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Subject: Cambridge IGCSE Mathematics (0580) | Level: Extended
By the end of these notes, you should be able to:
Frequency Density = Frequency ÷ Class Width
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:
| Feature | Bar Chart | Histogram |
|---|---|---|
| Type of data | Discrete or non-numerical | Continuous, grouped data |
| Gaps between bars | Yes — gaps between bars | No — bars always touch |
| What the height shows | Frequency (directly) | Frequency Density |
| What determines frequency | Height of the bar | Area 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).
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=Class WidthFrequency
And because the area of a bar = height × width:
Frequency=Frequency Density×Class Width
This means: Area of a bar = Frequency
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