A-level · Data presentation

Measures of location — mean, median, mode and quartilesExam-style questions

The three averages (mean, median, mode) and the other measures of location (quartiles and percentiles); how to find them from a list and from a frequency table; and how to estimate the median and quartiles of grouped continuous data by linear interpolation.

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11 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
The times, $t$ $t$ minutes, taken by $60$ $60$ runners to complete a race are summarised below.
- $20 \le t < 24$ : frequency $8$
- $24 \le t < 26$ : frequency $14$
- $26 \le t < 30$ : frequency $20$
- $30 \le t < 38$ : frequency $18$
(a) Use linear interpolation to estimate the median time. (2 marks)
(b) Estimate the mean time. (2 marks)
(c) Estimate the standard deviation of the times. You may use $\sum ft^2 = 49110$ $\sum f t^{2} = 49110$ . (2 marks)
(d) Describe, with a reason, the skewness of the distribution. (1 mark)
Level 3 · 7 marksTry it
2
The table shows the number of pets owned by $20$ people.

$\begin{array}{c|cccc} \text{pets } x & 1 & 2 & 3 & 4 \\\\ \hline \text{frequency} & 6 & 9 & 3 & 2 \end{array}$

Find the mean number of pets.
Level 3 · 2 marksTry it
3
The grouped table shows the masses of $40$ parcels.

$\begin{array}{c|cccc} \text{mass (kg)} & 0\text{–}10 & 10\text{–}20 & 20\text{–}30 & 30\text{–}40 \\\\ \hline \text{frequency} & 8 & 12 & 15 & 5 \end{array}$

Estimate the mean mass.
Level 3 · 2 marksTry it
4
For the grouped data

$\begin{array}{c|cccc} \text{value} & 0\text{–}10 & 10\text{–}20 & 20\text{–}30 & 30\text{–}40 \\\\ \hline \text{frequency} & 8 & 15 & 12 & 5 \end{array}$

use linear interpolation to estimate the median.
Level 3 · 3 marksTry it
5
The mean of the five numbers $x, 10, 14, 16, 25$ is $16$ . Find the value of $x$ .
Level 3 · 2 marksTry it

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