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.

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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

The table shows the numbers of points scored by two basketball teams in their most recent games.

Team	Points scored in each game
Lions	$58, \; 71, \; 64, \; 72, \; 69, \; 62$
Tigers	$82, \; 75, \; x, \; 86, \; 79$

mean number of points scored by the Lions : mean number of points scored by the Tigers

= 6 : 7

Work out the value of

x

.

(5 marks)

Level 3 · 5 marksTry it

2
Eleven students each did as many press-ups as they could. Here are their results.

$22 \quad 15 \quad 30 \quad 18 \quad 15 \quad 27 \quad 12 \quad 15 \quad 24 \quad 20 \quad 19$

(a) Ravi says, "The median is $27$ , because $27$ is the middle number of the list."

Explain what is wrong with Ravi's method.

(b) Work out the median number of press-ups.

(c) Work out the mean number of press-ups. Give your answer correct to 1 decimal place.
Level 3 · 5 marksTry it
3
In their last seven matches, the numbers of goals scored by two teams were:

Ashby Town: $1, \; 2, \; 2, \; 3, \; 2, \; 4, \; 0$

Byrne United: $0, \; 5, \; 1, \; 6, \; 0, \; 2, \; 0$

(a) Show that the two teams have the same mean number of goals per match.

(b) Work out the range for each team.

(c) Use your answers to compare the goal scoring of the two teams.
Level 3 · 6 marksTry it