The table shows the distribution of the masses of the actors in a theatre group. Draw a histogram to show the data. Mass in kilograms m Frequency 60 ⩽ m < 63 9 63 ⩽ m < 64 12 64 ⩽ m < 65 15 65 ⩽ m < 66 17 66 ⩽ m < 68 10 68 ⩽ m < 72 8

As the class widths are unequal, we have to find the frequency density of each class to draw the histogram. The frequency density table looks like: Mass in kilograms m Frequency Class width c w Frequency density f ÷ c w 60 ⩽ m < 63 9 3 9 3 = 3 63 ⩽ m < 64 12 1 12 1 = 12 64 ⩽ m < 65 15 1 15 1 = 15 65 ⩽ m < 66 17 1 17 1 = 17 66 ⩽ m < 68 10 2 10 2 = 5 68 ⩽ m < 72 8 4 8 4 = 2 The histogram is shown below. The mass in kilogram of the actors is represented in x - axis and corresponding frequency density is represented in y - axis.

A researcher took a questionnaire to 64 households. The grouped frequency table shows the time taken ( t minutes) by various homeowners to complete a questionnaire. Time taken ( t ) in minutes No. of home owners 0 ≤ t < 2 2 2 ≤ t < 3 18 3 ≤ t < 4 25 4 ≤ t < 6 12 6 ≤ t < 9 5 9 ≤ t < 15 2 Using a scale of 1 cm to represent 2 minutes , construct a horizontal axis for 0 ≤ t < 15 . Using a vertical scale of 1 cm per 2 units, draw a histogram to represent this data.

As the class widths are unequal, we have to find the frequency density of each class to draw the histogram. The frequency density table looks like: Time taken in seconds t frequency f Class width ( C W ) Frequency density f ÷ C W 0 ≤ t < 2 2 2 2 2 = 1 2 ≤ t < 3 18 1 18 1 = 18 3 ≤ t < 4 25 1 25 1 = 25 4 ≤ t < 6 12 2 12 2 = 6 6 ≤ t < 9 5 3 5 3 = 1 . 67 9 ≤ t < 15 2 6 2 6 = 1 3 = 0 . 33 The time in minutes is represented on x - axis and corresponding frequency density is represented on y - axis. The histogram is shown below.

E M B I B E

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 20 - Histograms and Frequency Distribution Diagrams>Exercise 20.2>Q 2

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Earn 100

The table shows the mass of young children visiting a clinic (to the nearest kg.). Draw a histogram to illustrate the data.

Mass in kilogram $(m)$ Frequency $(f)$

$6 ⩽ m < 9$ $9$

$9 ⩽ m < 12$ $12$

$12 ⩽ m < 18$ $30$

$18 ⩽ m < 21$ $15$

$21 ⩽ m < 30$ $18$

Important Questions on Histograms and Frequency Distribution Diagrams

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 20 - Histograms and Frequency Distribution Diagrams>Exercise 20.2>Q 3

The table shows the distribution of the masses of the actors in a theatre group. Draw a histogram to show the data.

Mass in kilograms $(m)$	Frequency
$60 ⩽ m < 63$	$9$
$63 ⩽ m < 64$	$12$
$64 ⩽ m < 65$	$15$
$65 ⩽ m < 66$	$17$
$66 ⩽ m < 68$	$10$
$68 ⩽ m < 72$	$8$

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 20 - Histograms and Frequency Distribution Diagrams>Examination practice>Q 2

A researcher took a questionnaire to $64$ households. The grouped frequency table shows the time taken ( $t$ minutes) by various homeowners to complete a questionnaire.

Time taken $(t)$ in minutes	No. of home owners
$0 \leq t < 2$	$2$
$2 \leq t < 3$	$18$
$3 \leq t < 4$	$25$
$4 \leq t < 6$	$12$
$6 \leq t < 9$	$5$
$9 \leq t < 15$	$2$