number of members (20)
M1 total minutes needed over 6 days = 28 x 6 = 168
M1 sum of first five days = 20+35+15+40+25 = 135
A1 day 6 = 33 minutes, cao
Answer: 33 minutes
Question 15
B1 B) 12, cao
Answer: B) 12
Question 16
(a) B1 mode = 7, cao
(a) Answer: 7
(b) M1 identifies highest value (10) and lowest value (4)
(b) A1 range = 6, cao
(b) Answer: 6
Question 17
B1 A) 28, cao
Answer: A) 28
Question 18
B1 B) Set Q, cao
Answer: B) Set Q
Question 19
B1 C) 15, cao
Answer: C) 15
Question 20
M1 original total of the four numbers = 15 x 4 = 60
M1 new total after adding 25: 60 + 25 = 85
A1 new mean = 85 / 5 = 17, cao
Answer: 17
Question 21
M1 sum of the four expressions = 7x + 12 (oe, unsimplified acceptable)
M1 forms the equation (7x+12)/4 = x+9, oe
M1 correct rearrangement: 7x+12 = 4x+36, leading to 3x = 24
A1 x = 8, cao
Answer: x = 8
Question 22
(a) M1 sum of the six amounts = £300
(a) A1 mean = £50, cao
(a) Answer: £50
(b) M1 list already ordered, middle pair identified (£30, £40)
(b) A1 median = £35, cao
(b) Answer: £35
(c) B1 identifies that £150 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 (£35) is not affected by the extreme value £150, so it better represents the typical amount saved; the mean (£50) is pulled upward by this one large gift-boosted amount.
Question 23
B1 B) 34, cao
Answer: B) 34
Question 24
B1 six whole numbers with a total of 66 (satisfying mean = 11)
B1 middle pair (when ordered) averaging to 11 (satisfying median = 11)
B1 value 9 appearing more often than any other value (satisfying mode = 9)
B1 difference between highest and lowest value equal to 12 (satisfying range = 12); ft any other valid set meeting all four conditions
Answer: 4, 9, 9, 13, 15, 16 (or any other valid set satisfying all four conditions)