What does the area of a bar on a histogram show?

the frequency. Area = frequency density × class width.

How is frequency density calculated?

frequency ÷ class width. It is the height of the bar.

What goes on the vertical axis of a histogram?

frequency density. That is what makes unequal class widths fair.

Histograms · Cambridge IGCSE Mathematics 0580 revision

In plain words

A histogram looks like a bar chart, but there's a difference that matters: it's the area of each bar, not its height, that shows the frequency. That lets it handle groups of different widths fairly.

Three things to know

The height of each bar is the frequency density: frequency ÷ class width.
So frequency = frequency density × class width, which is the area of the bar.
With equal class widths a histogram looks like a bar chart with no gaps. With unequal widths, always work with areas.

Worked example

A class from 10 to 30 has a frequency of 40. Find the frequency density.

Class width = 30 − 10 = 20.
Frequency density = frequency ÷ class width = 40 ÷ 20.
= 2.

Tips and tricks

The vertical axis is frequency density, not frequency. Label it.
To read a frequency off a histogram, multiply the height of the bar by its width.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Histograms: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What does the area of a bar on a histogram show?
- the class width
- the frequency (the answer)
- the frequency density
- the mean
Area = frequency density × class width.
How is frequency density calculated?
- frequency × class width
- frequency ÷ class width (the answer)
- class width ÷ frequency
- frequency + class width
It is the height of the bar.
A class has width 10 and frequency 50. What is its frequency density?
- 500
- 60
- 5 (the answer)
- 0.2
50 ÷ 10.
A bar has width 5 and height 4. What frequency does it show?
- 9
- 1.25
- 20 (the answer)
- 0.8
5 × 4.
What goes on the vertical axis of a histogram?
- frequency
- frequency density (the answer)
- class width
- cumulative frequency
That is what makes unequal class widths fair.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 7 marks. Write your answers on paper, then check them.

Histograms

Cambridge IGCSE Mathematics 0580 · 7 marks · papermunch.org

Name ______________________________ Date ______________

A class from 20 to 25 has a frequency of 30. Find its frequency density.[2]
Show answerHide answer
6. 30 ÷ 5.
I got this one
A bar on a histogram goes from 40 to 60 and has a height of 1.5. Find the frequency it represents.[2]
Show answerHide answer
30. 1.5 × 20.
I got this one
The class 0 to 10 has frequency 20 and the class 10 to 30 has frequency 20. Which bar is taller, and why?[3]
Show answerHide answer
The 0 to 10 bar. Its frequency density is 2; the other's is 1, because the same frequency is spread over twice the width.
I got this one

Answers: Histograms

1. 6. 30 ÷ 5.
2. 30. 1.5 × 20.
3. The 0 to 10 bar. Its frequency density is 2; the other's is 1, because the same frequency is spread over twice the width.