Averages (Part 2) - Worksheets, Questions and Revision

16 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 8)Read the revision guide

Next in this strand

Revision Library

revisionlibrary.co.uk

FOUNDATION

2.14B Averages (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Here are the number of goals scored by a school football team in their last 8 matches:
2, 1, 3, 2, 0, 2, 1, 4
Write down the mode of the number of goals scored.

(Total for Question 1 is 1 mark)

Here are the times, in minutes, taken by 7 students to travel to school:
12, 18, 9, 25, 14, 20, 11
Write down the median travel time.

(Total for Question 2 is 1 mark)

Here are the numbers of books read last month by 5 friends:
3, 7, 2, 9, 5
Put a ring around the range of this list of numbers.

A) 5
B) 6
C) 7
D) 9

(Total for Question 3 is 1 mark)

Here are the heights, in centimetres, of 6 tomato plants grown in a greenhouse:
142, 118, 135, 127, 109, 151
Work out the range of the heights.

(Total for Question 4 is 2 marks)

A cricketer scored these numbers of runs in 6 innings:
34, 28, 45, 31, 26, 40
Work out the mean number of runs per innings.

(Total for Question 5 is 3 marks)

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

(a)If you add 4 to every value in a data set, the mean also increases by 4.(1)

(b)If you add 4 to every value in a data set, the range stays the same.(1)

(c)If a data set has an even number of values, the median is always one of the values in the data set.(1)

(Total for Question 6 is 3 marks)

The table shows the number of siblings reported by the students in a Year 8 class.

Number of siblings	0	1	2	3
Frequency	5	10	6	4

(a)Work out how many students were surveyed.(1)

(b)Write down the modal number of siblings.(1)

(c)Work out the number of students with at least 2 siblings.(2)

(d)Calculate the mean number of siblings.(3)

(Total for Question 7 is 7 marks)

The bar chart shows the number of goals scored by a hockey team in each of its matches this season.

Figure (to be drawn): Bar chart. x-axis labelled 'Number of goals' with categories 0, 1, 2, 3, 4. y-axis labelled 'Frequency (number of matches)', scaled 0 to 5 with a gridline at every integer. Bar heights: 0 goals = 3, 1 goal = 4, 2 goals = 5, 3 goals = 2, 4 goals = 1.

(a)Write down the number of matches in which the team scored 2 goals.(1)

(b)Work out the total number of matches played this season.(1)

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

(Total for Question 8 is 5 marks)

Amir recorded the number of press-ups he did on 5 days:
18, 22, 25, 20, 15
Show that the mean number of press-ups per day is 20.

(Total for Question 9 is 2 marks)

Priti was asked to find the mean of these numbers:
7, 12, 9, 15, 11, 6
Her working is shown below:
7 + 12 + 9 + 15 + 11 + 6 = 62
Mean = 62 / 6 = 10.33 (2 dp)
Priti has made an error. Identify her error and work out the correct mean.

(Total for Question 10 is 3 marks)

A survey asked 20 students to name their favourite school subject. The results are shown in the table.

Subject	Maths	English	Science	Art
Frequency	6	4	7	3

(a)Write down the modal subject.(1)

(b)Explain why it is not possible to calculate the mean or the median favourite subject.(2)

(Total for Question 11 is 3 marks)

Here are the scores, relative to par, of 6 golfers after the first round of a tournament:
-3, 2, -1, 0, -5, 4

(a)Work out the range of the scores.(2)

(b)Calculate the mean score.(3)

(Total for Question 12 is 5 marks)

Grace recorded the number of steps she walked, in thousands, on 4 days. The mean number of steps per day was 8. On the 5th day she walked 13 thousand steps. Work out her new mean number of steps per day over the 5 days.

(Total for Question 13 is 3 marks)

At a weekend running club, the combined mean finishing time for all 10 runners is 42 minutes. Of these 10 runners, 6 are in the beginners' group, with a mean finishing time of 38 minutes. The rest are in the advanced group. Work out the mean finishing time of the runners in the advanced group.

(Total for Question 14 is 4 marks)

Here are the delivery times, in minutes, for 13 parcels delivered by a courier in one day:
22, 35, 18, 40, 27, 31, 45, 29, 33, 38, 24, 50, 19

(a)Find the median delivery time.(2)

(b)Work out the range of the delivery times.(2)

(c)The courier says, 'Most parcels take about half an hour to deliver.' Use the median to comment on whether this claim is reasonable.(2)

(Total for Question 15 is 6 marks)

Rhys recorded his journey times, in minutes, to work on 7 days:
21, 22, 23, 24, 25, 26, 95
(Day 7 included a cancelled train.)

