GCSE · Cumulative frequency & box plots

Cumulative frequency diagramsExam-style questions

How to build a running total from a grouped frequency table, why every point is plotted at the upper class boundary rather than the midpoint, and how to read estimates off the curve in both directions.

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11 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

120

runners took part in a fun run.

The table gives information about the times, in minutes, that they took to finish.

Time ( $t$ minutes)	Frequency
$20 < t \le 25$	$8$
$25 < t \le 30$	$22$
$30 < t \le 35$	$46$
$35 < t \le 40$	$30$
$40 < t \le 45$	$14$

(a) Complete the cumulative frequency table.

Time ( $t$ minutes)	Cumulative frequency
$20 < t \le 25$
$20 < t \le 30$
$20 < t \le 35$
$20 < t \le 40$
$20 < t \le 45$

(1 mark)
(b) On the grid, draw a cumulative frequency graph for your table.(2 marks)
(c) Use your graph to find an estimate for the interquartile range.

(2 marks)
(d) Use your graph to find an estimate for the number of these runners who took more than

38

minutes.

(2 marks)

Level 4 · 7 marksTry it