9.7 Histograms

Subject: Cambridge IGCSE Mathematics (0580) | Level: Extended


2026 Syllabus Objectives

By the end of these notes, you should be able to:

  1. Draw and interpret histograms.
  2. Calculate with frequency density.
  3. Understand that the vertical axis of a histogram is always labelled Frequency Density, where:

Frequency Density = Frequency ÷ Class Width


What is a Histogram?

A histogram is a special type of bar chart used to display continuous data (data that can take any value within a range, like heights, weights, or speeds) that has been grouped into class intervals (also called groups or classes).

At first glance, a histogram looks like a bar chart — but there are some very important differences.

Histogram vs Bar Chart — Key Differences:

FeatureBar ChartHistogram
Type of dataDiscrete or non-numericalContinuous, grouped data
Gaps between barsYes — gaps between barsNo — bars always touch
What the height showsFrequency (directly)Frequency Density
What determines frequencyHeight of the barArea of the bar

The most important rule to remember is:

In a histogram, it is the area of each bar — not its height — that represents the frequency (how many data values are in that group).


What is Frequency Density?

Because histograms are often drawn with unequal class widths (some groups are wider than others), we cannot simply use frequency as the height of each bar. If we did, wider bars would look more important than they really are, which would be misleading.

Instead, we use frequency density as the height of each bar. This levels the playing field — it tells us how "packed" or "dense" the data is within each class interval, relative to how wide that interval is.

The Formula:

Frequency Density=FrequencyClass Width\boxed{Frequency\ Density = \dfrac{Frequency}{Class\ Width}}

  • Frequency = the number of data values in that class interval
  • Class Width = the size of the interval = upper boundary − lower boundary

And because the area of a bar = height × width:

Frequency=Frequency Density×Class WidthFrequency = Frequency\ Density \times Class\ Width

This means: Area of a bar = Frequency

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