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
Sasha recorded the time, in seconds, that each of $13$ people took to solve a puzzle. Here are her results:

$32, \quad 18, \quad 45, \quad 27, \quad 21, \quad 38, \quad 25, \quad 30, \quad 22, \quad 36, \quad 28, \quad 41, \quad 24$

(a) Work out the interquartile range of these times.

(b) Sasha then finds that the time of $45$ seconds was written down wrongly. It should have been $145$ seconds.

State the effect this correction has on the range and on the interquartile range of the times. Give a reason for your answer.
Level 3 · 5 marksTry it
2
The cumulative frequency diagram shows the time, in minutes, that each of $80$ patients waited to be seen at a clinic.(a) Use the diagram to estimate the median waiting time.

(b) Use the diagram to estimate the interquartile range of the waiting times.
Level 3 · 5 marksTry it