A-level · Data presentation

Measures of spread, standard deviation and codingExam-style questions

Range, interquartile and interpercentile range, and — the big one — variance and standard deviation from sums Σx and Σx² (and Σfx, Σfx²). Plus coding: how a linear change of variable rescales the mean and standard deviation, and how to decode back to the original data.

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

DifficultyAll Level 2 Level 3 Level 4

1
A radio station records the length, $x$ seconds, of each of the 40 advertisements that it broadcasts one morning.

The lengths are coded using

$y = \frac{x - 30}{5}$

and the coded data are summarised by

$\sum y = 26 \qquad \sum y^2 = 212$
(a) Find the mean of $x$

(2 marks)
(b) Find the standard deviation of $x$

(3 marks)

The station manager converts each length into minutes.
(c) Find the mean and the standard deviation of the lengths in minutes.

(2 marks)
Level 2 · 7 marksTry it
2
A data set has smallest value $5$ , largest value $30$ , lower quartile $12$ and upper quartile $20$ . Find the range and the interquartile range.
Level 2 · 2 marksTry it
3
The masses, $x$ grams, of $24$ eggs from a farm are summarised as follows.

$\sum (x - 60) = -36.0 \qquad \sum (x - 60)^2 = 471.6$

Find the variance of these masses and hence find the value of $\sum x^2$ .

(4 marks)
Level 2 · 4 marksTry it