GCSE · Averages & range

Mean, median, mode & rangeExam-style questions

The three averages and the range from a raw list — what each one is actually for, why the median needs the data sorted first, why the range is a measure of spread and not an average, and why every reverse-mean question is really a question about the total.

Start practising Read the lesson

14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Seven pupils each solved a puzzle. Their times, in seconds, were:

$32 \quad 41 \quad 38 \quad 35 \quad 44 \quad 39 \quad 36$

(a) Work out the median of these seven times.

(b) Write down the range of these seven times.

An eighth pupil then solves the puzzle in $115$ seconds.

(c) Work out the median of all eight times.

(d) Write down the range of all eight times.

(e) The mean of all eight times is $47.5$ seconds. Explain why the median is a better description of a typical time for these eight pupils than the mean is.
Level 4 · 7 marksTry it
2
A small company has nine employees. Their annual salaries are:

£19 000, £21 000, £22 000, £21 000, £24 000, £23 000, £21 000, £26 000, £120 000

(a) Work out the mean salary.

(b) Work out the median salary.

(c) The owner wants to quote a single figure as "a typical salary at this company". State which of the mean and the median is the fairer figure to quote, and give a reason for your answer.

(d) The company also records the department each of the nine employees works in:

Sales, Sales, Admin, Sales, Workshop, Admin, Sales, Workshop, Admin

Write down the modal department, and explain why neither the mean nor the median can be used for this data.
Level 4 · 8 marksTry it
3
Here are five numbers.

$12 \quad 7 \quad 15 \quad 9 \quad x$

The mean of the five numbers is $13$ .

(a) Work out the value of $x$ .

(b) Work out the median of the five numbers.
Level 4 · 5 marksTry it