Averages (GCSE Maths) - Worksheets, Questions and Revision

16 original exam-style questions - 8 pages of questions with a full mark scheme - free printable PDF.

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2.14 Averages

EDEXCEL 1MA1 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Here are the shoe sizes of 9 students in a class:
5, 6, 5, 7, 8, 5, 6, 9, 5
Write down the mode of the shoe sizes.

(Total for Question 1 is 1 mark)

Here are the ages, in years, of 5 cousins at a party:
11, 15, 8, 20, 13
Write down the median age.

(Total for Question 2 is 1 mark)

Here are the number of goals scored by a hockey team in 7 matches:
4, 4, 6, 7, 7, 7, 9
Put a ring around the mode of this list of numbers.

A) 4
B) 6
C) 7
D) 9

(Total for Question 3 is 1 mark)

Here are the daily maximum temperatures, in degrees Celsius, recorded in Leeds over 6 days:
14, 9, 17, 6, 12, 19
Work out the range of the temperatures.

(Total for Question 4 is 2 marks)

Bethany records the number of pages she reads each night for 5 nights:
18, 22, 15, 25, 20
Work out the mean number of pages she read per night.

(Total for Question 5 is 3 marks)

For each statement, write down whether it is True or False.

(a)The range of a set of data can never be negative.(1)

(b)The mean of a set of data is always equal to one of the values in the data set.(1)

(c)To find the median of 10 numbers placed in order, you find the mean of the 5th and 6th values.(1)

(Total for Question 6 is 3 marks)

Here are the numbers of text messages sent by 8 students in one day:
12, 15, 12, 18, 20, 15, 12, 16

(a)Write down the mode of the number of messages sent.(1)

(b)Find the median number of messages sent.(2)

(c)Work out the range of the number of messages sent.(1)

(d)Calculate the mean number of messages sent.(2)

(Total for Question 7 is 6 marks)

The table shows the number of bags carried by shoppers leaving a supermarket, recorded during a survey.

Number of bags	1	2	3	4
Frequency	6	9	7	3

(a)Work out how many shoppers took part in the survey.(1)

(b)Write down the mode of the number of bags carried.(1)

(c)Work out the number of shoppers who carried more than 2 bags.(2)

(Total for Question 8 is 4 marks)

The table shows the number of goals scored by a football team in each of its matches last season.

Goals scored	0	1	2	3	4
Frequency	4	7	8	4	2

(a)Show that the team played 25 matches last season.(1)

(b)Calculate the mean number of goals scored per match.(3)

(Total for Question 9 is 4 marks)

Here are the midday temperatures, in degrees Celsius, recorded in Aberdeen on six days in January:
-3, 5, -1, 8, 0, -6

(a)Write these temperatures in order from lowest to highest.(1)

(b)Work out the range of the temperatures.(2)

(c)Calculate the mean temperature.(2)

(Total for Question 10 is 5 marks)

Priya and Sam each play a video game 5 times. Their scores are shown below.
Priya: 12, 18, 9, 15, 21
Sam: 14, 16, 15, 17, 13

(a)Work out the mean score for Priya and the mean score for Sam.(3)

(b)Work out the range of each person's scores.(2)

(c)Ahmed says, 'Priya and Sam played equally well because they have the same mean score.' Comment on whether Ahmed is correct, using the range to support your answer.(2)

(Total for Question 11 is 7 marks)

The mean of five numbers is 9. Four of the numbers are 6, 8, 11 and 7. Work out the fifth number.

(Total for Question 12 is 3 marks)

The stem-and-leaf diagram below shows the times, in minutes, taken by 15 runners to complete a fun run.

(a)Write down the number of runners who took less than 30 minutes.(1)

(b)Find the median time taken.(2)

(c)Work out the range of the times.(2)

(Total for Question 13 is 5 marks)

A shop manager wants to advertise the 'typical' price of trainers sold last week. The price, in pounds sterling, of each of the 9 pairs of trainers sold were:
40, 42, 45, 40, 41, 43, 40, 250, 44

(a)Calculate the mean price.(2)

(b)Find the median price.(2)

(c)The manager wants to use the average that best represents the 'typical' price. State whether the mean or the median should be used, giving a reason.(2)

(Total for Question 14 is 6 marks)

Class 10A (28 students) and Class 10B (25 students) sat the same maths test, out of 20 marks.
Class 10A: mean score = 14, range = 12
Class 10B: mean score = 14, range = 6

(a)Both classes have the same mean score. State what this tells you about the average performance of the two classes.(1)

(b)Use the ranges to explain why the performance within the two classes was different.(2)

(Total for Question 15 is 3 marks)

Class 10A (28 students) and Class 10B (25 students) sat the same maths test, out of 20 marks.
Class 10A: mean score = 14
Class 10B: mean score = 14

(a)Work out the total marks scored by all the students in Class 10A.(2)

(b)Work out the total marks scored by all the students in Class 10B.(2)

(c)Calculate the combined mean score of all 53 students in Class 10A and Class 10B together.(3)

(Total for Question 16 is 7 marks)

