Histograms [H]

This lesson covers histograms — a Higher tier topic on the AQA GCSE Mathematics specification. Unlike bar charts, histograms use frequency density on the vertical axis and can have bars of unequal width. Understanding how to draw, read, and interpret histograms is essential for the Higher paper.

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How Histograms Differ from Bar Charts

Feature	Bar Chart	Histogram
Vertical axis	Frequency	Frequency density
Bar width	All the same	Can vary (based on class width)
Gaps between bars	Yes (for discrete/categorical data)	No gaps
What represents the frequency	Height of the bar	Area of the bar
Data type	Discrete or categorical	Continuous

The crucial difference is that in a histogram, the area of each bar represents the frequency, not the height.

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Frequency Density

Frequency density = frequency / class width

Or equivalently:

Frequency = frequency density x class width

The class width is the difference between the upper and lower boundaries of the class interval.

Worked Example — Calculating Frequency Density