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.

Start practising Read the lesson

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 midwife records the birth mass, $w$ kg, of each of the first 15 babies born at a maternity unit in January. The masses are coded using

$x = 10(w - 3)$

and the coded data are summarised by

$\sum x = 24 \qquad \sum x^2 = 330$
(a) Find the mean of $w$

(3 marks)
(b) Find the standard deviation of $w$

(3 marks)

The midwife then includes the 16th baby born at the unit in January. With this baby included,

$\sum x = 30$
(c) Find

(i) the birth mass of the 16th baby,

(ii) the value of the standard deviation of $x$ when all 16 babies are included.

(4 marks)
Level 4 · 10 marksTry it