Drawing histograms

The Maths Habit Handout to print

Beach A has 60 people on 30 m of sand.
Beach B has 45 people on 15 m of sand.

Which beach is more crowded?

B: 3 people per metre, A has 2

02468101201234567Time (minutes)People per minute

12 people took between 0 and 4 minutes. Each square is one person. How tall is their bar?

3: twelve squares, 4 wide

02468101201234567Time (minutes)People per minute

12 more people took between 4 and 6 minutes. How tall is their bar?

6: the same 12 people in half the width

02468101201234567Time (minutes)People per minute

18 people took between 6 and 12 minutes. How tall is their bar?

18 ÷ 6 = 3

Area = frequency.
Height
= frequency ÷ class width

Class width
How wide a class is: its upper bound take away its lower bound.
Frequency density
Frequency divided by class width. It is the height of the bar.

frequency density= frequency ÷ class width

What is the class width?

20 < h ≤ 35 15

Frequency 12, class width 5.
What is the frequency density?

2.4

The class 30 < t ≤ 50 has a frequency of 9.
What is the frequency density?

0.45

Work out the frequency density.

  1. 0 < x ≤ 5, frequency 20

    4

  2. 10 < x ≤ 30, frequency 14

    0.7

  3. 50 < x ≤ 55, frequency 12

    2.4

  4. 100 < x ≤ 150, frequency 30

    0.6

  5. 2.5 < x ≤ 4, frequency 9

    6
Mass (kg)FrequencyClass
width		Frequency
density
0 < m ≤ 4641.5
4 < m ≤ 6924.5
6 < m ≤ 8723.5
8 < m ≤ 14661
Length (cm)FrequencyClass
width		Frequency
density
0 < x ≤ 2010
20 < x ≤ 3012
30 < x ≤ 359
35 < x ≤ 506
Mass (kg)FrequencyClass
width		Frequency
density
0 < m ≤ 46
4 < m ≤ 69
6 < m ≤ 87
8 < m ≤ 146
Age (years)FrequencyClass
width		Frequency
density
0 < a ≤ 107100.7
10 < a ≤ 15851.6
15 < a ≤ 2512101.2
25 < a ≤ 456200.3

Which bar shows the most people?

The first: 20 people. The area shows the frequency, not the height.

Histograms worksheet, page 1

Answer sheet

  1. Two classes have the same frequency. One class is twice as wide as the other. What can you say about the heights of their bars?

    The wider bar is half as tall

  2. A bar is 5 wide and 2.4 high. Sam says its frequency is 2.4. Is he right?

    No: 5 × 2.4 = 12

  1. The class 10 < t ≤ 25 has a frequency of 12. Work out the frequency density.

    0.8

  2. The class 20 < m ≤ 40 has a frequency of 16. How tall is its bar?

    Height 0.8
    00.40.81.21.62Frequency density0102030405060Mass, m (kg)

  3. A bar is 5 wide and 3.6 tall. Sam says its frequency is 3.6. Find the correct frequency.

    18
Exit tickets to print