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
40 pupils took a test. The grouped frequency table shows their scores.
Score, $s$ Frequency
$0 < s \le 10$ 3
$10 < s \le 20$ 9
$20 < s \le 30$ 15
$30 < s \le 40$ 10
$40 < s \le 50$ 3
(a) Write down the cumulative frequency for each of the five classes.

(b) Write down the coordinates of the point that should be plotted for the class $30 < s \le 40$ .

(c) Explain what the cumulative frequency for the class $20 < s \le 30$ tells you about the pupils' scores.
Level 2 · 3 marksTry it
2
The cumulative frequency graph gives information about the times, in minutes, that $60$ students took to finish a puzzle.(a) Use the graph to find an estimate for the median time. (1 mark)
(b) Use the graph to find an estimate for the interquartile range of the times. (2 marks)
(c) Use the graph to find an estimate for the number of students who took longer than $25$ minutes. (1 mark)
Level 3 · 4 marksTry it
3
The table shows the amounts spent in one week by 80 shoppers at a supermarket.
Amount spent, $x$ (£) Frequency
$0 < x \le 20$ 8
$20 < x \le 40$ 22
$40 < x \le 60$ 26
$60 < x \le 80$ 17
$80 < x \le 100$ 7
(a) Write down the cumulative frequency for each of the five classes.

(b) Draw a cumulative frequency diagram for this information.

(c) Use your diagram to estimate the number of shoppers who spent £50 or less.
Level 3 · 5 marksTry it
4
The cumulative frequency diagram shows the number of hours that each of 100 students spent revising in one month.(a) Use the diagram to estimate the number of students who revised for 12 hours or less.

(b) $75$ of the students revised for less than $h$ hours. Use the diagram to estimate the value of $h$ .

(c) Explain why your answer to part (a) can only be an estimate.
Level 3 · 5 marksTry it
5
The cumulative frequency graph shows the times, in minutes, taken by $80$ students to travel to school.(a) Estimate the median time. [1]

(b) Estimate the interquartile range. [2]

(c) Estimate the number of students who took longer than $45$ minutes. [1]
Level 3 · 4 marksTry it

Score, $s$	Frequency
$0 < s \le 10$	3
$10 < s \le 20$	9
$20 < s \le 30$	15
$30 < s \le 40$	10
$40 < s \le 50$	3

Amount spent, $x$ (£)	Frequency
$0 < x \le 20$	8
$20 < x \le 40$	22
$40 < x \le 60$	26
$60 < x \le 80$	17
$80 < x \le 100$	7

6 more questions on cumulative frequency diagrams

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