GCSE Maths (AQA) chapter 6: Statistics MCQs with answers
By Team Megalecture · Updated 4 Nov 2026
21 exam-style questions on Statistics, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.
S1–S3 Sampling and statistical diagrams10 questions
S4–S6 Averages, spread and scatter graphs11 questions
Ten Statistics questions with answers
Try each one, then open the answer. These ten stay the same; the test draws new ones every time.
1. A table shows times t minutes: 0 < t ≤ 10, frequency 4; 10 < t ≤ 20, frequency 10; 20 < t ≤ 30, frequency 6. What is an estimate of the mean?
A
106.7 minutes
B
16 minutes
C
15 minutes
D
20 minutes
Show answer
Answer: B. Use midpoints: 4 × 5 + 10 × 15 + 6 × 25 = 20 + 150 + 150 = 320, and 320 ÷ 20 = 16 minutes. Dividing by 3 (the number of classes) gives 106.7.
2. The mean of five numbers is 12. A sixth number is added and the mean becomes 13. What is the sixth number?
A
18
B
13
C
1
D
78
Show answer
Answer: A. The totals are 5 × 12 = 60 and 6 × 13 = 78, so the sixth number is 78 − 60 = 18.
3. Find the interquartile range of 2, 4, 5, 7, 8, 10, 11, 13, 15, 16, 20.
A
18
B
9
C
10
D
8
Show answer
Answer: C. There are 11 values. The lower quartile is the 3rd value (5) and the upper quartile is the 9th (15), so IQR = 15 − 5 = 10. 18 is the range.
4. In a survey of 72 people, 20 chose tea. What angle should the tea sector be in a pie chart?
A
20°
B
72°
C
100°
D
260°
Show answer
Answer: C. Each person is 360° ÷ 72 = 5°, so 20 people is 100°. 20° gives one degree per person.
5. In a pie chart, the sector for football has angle 135° and represents 45 students. How many students are in the survey?
A
135
B
360
C
60
D
120
Show answer
Answer: D. 135° is 45 students, so 1 student is 3°, and 360° ÷ 3° = 120 students.
6. In a grouped frequency table, the class 10 < t ≤ 30 has frequency 24. What is its frequency density for a histogram?
A
0.83
B
1.2
C
480
D
2.4
Show answer
Answer: B. Frequency density = frequency ÷ class width = 24 ÷ 20 = 1.2. Dividing by 10 (the lower bound) instead of the width gives 2.4.
7. A data set has lower quartile 20 and upper quartile 30. An outlier is more than 1.5 × IQR above the upper quartile. Which value is an outlier?
A
46
B
44
C
40
D
35
Show answer
Answer: A. IQR = 10, so the limit is 30 + 1.5 × 10 = 45. Only 46 is above 45.
8. Why is the mean calculated from a grouped frequency table only an estimate?
A
the frequencies might be wrong
B
the mean must be a whole number
C
the exact values in each class are not known, so midpoints are used
D
the classes are too wide to add
Show answer
Answer: C. Grouping loses the individual values, so each value is assumed to be at its class midpoint.
9. To estimate the average homework time of all students in a school, Ravi asks the 20 students in his own class. Why might his sample be biased?
A
a sample of 20 is always too large
B
one class may not represent all year groups in the school
C
sampling always gives the exact population value
D
students should be chosen in alphabetical order
Show answer
Answer: B. His class is one year group, which may get more or less homework than others, so it may not represent the whole population. A random sample from the whole school would be better.
10. Which diagram is most suitable for showing monthly sales of a shop over two years?
A
a pie chart
B
a time series line graph
C
a histogram
D
a scatter graph
Show answer
Answer: B. Data collected at regular time intervals is shown with a time series graph, which shows trends and seasonal patterns.
21, each with the answer and a short explanation, across 2 topics: S1–S3 Sampling and statistical diagrams, S4–S6 Averages, spread and scatter graphs. Every chapter test draws ten of them, so you can take it many times.
Is the GCSE Maths (AQA) chapter 6 test free?
Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.
How is the chapter test marked?
The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.