Mark scheme · 2.14 Averages

Question 1

B1 5 cao
Answer: 5

Question 2

B1 13 cao
Answer: 13

Question 3

B1 C (7) cao
Answer: C) 7

Question 4

M1 19 and 6 identified as the highest and lowest values, oe (19 - 6)
A1 13 cao
Answer: 13 degrees C

Question 5

M1 18 + 22 + 15 + 25 + 20 (= 100), oe
M1 100 / 5
A1 20 cao
Answer: 20 pages

Question 6

(a) B1 True cao
(a) Answer: True
(b) B1 False cao
(b) Answer: False
(c) B1 True cao
(c) Answer: True

Question 7

(a) B1 12 cao
(a) Answer: 12
(b) M1 numbers placed in order: 12, 12, 12, 15, 15, 16, 18, 20, oe
(b) A1 15 cao
(b) Answer: 15
(c) B1 8 cao (20 - 12)
(c) Answer: 8
(d) M1 (12 + 15 + 12 + 18 + 20 + 15 + 12 + 16) / 8, oe (sum = 120 seen)
(d) A1 15 cao
(d) Answer: 15

Question 8

(a) B1 25 cao (6 + 9 + 7 + 3)
(a) Answer: 25
(b) B1 2 cao
(b) Answer: 2
(c) M1 7 + 3, oe (frequencies for 3 bags and 4 bags identified)
(c) A1 10 cao
(c) Answer: 10

Question 9

(a) B1 4 + 7 + 8 + 4 + 2 = 25, cso (answer of 25 is given, so working must be shown)
(a) Answer: 25 (shown)
(b) M1 fx products found: 0, 7, 16, 12, 8, oe (at least 3 correct)
(b) M1 (0 + 7 + 16 + 12 + 8) / 25
(b) A1 1.72 cao
(b) Answer: 1.72 goals

Question 10

(a) B1 -6, -3, -1, 0, 5, 8, cao
(a) Answer: -6, -3, -1, 0, 5, 8
(b) M1 8 - (-6), oe
(b) A1 14 cao
(b) Answer: 14 degrees C
(c) M1 -3 + 5 - 1 + 8 + 0 - 6 (= 3), oe, / 6
(c) A1 0.5 cao
(c) Answer: 0.5 degrees C

Question 11

(a) M1 Priya: 12+18+9+15+21 (= 75), oe
(a) M1 Sam: 14+16+15+17+13 (= 75), oe
(a) A1 both means = 15 cao
(a) Answer: Priya: 15, Sam: 15
(b) M1 21 - 9 and 17 - 13, oe (at least one correct range identified)
(b) A1 Priya = 12 and Sam = 4, both cao
(b) Answer: Priya: 12, Sam: 4
(c) B1 states that Ahmed is not (fully) correct / disagrees with Ahmed
(c) B1 correct reason referring to the range, e.g. Sam's range (4) is smaller than Priya's range (12), so Sam's scores were more consistent, oe
(c) Answer: Ahmed is not correct. Although the means are equal, Sam's range (4) is much smaller than Priya's range (12), so Sam's scores were more consistent than Priya's.

Question 12

M1 9 x 5 (= 45), oe
M1 45 - (6 + 8 + 11 + 7), oe (45 - 32)
A1 13 cao
Answer: 13

Question 13

(a) B1 3 cao
(a) Answer: 3
(b) M1 identifies the 8th value out of 15 ordered values
(b) A1 36 cao
(b) Answer: 36 minutes
(c) M1 53 - 25, oe
(c) A1 28 (minutes) cao
(c) Answer: 28 minutes

Question 14

(a) M1 (40+42+45+40+41+43+40+250+44) / 9, oe (sum = 585 seen)
(a) A1 65 cao
(a) Answer: GBP 65
(b) M1 prices placed in order: 40, 40, 40, 41, 42, 43, 44, 45, 250, oe
(b) A1 42 cao
(b) Answer: GBP 42
(c) B1 median
(c) B1 correct reason, e.g. GBP250 is an outlier / much higher than the other prices, so it makes the mean too high to be typical, oe
(c) Answer: The median (GBP 42) should be used, because the price of GBP250 is an outlier that pulls the mean (GBP65) higher than most of the prices.

Question 15

(a) B1 on average, the two classes performed equally well / the same, oe
(a) Answer: On average, the two classes performed equally well.
(b) B1 Class 10A's scores were more spread out / varied, since its range (12) is greater than Class 10B's range (6)
(b) B1 Class 10B's scores were more consistent / closer together, since its range (6) is smaller
(b) Answer: Class 10A's scores were more spread out (range 12) while Class 10B's scores were more consistent (range 6), so the students in 10B performed more similarly to each other.

Question 16

(a) M1 14 x 28, oe
(a) A1 392 cao
(a) Answer: 392
(b) M1 14 x 25, oe
(b) A1 350 cao
(b) Answer: 350
(c) M1 392 + 350 (= 742), ft their (a) and (b)
(c) M1 742 / 53, ft (28 + 25 students)
(c) A1 14 cao
(c) Answer: 14

Question 16

7 marks

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Averages (GCSE Maths) - Worksheets, Questions and Revision

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