Histograms | CIE IGCSE Maths: Extended Paper 2 & Paper 4 2023

1

2 marks

The height, $h$ cm, of each of 120 plants is measured.
The frequency table shows this information.

Height, h cm	$0 < h \leq 10$	$10 < h \leq 20$	$20 < h \leq 30$	$30 < h \leq 50$
Frequency	2	18	62	38

A histogram is drawn to show the information in the frequency table.
The height of the bar representing the interval $10 < h \leq 20$ is 7.2 cm.

Calculate the height of the bar representing the interval $30 < h \leq 50$ .

............................................ cm

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1

2 marks

The frequency table shows the times, $t$ minutes, each of 100 children spent exercising in one week.

Time ( $t$ minutes)	$0 < t \leq 60$	$60 < t \leq 100$	$100 < t \leq 160$	$160 < t \leq 220$	$220 < t \leq 320$
Frequency	41	24	23	8	4

A histogram is drawn to show the information in the frequency table.
The height of the bar for the interval $60 < t \leq 100$ is 10.8 cm.

Calculate the height of the bar for the interval $160 < t \leq 220$ .

............................................ cm

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1

6 marks

cie-igcse-2019-oct-nov-p4-tz1-q6c

Calculate an estimate of the mean.

............................................... kg

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Time ( $t$ seconds)	$0 < t \leq 10$	$10 < t \leq 15$	$15 < t \leq 20$	$20 < t \leq 40$	$40 < t \leq 75$
Frequency	$9$	$18$	$22$	$30$	$21$

Time ( $t$ seconds)	$0 < t \leq 10$	$10 < t \leq 15$	$15 < t \leq 20$	$20 < t \leq 40$	$40 < t \leq 75$
Height of bar (cm)	$3.6$	$14.4$	$17.6$

Time ( $t$ minutes)	$0 < t \leq 10$	$10 < t \leq 15$	$15 < t \leq 20$	$20 < t \leq 40$
Frequency	7	19	$16$	$8$

Age ( $y$ years)	$15 < y \leq 25$	$25 < y \leq 30$	$30 < y \leq 50$	$50 < y \leq 80$
Number of people	35	32	44	12

CIE IGCSE Maths: Extended

Topic Questions

4.6 Histograms

Size	Small	Medium	Large
Mass ( $m$ grams)	$46 < m \leq 52$	$52 < m \leq 62$	$62 < m \leq 80$
Number of eggs sold	$78$	$180$	$162$

Speed ( $v$ km/h)	$0 < v \leq 40$	$40 < v \leq 50$	$50 < v \leq 80$
Frequency	$50$	$120$	$30$

Area ( $A$ m²)	$20 < A \leq 60$	$60 < A \leq 100$	$100 < A \leq 150$	$150 < A \leq 250$
Frequency	32	64	80	24

Temperature (t °C)	$0 < t \leq 10$	$10 < t \leq 15$	$15 < t \leq 20$	$20 < t \leq 25$	$25 < t \leq 35$
Number of days	50	85	100	120	10

Time ( $t$ seconds)	$20 < t \leq 30$	$30 < t \leq 35$	$35 < t \leq 40$	$40 < t \leq 60$	$60 < t \leq 100$
Frequency	38	27	21	16	18

Mass ( $m$ kg)	$0 < m \leq 4$	$4 < m \leq 6$	$6 < m \leq 7$	$7 < m \leq 10$
Frequency	$32$			$42$
Height of bar on histogram (cm)	$1.6$	$2$	$1.2$	$2.8$

Height ( $h$ cm)	$60 < h \leq 70$	$70 < h \leq 90$	$90 < h \leq 100$	$100 < h \leq 110$	$110 < h \leq 115$	$115 < h \leq 125$
Frequency	8	26	35	67	28	16

Time (T minutes)	Number of people
$10 < T \leq 30$	16
$30 < T \leq 40$	18
$40 < T \leq 45$	22
$45 < T \leq 50$	40
$50 < T \leq 60$	21
$60 < T \leq 70$	3

Mass ( $x$ tonnes)	$100 < x \leq 200$	$200 < x \leq 250$	$250 < x \leq 300$	$300 < x \leq 500$
Frequency	8	20	12	12

Time ( $t$ minutes)	$0 < t \leq 5$	$5 < t \leq 15$	$15 < t \leq 30$	$30 < t \leq 50$	$50 < t \leq 70$
Number of people	$6$		$27$		$10$

Height( $h$ cm)	Frequency
$140 < h ⩽ 150$	$15$
$150 < h ⩽ 155$	$30$
$155 < h ⩽ 160$	$51$
$160 < h ⩽ 165$	$36$
$165 < h ⩽ 180$	$18$