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
Here are the ages, in years, of the $11$ members of a chess club, written in order:

$9, \quad 11, \quad 12, \quad 14, \quad 14, \quad 15, \quad 17, \quad 18, \quad 20, \quad 21, \quad 26$

(a) Write down the median age.

(b) Work out the interquartile range of the ages.
Level 2 · 4 marksTry it
2
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
3
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
4
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
5
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

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