Frequency density
Objective. Interpret unequal class widths using frequency density.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Frequency density is used in histograms to fairly represent data grouped into classes of unequal width, calculated as frequency ÷ class width. Unlike a standard bar chart, a histogram's bar height is not the frequency itself but this frequency density, so that the bar's area (not height) represents the frequency of that group. For example, a class of width 10 with a frequency of 30 has a frequency density of 30 ÷ 10 = 3, which becomes the height of that bar on the histogram. This method ensures that groups with wider class widths are not visually exaggerated compared with narrower groups containing the same frequency.
Worked example
A class interval of 20–35 has a frequency of 18. Calculate the frequency density for this class to use on a histogram.
- 1Find the class width: 35 − 20 = 15.
- 2Use the formula frequency density = frequency ÷ class width.
- 3Substitute the values: 18 ÷ 15.
- 418 ÷ 15 = 1.2.
Answer: 1.2
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Practice
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Start practisingCommon mistake. Pupils often plot the frequency itself as the bar height, ignoring the class width entirely, which distorts the histogram when classes have unequal widths. Always divide frequency by class width to find the frequency density for the bar height.
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