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

1
(a) The mean of eight numbers is $21$ .

One of the eight numbers is removed. The mean of the remaining seven numbers is $22$ .

Work out the number that was removed.

(b) The mean of five numbers is $12$ .

A sixth number is then included, and the mean of all six numbers is $13$ .

Work out the sixth number.
Level 5 · 6 marksTry it
2
Thirty students took a test. The mean mark for all thirty students was $62$ .

The twelve girls in the group had a mean mark of $65$ .

(a) Work out the mean mark of the eighteen boys.

(b) Two more students then take the same test. The mean mark of all thirty-two students is $62.5$ .

Work out the mean mark of the two extra students.
Level 5 · 7 marksTry it