Cumulative Frequency Diagrams

1 mark

The table shows information about the speeds of $100$ lorries.

Speed ( $s$ ) in km/h	Frequency
$0 < s ⩽ 20$	$2$
$20 < s ⩽ 40$	$9$
$40 < s ⩽ 60$	$23$
$60 < s ⩽ 80$	$31$
$80 < s ⩽ 100$	$27$
$100 < s ⩽ 120$	$8$

Complete the cumulative frequency table for this information.

Speed ( $s$ ) in km/h	Cumulative frequency
$0 < s ⩽ 20$	$2$
$0 < s ⩽ 40$
$0 < s ⩽ 60$
$0 < s ⩽ 80$
$0 < s ⩽ 100$
$0 < s ⩽ 120$

How did you do?

2 marks

On the grid, draw a cumulative frequency graph for your table.

q5a-easy-6-4-cumulative-frequency-edexcel-gcse-maths

How did you do?

2 marks

Find an estimate for the number of lorries with a speed of more than $90$ km/h.

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2 marks

The cumulative frequency graphs show information about the times taken by 100 male runners and by 100 female runners to finish the London marathon.

q6-hrd-6-4-cumulative-frequency-edexcel-gcse-maths

A male runner is chosen at random.

Find an estimate for the probability that this runner took less than 4 hours to finish the London marathon.

How did you do?

4 marks

Use medians and interquartile ranges to compare the distribution of the times taken by the male runners with the distribution of the times taken by the female runners.

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1 mark

Charlotte grows some potatoes.

The table shows information about the weights of her potatoes.

Weight ( $w$ grams)	Frequency
$100 < w ⩽ 120$	$5$
$120 < w ⩽ 140$	$25$
$140 < w ⩽ 160$	$30$
$160 < w ⩽ 180$	$15$
$180 < w ⩽ 200$	$5$

Complete the cumulative frequency table.

Weight ( $w$ grams)	Cumulative frequency
$100 < w ⩽ 120$
$100 < w ⩽ 140$
$100 < w ⩽ 160$
$100 < w ⩽ 180$
$100 < w ⩽ 200$

How did you do?

2 marks

On the grid opposite, draw a cumulative frequency graph for your table.

x_jTmCoZ_q7b-medium-6-4-cumulative-frequency-edexcel-gcse-maths

How did you do?

2 marks

Use your graph to find an estimate for the interquartile range.

How did you do?

3 marks

Use your graph to find an estimate for the percentage of Charlotte's potatoes with a weight less than 150 grams.

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Age ( $a$ years)	Cumulative frequency
$0 < a ⩽ 20$	$25$
$0 < a ⩽ 30$	$70$
$0 < a ⩽ 40$	$138$
$0 < a ⩽ 50$	$175$
$0 < a ⩽ 60$	$186$
$0 < a ⩽ 70$	$194$
$0 < a ⩽ 80$	$200$

Weight ( $w$ kg)	Frequency
$0 < w ⩽ 1$	$19$
$1 < w ⩽ 2$	$17$
$2 < w ⩽ 3$	$15$
$3 < w ⩽ 4$	$12$
$4 < w ⩽ 5$	$10$
$5 < w ⩽ 6$	$7$

Weight ( $w$ kg)	Cumulative frequency
$0 < w ⩽ 1$
$0 < w ⩽ 2$
$0 < w ⩽ 3$
$0 < w ⩽ 4$
$0 < w ⩽ 5$
$0 < w ⩽ 6$

Mark ( $m$ )	Frequency
$0 < m ⩽ 20$	$40$
$20 < m ⩽ 40$	$70$
$40 < m ⩽ 60$	$60$
$60 < m ⩽ 80$	$15$
$80 < m ⩽ 100$	$10$
$100 < m ⩽ 120$	$5$

