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Exam-Style Questions on Averages

Problems on Averages adapted from questions set in previous Mathematics exams.


GCSE Higher

The following table shows the time taken by fifty people to answer their emails one day.

Time, t minutes Number of people
0 < t ≤ 10 5
10 < t ≤ 20 12
20 < t ≤ 30 13
30 < t ≤ 40 15
40 < t ≤ 50 5

(a) In which class interval is the median?

(b) How many people took more than 20 minutes?

(c) What is the modal class interval?

(d) Find an estimate for the mean time taken showing all of your working.


GCSE Higher

A basket contains apples and oranges. The mean weight of the 9 apples in the basket is 265g. The mean weight of all 21 items of fruit in the basket is 290g.

Work out the mean weight of the oranges.


GCSE Higher

The following table show data collected by a researcher about the length of monitor lizards living in a park in Bangkok.

Length (cm)Frequency
\(0\lt l \le 50\)9
\(50\lt l \le 100\)13
\(100\lt l \le 150\)22
\(150\lt l \le 200\)19
\(200\lt l \le 250\)11
\(250\lt l \le 300\)3

(a) Which is the modal group?

(b) Calculate an estimate for the mean lizard length.

(c) The researcher claims that the range of lengths must lie between 2m and 3m. Explain how the researcher came to this conclusion.

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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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