Statistics Worksheet with Answers

Revision Library

revisionlibrary.co.uk

KS3 · Statistics

KS3.M-S1 Statistics

AQA KS3.M-S1 · Calculator allowed · about 95 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

1

Here are the ages, in years, of 7 cousins at a family gathering: 4, 7, 4, 9, 6, 4, 8.

(a)Write down the mode of the ages.(1)

(b)Find the median of the ages.(1)

(c)Find the range of the ages.(1)

2

Miss Okafor asked all 20 pupils in her Year 7 form group how many siblings (brothers and sisters) they each have. The results are shown in the frequency table below.
Number of siblings (x): 0, 1, 2, 3, 4
Frequency (f): 5, 7, 4, 3, 1

(a)Write down the mode.(1)

(b)Find the median number of siblings.(2)

(c)Calculate the mean number of siblings.(2)

3

The salaries, in thousands of pounds, of 9 employees at a small firm in Cardiff are: 18, 19, 20, 21, 22, 23, 24, 25, 95.

(a)Which average best describes the typical salary, without being distorted by the outlier of 95?(1)

A) Mean
B) Median
C) Mode
D) Range

(b)Explain why your chosen average is more suitable than the mean here.(1)

4

Mr Hughes's class of 30 pupils voted for their favourite sport. The bar chart results were: Football 12 pupils, Netball 8 pupils, Swimming 6 pupils, Athletics 4 pupils.

(a)Which sport was the most popular?(1)

(b)How many more pupils chose football than chose swimming?(1)

(c)What fraction of the class chose netball? Give your answer in its simplest form.(2)

5

A school library pictogram shows the number of books borrowed each day, using the key: 1 symbol = 4 books. Monday: 3 symbols. Tuesday: 2.5 symbols. Wednesday: 4 symbols. Thursday: 1.5 symbols.

(a)How many books were borrowed on Monday?(1)

(b)How many books were borrowed on Tuesday?(1)

(c)Work out the total number of books borrowed from Monday to Thursday.(2)

6

Staff at Bridgtown Academy were asked whether they prefer tea, coffee or neither. Some results are shown in the two-way table below.
Boys: Tea 15, Coffee unknown, Neither 5, Total 32.
Girls: Tea unknown, Coffee 10, Neither 3, Total 28.

(a)Work out the number of boys who prefer coffee.(2)

(b)Work out the number of girls who prefer tea.(2)

(c)Work out the total number of staff who prefer tea (boys and girls combined).(1)

7

A pie chart shows the favourite subject of 90 pupils. The sector angles are: Maths 140 degrees, Science 100 degrees, English 80 degrees, Art 40 degrees.

(a)Work out the number of pupils whose favourite subject is Science.(2)

(b)Work out the number of pupils whose favourite subject is Art.(1)

(c)How many more pupils chose Maths than chose English?(2)

8

A survey of 40 people asked their favourite drink. The results are: Tea 10, Coffee 14, Juice 8, Water 8. This data is to be shown on a pie chart.

(a)Work out the angle that should be used to represent Tea.(2)

(b)Work out the angle that should be used to represent Coffee.(1)

(c)Work out the combined angle used to represent Juice and Water together.(2)

9

Freya recorded the number of hours she spent revising and her test score (out of 100) for 8 different tests:
(1 hour, 42), (2 hours, 50), (3 hours, 55), (3 hours, 60), (4 hours, 65), (5 hours, 70), (6 hours, 78), (7 hours, 85).
She plotted these on a scatter graph and drew a line of best fit.

