Histograms

Tier: #Higher

How to

A histogram displays frequency for grouped continuous data. The key rule: it is the area of each bar, not the height, that represents frequency.

$$\text{Frequency density} = \frac{\text{Frequency}}{\text{Class width}}$$

Drawing a histogram: calculate frequency density for each class, then plot bars with height equal to frequency density. The bars must touch — there are no gaps.

Reading a histogram: to find the frequency for a class, multiply the bar height by the class width: $$\text{Frequency} = \text{Frequency density} \times \text{Class width}$$

Example: A bar has height (frequency density) $4$ and class width $5$, so frequency $= 4 \times 5 = 20$.

Common error: reading histogram bars as if height = frequency — always check whether a frequency density scale is used, and always multiply by the class width to recover frequencies.

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