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
Class A and class B were each given the same puzzle to solve.

The cumulative frequency diagram shows the time, in seconds, taken by each of the $60$ pupils in class A.(a) Use the diagram to estimate the median time for class A.

(b) Use the diagram to estimate the interquartile range of the times for class A.

(c) For class B, the median time was $34$ seconds and the interquartile range was $21$ seconds.

Compare the times taken by class A with the times taken by class B.
Level 4 · 7 marksTry it
2
Nine numbers are written in order of size:

$4, \quad 7, \quad 9, \quad 11, \quad 14, \quad 16, \quad x, \quad 21, \quad 28$

The interquartile range of the nine numbers is $12$ .

(a) Write down the median of the nine numbers.

(b) Work out the value of $x$ .
Level 4 · 4 marksTry it
3
A shop recorded the amount spent by each of $15$ customers one morning. The amounts, in pounds, were:

$12, \quad 27, \quad 5, \quad 17, \quad 9, \quad 68, \quad 14, \quad 3, \quad 22, \quad 8, \quad 19, \quad 6, \quad 24, \quad 11, \quad 15$

(a) Work out the interquartile range of the amounts spent.

(b) Ravi says, "The range of the amounts is £ $65$ , so the amounts spent that morning were very spread out."

Explain why the interquartile range gives a more reliable picture of the spread of these amounts than the range does.
Level 4 · 5 marksTry it