(a)Describe the type of correlation shown by the scatter graph.(1)

(b)Use the line of best fit to estimate the test score for a pupil who revises for 4.5 hours.(2)

(c)Explain why it would not be reliable to use this line of best fit to predict the test score of a pupil who revises for 15 hours.(1)

10

The grouped frequency table shows the time, t minutes, taken by 40 pupils to complete a puzzle.
0 < t ≤ 10: frequency 6
10 < t ≤ 20: frequency 10
20 < t ≤ 30: frequency 14
30 < t ≤ 40: frequency 8
40 < t ≤ 50: frequency 2

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

(b)Find the class that contains the median.(2)

11

The grouped frequency table shows the number of texts sent in a day by 40 pupils.
0-9 texts: frequency 8
10-19 texts: frequency 12
20-29 texts: frequency 15
30-39 texts: frequency 5

(a)Write down the midpoint of the 20-29 class.(1)

(b)Calculate an estimate for the mean number of texts sent.(3)

12

Two classes sat the same maths test out of 20 marks. Class 8A (taught by Miss Okafor) had mean score 14.2 and range 8. Class 8B (taught by Mr Singh) had mean score 15.6 and range 15.

(a)Which class had the higher average test score?(1)

(b)Which class was more consistent? Give a reason for your answer.(2)

(c)Comment on which class performed better overall, using both the mean and the range in your answer.(2)

13

The stem-and-leaf diagram shows the ages, in years, of people at a wedding reception.

1	2 5 8
2	0 3 3 6 9
3	1 4 7

Key: 1 | 2 means 12 years

(a)How many people are represented in the diagram?(1)

(b)Find the median age.(2)

(c)Find the range of the ages.(1)

14

The marks out of 50 for 10 students in a maths test are: 23, 31, 45, 22, 38, 41, 27, 33, 19, 44.

(a)Construct an ordered stem-and-leaf diagram to show this data, including a key.(3)

(b)Find the range of the marks.(1)

(c)Find the median mark.(2)

15

The grouped frequency table shows the distance, d km, travelled to school by 25 pupils.
0 ≤ d < 2: frequency 5
2 ≤ d < 4: frequency 9
4 ≤ d < 6: frequency 7
6 ≤ d < 8: frequency 3
8 ≤ d < 10: frequency 1
A frequency polygon is drawn by plotting a point at the midpoint of each class, at the height of its frequency.

(a)Write down the coordinates of the point plotted for the class 4 ≤ d < 6.(1)

(b)How many pupils travel less than 4 km to school?(2)

(c)Calculate an estimate for the mean distance travelled to school.(3)

16

A two-way table shows members of Riverside Gym by age group and membership type, where x is unknown.
Under 30: Standard = 2x, Premium = 15, Total = not given.
30 and over: Standard = 18, Premium = x, Total = not given.
The grand total of all members is 90.

(a)Form an equation in x and solve it.(3)

(b)Hence work out the number of Premium members aged 30 and over.(1)

(c)Work out the total number of Standard members.(2)

17

The mean of 6 numbers is 9. Five of the numbers are 5, 7, 10, 12 and 8.

(a)Find the sixth number.(3)

(b)A seventh number, 20, is added to the original six numbers. Work out the new mean of all seven numbers.(2)

18

Kwame drew a pie chart to show the pets owned by pupils in his year group. The Dog sector has an angle of 108 degrees, representing 27 pupils.

(a)Work out how many degrees on the pie chart represent 1 pupil.(2)

(b)The Cat sector has an angle of 72 degrees. Work out the number of pupils who own a cat.(2)

(c)Work out the total number of pupils surveyed for the pie chart.(2)

19

Aaliyah wants to find out how much time Year 8 pupils spend on homework each week. She surveys the first 20 pupils who arrive at school on a Monday morning.

(a)Give one reason why this sample may not be representative of all Year 8 pupils.(1)

(b)Suggest a better method Aaliyah could use to choose a sample of 20 pupils from Year 8, and explain why it would be an improvement.(2)

(c)Aaliyah's sample of 20 pupils had a mean of 3.5 hours of homework per week. There are 180 pupils in Year 8 altogether. Use her sample to estimate the total number of hours of homework done by Year 8 per week.(2)

20

Two local football teams recorded the number of goals scored per match over a season. Team A played 15 matches with a mean of 1.8 goals per match. Team B played 25 matches with a mean of 2.4 goals per match.