Edexcel IGCSE Maths

Topic Questions

Cumulative Frequency Diagrams

Time ( $t$ minutes)	Frequency
$0 < t ⩽ 20$	$5$
$20 < t ⩽ 40$	$30$
$40 < t ⩽ 60$	$20$
$60 < t ⩽ 80$	$15$
$80 < t ⩽ 100$	$8$
$100 < t ⩽ 120$	$2$

Mass ( $p$ grams)	$0 < p \leq 50$	$50 < p \leq 100$	$100 < p \leq 125$	$125 < p \leq 150$	$150 < p \leq 200$
Frequency	$2$	$5$	$4$	$6$	$3$

Mass ( $p$ grams)	$p \leq 50$	$p \leq 100$	$p \leq 125$	$p \leq 150$	$p \leq 200$
Cumulative frequency					$20$

Distance travelled (d km)	Cumulative frequency
$0 < d ⩽ 5$	17
$0 < d ⩽ 10$	32
$0 < d ⩽ 15$	57
$0 < d ⩽ 20$	70
$0 < d ⩽ 25$	76
$0 < d ⩽ 30$	80

Miles per gallon, $x$	Frequency
$40 < x ⩽ 50$	6
$50 < x ⩽ 60$	16
$60 < x ⩽ 70$	28
$70 < x ⩽ 80$	10

Mark,	Frequency
	9
$50 < m ⩽ 60$	16
$60 < m ⩽ 70$	20
$70 < m ⩽ 80$	8
$80 < m ⩽ 90$	7

Annual salary, p (£ thousands)	Cumulative frequency
$p ⩽ 10$
$p ⩽ 20$
$p ⩽ 30$
$p ⩽ 50$
$p ⩽ 80$

Height ( $x$ cm)	Number of students
$140 < x ⩽ 150$	$4$
$150 < x ⩽ 160$	$5$
$160 < x ⩽ 170$	$16$
$170 < x ⩽ 180$	$27$
$180 < x ⩽ 190$	$5$
$190 < x ⩽ 200$	$3$

Weekly wage( $£ x$ )	Frequency
$100 < x ⩽ 200$	$8$
$200 < x ⩽ 300$	$15$
$300 < x ⩽ 400$	$30$
$400 < x ⩽ 500$	$17$
$500 < x ⩽ 600$	$7$
$600 < x ⩽ 700$	$3$

Time ( $t$ minutes)	Frequency
$20 < t ⩽ 30$	$4$
$30 < t ⩽ 40$	$16$
$40 < t ⩽ 50$	$36$
$50 < t ⩽ 60$	$24$
$60 < t ⩽ 70$	$14$
$70 < t ⩽ 80$	$6$

Time (t minutes)	Frequency
$25 < t ⩽ 35$	12
$35 < t ⩽ 45$	24
$45 < t ⩽ 55$	28
$55 < t ⩽ 65$	12
$65 < t ⩽ 75$	10
$75 < t ⩽ 85$	4

Time (t minutes)	Cumulative frequency
$25 < t ⩽ 35$	12
$25 < t ⩽ 45$
$25 < t ⩽ 55$
$25 < t ⩽ 65$
$25 < t ⩽ 75$
$25 < t ⩽ 85$

Mark ( $m$ )	Cumulative frequency
$0 < m ⩽ 10$	$8$
$0 < m ⩽ 20$	$23$
$0 < m ⩽ 30$	$48$
$0 < m ⩽ 40$	$65$
$0 < m ⩽ 50$	$74$
$0 < m ⩽ 60$	$80$

Time taken (t minutes)	Frequency
$0 < t ⩽ 10$	7
$10 < t ⩽ 20$	26
$20 < t ⩽ 30$	24
$30 < t ⩽ 40$	14
$40 < t ⩽ 50$	7
$50 < t ⩽ 60$	2

Time waited ( $t$ minutes)	Frequency
$0 < t ⩽ 5$	8
$5 < t ⩽ 10$	15
$10 < t ⩽ 15$	17
$15 < t ⩽ 20$	28
$20 < t ⩽ 25$	33
$25 < t ⩽ 30$	19