(a)Calculate the mean of all 7 journey times.(3)

(b)Calculate the mean of the first 6 journey times only (excluding day 7).(2)

(c)Use your answers to parts (a) and (b) to explain why the mean of all 7 days is not a fair representation of Rhys's typical journey time.(2)

(Total for Question 16 is 7 marks)

Mark scheme · 2.14B Averages (Part 2)

Question 1

B1 2 cao
Answer: 2

Question 2

B1 14 cao
Answer: 14 minutes

Question 3

B1 C (7) cao
Answer: C) 7

Question 4

M1 151 and 109 identified as the highest and lowest values, oe (151 - 109)
A1 42 cao
Answer: 42 cm

Question 5

M1 34 + 28 + 45 + 31 + 26 + 40 (= 204), oe
M1 204 / 6
A1 34 cao
Answer: 34 runs

Question 6

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

Question 7

(a) B1 25 cao (5 + 10 + 6 + 4)
(a) Answer: 25
(b) B1 1 cao
(b) Answer: 1
(c) M1 6 + 4, oe (frequencies for 2 siblings and 3 siblings identified)
(c) A1 10 cao
(c) Answer: 10
(d) M1 fx products found: 0, 10, 12, 12, oe (at least 3 correct)
(d) M1 (0 + 10 + 12 + 12) / 25
(d) A1 1.36 cao
(d) Answer: 1.36 siblings

Question 8

(a) B1 5 cao
(a) Answer: 5
(b) B1 15 cao (3 + 4 + 5 + 2 + 1)
(b) Answer: 15
(c) M1 fx products found: 0, 4, 10, 6, 4, oe (at least 3 correct)
(c) M1 (0 + 4 + 10 + 6 + 4) / 15
(c) A1 1.6 cao
(c) Answer: 1.6 goals

Question 9

M1 18 + 22 + 25 + 20 + 15 (= 100), oe
A1 100 / 5 = 20 cso (answer of 20 is given, so working must be shown)
Answer: 20 (shown)

Question 10

B1 identifies that the total (62) is incorrect / an addition error has been made
B1 60 stated as the correct total
B1 10 cao (60 / 6)
Answer: Priti's addition is wrong; the correct total is 60, so the correct mean is 10.

Question 11

(a) B1 Science cao
(a) Answer: Science
(b) B1 mean: subject names are not numbers, so they cannot be added and divided, oe
(b) B1 median: the subjects have no numerical order, so they cannot be placed in order from lowest to highest, oe
(b) Answer: The mean cannot be calculated because the data (subject names) are not numbers, so they cannot be added and divided. The median cannot be found because the subjects cannot be placed in numerical order.

Question 12

(a) M1 4 and -5 identified as the highest and lowest values, oe (4 - (-5))
(a) A1 9 cao
(a) Answer: 9
(b) M1 -3 + 2 - 1 + 0 - 5 + 4 (= -3), oe
(b) M1 -3 / 6
(b) A1 -0.5 cao
(b) Answer: -0.5

Question 13

M1 8 x 4 (= 32), oe
M1 32 + 13 (= 45), oe, / 5
A1 9 cao
Answer: 9 thousand steps

Question 14

M1 10 x 42 (= 420), oe
M1 6 x 38 (= 228), oe
M1 (420 - 228) / (10 - 6), oe (192 / 4)
A1 48 cao
Answer: 48 minutes

Question 15

(a) M1 times placed in order: 18, 19, 22, 24, 27, 29, 31, 33, 35, 38, 40, 45, 50, oe
(a) A1 31 cao
(a) Answer: 31 minutes
(b) M1 50 - 18, oe
(b) A1 32 cao
(b) Answer: 32 minutes
(c) B1 compares the median (31 minutes) with half an hour (30 minutes)
(c) B1 valid comment, e.g. the median is very close to 30 minutes, so the claim is reasonable, oe
(c) Answer: The median (31 minutes) is very close to half an hour (30 minutes), so the courier's claim is reasonable.

Question 16

(a) M1 21 + 22 + 23 + 24 + 25 + 26 + 95 (= 236), oe
(a) M1 236 / 7
(a) A1 33.7 awrt
(a) Answer: 33.7 minutes (awrt)
(b) M1 21 + 22 + 23 + 24 + 25 + 26 (= 141), oe
(b) A1 23.5 cao
(b) Answer: 23.5 minutes
(c) B1 compares the two means, e.g. the mean of all 7 days (33.7) is much higher than the mean of the usual 6 days (23.5), ft their (a) and (b)
(c) B1 correct reason, e.g. the single unusually high value (95, caused by a cancelled train) pulls the overall mean up, so it does not represent a typical day, oe
(c) Answer: The mean of all 7 days (33.7) is much higher than the mean of the usual 6 days (23.5), because the single outlier of 95 minutes (caused by a cancelled train) pulls the overall mean up, so it does not fairly represent Rhys's typical journey time.

Question 16

7 marks

Did your answer earn the marks?

Mark my answers

Averages (Part 2) - Worksheets, Questions and Revision

More on this topic

Next in this strand

2.14B Averages (Part 2)

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Mark your answers

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16