(a)Work out the total number of goals scored by Team A over the season.(1)

(b)Work out the total number of goals scored by Team B over the season.(1)

(c)Work out the mean number of goals scored per match for both teams combined.(3)

Mark scheme · KS3.M-S1 Statistics

Question 1

(a) B1 4 cao
(a) Answer: 4
(b) B1 6 cao
(b) Answer: 6
(c) B1 5 cao
(c) Answer: 5

Question 2

(a) B1 1 cao
(a) Answer: 1
(b) M1 Uses cumulative frequencies (5, 12, 16, 19, 20) to locate the 10th and 11th values
(b) A1 1 cao
(b) Answer: 1
(c) M1 Sum of (x times f) = 0x5 + 1x7 + 2x4 + 3x3 + 4x1 = 28, divided by 20
(c) A1 1.4 cao
(c) Answer: 1.4

Question 3

(a) B1 B cao
(a) Answer: B (Median)
(b) B1 States that 95 is an outlier/anomaly that would inflate the mean, giving a distorted impression of a typical salary, whereas the median is not affected by extreme values oe
(b) Answer: The mean is pulled up by the outlier of 95, so it does not represent a typical salary; the median is unaffected by extreme values.

Question 4

(a) B1 Football cao
(a) Answer: Football
(b) B1 6 cao
(b) Answer: 6
(c) M1 8/30 seen
(c) A1 4/15 cao
(c) Answer: 4/15

Question 5

(a) B1 12 cao
(a) Answer: 12
(b) B1 10 cao
(b) Answer: 10
(c) M1 12 + 10 + 16 + 6 (correct four values added, ft from parts a and b)
(c) A1 44 cao
(c) Answer: 44

Question 6

(a) M1 32 - 15 - 5
(a) A1 12 cao
(a) Answer: 12
(b) M1 28 - 10 - 3
(b) A1 15 cao
(b) Answer: 15
(c) B1 30 cao, ft from parts a and b
(c) Answer: 30

Question 7

(a) M1 100/360 x 90 (correct method)
(a) A1 25 cao
(a) Answer: 25
(b) B1 10 cao, ft using pupils per degree = 90/360 = 0.25
(b) Answer: 10
(c) M1 (140-80)/360 x 90, or Maths count minus English count
(c) A1 15 cao
(c) Answer: 15

Question 8

(a) M1 360/40 = 9 (degrees per person), then 10 x 9
(a) A1 90 degrees cao
(a) Answer: 90 degrees
(b) B1 126 degrees cao, ft using 9 degrees per person
(b) Answer: 126 degrees
(c) M1 (8+8) x 9, ft using 9 degrees per person
(c) A1 144 degrees cao
(c) Answer: 144 degrees

Question 9

(a) B1 Positive correlation cao
(a) Answer: Positive correlation
(b) M1 Reads/interpolates a value between the 4 hour (65) and 5 hour (70) points
(b) A1 awrt 65 to 70 (e.g. 67 or 67.5)
(b) Answer: awrt 67.5 (accept 65 to 70)
(c) B1 States that 15 hours is well outside the range of the data collected (max 7 hours), so extrapolating this far may not follow the same trend oe
(c) Answer: 15 hours is far beyond the range of the recorded data (which only goes up to 7 hours), so the trend may not continue in the same way; this is extrapolation.

Question 10

(a) B1 20 < t ≤ 30 cao
(a) Answer: 20 < t ≤ 30
(b) M1 Uses cumulative frequencies (6, 16, 30, 38, 40) to locate the 20th value
(b) A1 20 < t ≤ 30 cao
(b) Answer: 20 < t ≤ 30

Question 11

(a) B1 24.5 cao
(a) Answer: 24.5
(b) M1 Uses midpoints 4.5, 14.5, 24.5, 34.5
(b) M1 Sum of (frequency x midpoint) = 36+174+367.5+172.5 = 750
(b) A1 18.75 cao awrt 18.8
(b) Answer: 18.75 (awrt 18.8)

Question 12

(a) B1 Class 8B cao
(a) Answer: Class 8B
(b) B1 Class 8A cao
(b) B1 States that Class 8A has a smaller range (8 compared to 15), meaning less variation/spread in scores oe
(b) Answer: Class 8A, because its range (8) is smaller than Class 8B's range (15), showing less spread in scores.
(c) B1 States Class 8B scored higher on average (higher mean), so on the whole did better in the test
(c) B1 States Class 8A's results were more consistent/less spread out (smaller range), making Class 8A's performance more reliable/predictable oe
(c) Answer: Class 8B performed better on average (higher mean), but Class 8A's results were more consistent (smaller range), so neither class is entirely better; it depends which measure matters more.

