Cumulative Frequency | CIE IGCSE Maths: Extended Topic Questions 2025

1

1 mark

Harry grows tomatoes.
This year he put his tomato plants into two groups, group A and group B.

Harry gave fertiliser to the tomato plants in group A.
He did not give fertiliser to the tomato plants in group B.

Harry weighed 60 tomatoes from group A.
The cumulative frequency graph shows some information about these weights.

q4a-hrd-6-4-cumulative-frequency-edexcel-gcse-maths

Use the graph to find an estimate for the median weight.

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1

7 marks

A student measures the height, $h$ cm, of each of 400 plants.

The cumulative frequency diagram shows the results.

q16a-paper2-spec2025-cie-igcse-further-maths

Use the diagram to find an estimate for

i)

the median

.......................................... cm[1]

ii)

the interquartile range

.......................................... cm[2]

iii)

the 80th percentile

.......................................... cm[2]

iv)

the number of plants with a height greater than 60cm.

[2]

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1a

2 marks

There are $200$ workers at a factory.
The cumulative frequency table gives information about their ages.

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

On the grid opposite, draw a cumulative frequency graph for this information.

q6a-easy-6-4-cumulative-frequency-edexcel-gcse-maths

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1b

2 marks

Graham says,
" $10$ % of workers at the factory are older than $65$ "

Is Graham correct?
You must show how you get your answer.

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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					$20$

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

Mark ( $m$ )	Cumulative frequency
$0 < m ⩽ 20$
$0 < m ⩽ 40$
$0 < m ⩽ 60$
$0 < m ⩽ 80$
$0 < m ⩽ 100$
$0 < m ⩽ 120$

Amount $($ m)$	$0 < m \leq 5$	$5 < m \leq 10$	$10 < m \leq 20$	$20 < m \leq 30$	$30 < m \leq 50$
Frequency	16	38	30	9	7

Amount $($ m)$	$m \leq 5$	$m \leq 10$	$m \leq 20$	$m \leq 30$	$m \leq 50$
Cumulative Frequency	16				100

Time ( $m$ minutes)	$0 < m \leq 10$	$10 < m \leq 40$	$40 < m \leq 60$	$60 < m \leq 90$	$90 < m \leq 100$	$100 < m \leq 120$
Frequency	3	39	43	55	11	9

Time ( $m$ minutes)	$m \leq 10$	$m \leq 40$	$m \leq 60$	$m \leq 90$	$m \leq 100$	$m \leq 120$
Cumulative frequency	3	42

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

Speed ( $v$ km/h)	$0 < v \leq 20$	$20 < v \leq 40$	$40 < v \leq 45$	$45 < v \leq 50$	$50 < v \leq 60$	$60 < v \leq 80$
Frequency	$16$	$34$	$62$	$58$	$26$	$4$

Speed ( $v$ km/h)	$v \leq 20$	$v \leq 40$	$v \leq 45$	$v \leq 50$	$v \leq 60$	$v \leq 80$
Cumulative Frequency	$16$	$50$			$196$	$200$

Height ( $h$ metres)	$1.3 < h \leq 1.4$	$1.4 < h \leq 1.5$	$1.5 < h \leq 1.6$	$1.6 < h \leq 1.7$	$1.7 < h \leq 1.8$	$1.8 < h \leq 1.9$
Frequency	7	18	30	24	27	14

Cumulative Frequency (CIE IGCSE Maths: Extended)

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