Histograms

Histograms display continuous data in classes. Unlike bar charts, the area of each bar represents frequency, not the height. The y-axis shows frequency density.

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Key facts to remember

1Frequency density = frequency ÷ class width.
2Frequency = frequency density × class width (area of bar).
3There are no gaps between bars in a histogram.
4Classes do not need to be equal width.
5The y-axis is always labelled "frequency density", not "frequency".

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Formulas

Frequency density

FD = Frequency ÷ Class width

Frequency

Frequency = FD × Class width

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Worked examples

Example 1

A class 20 ≤ t < 30 has frequency 40. Calculate the frequency density.

Working

Class width = 30 − 20 = 10
Frequency density = 40 ÷ 10 = 4

AnswerFrequency density = 4

Example 2

A bar on a histogram has frequency density 3 and class width 5. Find the frequency.

Working

Frequency = FD × class width = 3 × 5 = 15

AnswerFrequency = 15

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Common mistakes

✗Reading the height of the bar as the frequency instead of using frequency density × class width.

✗Leaving gaps between bars (histograms show continuous data — no gaps).

✗Forgetting to label the y-axis as frequency density.

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Exam tips

✓Always add a "class width" and "FD" column to your table before drawing a histogram.

✓To find frequency from a histogram: frequency = height × width (area of bar).

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