Question 13

(a) B1 11 cao
(a) Answer: 11
(b) M1 Identifies the 6th value in the ordered list of 11 values
(b) A1 23 cao
(b) Answer: 23
(c) B1 25 cao
(c) Answer: 25

Question 14

(a) B1 Leaves grouped correctly by stem (1, 2, 3, 4)
(a) B1 Leaves ordered correctly within each stem
(a) B1 Correct key given, e.g. 1 | 9 means 19
(a) Answer:
1 9
2 2 3 7
3 1 3 8
4 1 4 5
Key: 1 | 9 means 19
(b) B1 26 cao, ft from part a
(b) Answer: 26
(c) M1 Identifies the 5th and 6th values (31 and 33), ft from part a
(c) A1 32 cao
(c) Answer: 32

1	9
2	2 3 7
3	1 3 8
4	1 4 5

Question 15

(a) B1 (5, 7) cao
(a) Answer: (5, 7)
(b) M1 5 + 9
(b) A1 14 cao
(b) Answer: 14
(c) M1 Uses midpoints 1, 3, 5, 7, 9
(c) M1 Sum of (frequency x midpoint) = 5+27+35+21+9 = 97
(c) A1 3.88 km cao awrt 3.9
(c) Answer: 3.88 km (awrt 3.9 km)

Question 16

(a) M1 2x + 18 + 15 + x = 90 oe (correct equation)
(a) M1 3x + 33 = 90 (correctly simplified)
(a) A1 x = 19 cao
(a) Answer: x = 19
(b) B1 19 cao, ft from part a
(b) Answer: 19
(c) M1 2(19) + 18, ft from part a
(c) A1 56 cao
(c) Answer: 56

Question 17

(a) M1 Total of all 6 numbers = 9 x 6 = 54
(a) M1 Sum of the 5 known numbers = 5+7+10+12+8 = 42
(a) A1 12 cao
(a) Answer: 12
(b) M1 (54 + 20)/7, ft from part a
(b) A1 awrt 10.6 cao (e.g. 10.57)
(b) Answer: awrt 10.6 (10.57 to 2dp)

Question 18

(a) M1 108/27 (correct method)
(a) A1 4 degrees cao
(a) Answer: 4 degrees
(b) M1 72/4, ft from part a
(b) A1 18 cao
(b) Answer: 18
(c) M1 360/4, ft from part a
(c) A1 90 cao
(c) Answer: 90

Question 19

(a) B1 Valid reason, e.g. only includes pupils who arrive early / travel a certain way, so may not reflect pupils who arrive later or differently oe
(a) Answer: Pupils who arrive first may share characteristics (e.g. live nearby, travel by car) that do not represent all Year 8 pupils, so the sample is biased.
(b) B1 Valid method, e.g. use a random number generator to select 20 names from the full Year 8 register oe
(b) B1 Valid reason it improves representativeness, e.g. every pupil has an equal chance of being chosen, reducing bias oe
(b) Answer: Use a random number generator on the complete Year 8 register to select 20 pupils; this gives every pupil an equal chance of being chosen, making the sample more representative.
(c) M1 3.5 x 180 (correct method)
(c) A1 630 hours cao
(c) Answer: 630 hours

Question 20

(a) B1 27 cao
(a) Answer: 27
(b) B1 60 cao
(b) Answer: 60
(c) M1 Total goals = 27 + 60 = 87, ft from parts a and b
(c) M1 Total matches = 15 + 25 = 40
(c) A1 2.175 cao awrt 2.18
(c) Answer: 2.175 (awrt 2.18)

Statistics - Worksheets, Questions and Revision

Next in this strand

KS3.M-S1 Statistics

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

Question 17

Question 18

Question 19

Question 20

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

Question 17

Question 18

Question 19

Question 20