GCSE · Cumulative frequency & box plots

Quartiles & the interquartile rangeExam-style questions

Why the quartiles are a quarter and three quarters of the way *through the data* rather than along the number line, how to find them from an ordered list and from a cumulative frequency curve, and why the interquartile range beats the range as a measure of spread.

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8 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
During an experiment, $11$ $11$ temperatures were recorded in degrees Celsius. For these temperatures:
- the median was $20\,^{\circ}$ C
- the lower quartile was $14\,^{\circ}$ C
- the upper quartile was $29\,^{\circ}$ C
The temperatures are converted to degrees Fahrenheit using $F = 1.8C + 32$ $F = 1.8 C + 32$ .

(a) Work out the median of the temperatures in degrees Fahrenheit.

(b) Work out the interquartile range of the temperatures in degrees Fahrenheit.
Level 5 · 5 marksTry it
2
A grower has two fields of sunflowers.

For the $120$ $120$ sunflowers in field P, the heights have
- lower quartile $136$ cm
- median $145$ cm
- upper quartile $155$ cm
The heights, in centimetres, of a sample of $9$ $9$ sunflowers from field Q are

$128, \quad 134, \quad 140, \quad 148, \quad 152, \quad 157, \quad 166, \quad 172, \quad 195$

(a) Write down the median height of the sample from field Q.

(b) Work out the interquartile range of the heights of the sample from field Q.

(c) Estimate how many of the $120$ $120$ sunflowers in field P are taller than $155$ $155$ cm.

(d) Compare the heights of the sunflowers in field P with the heights of the sample from field Q.
Level 5 · 7 marksTry it