Histograms
Year 10 (IGCSE) 📈 Statistics & Probability Draw and interpret histograms with unequal class widths.
📊 Histograms vs Bar Charts
Histograms display continuous grouped data. There are no gaps between bars, and it is the area of each bar — not its height — that represents frequency.
⚡ Frequency Density
$$\text{Frequency density} = \frac{\text{Frequency}}{\text{Class width}}$$ Always label the $y$-axis as "Frequency density" on a histogram, not "Frequency".
📐 Drawing a Histogram
Convert raw frequencies to frequency densities before drawing the bars.
| Height (cm) | Freq | Width | Freq density |
|---|---|---|---|
| 150–160 | 10 | 10 | 1.0 |
| 160–165 | 15 | 5 | 3.0 |
| 165–180 | 24 | 15 | 1.6 |
🔍 Reading a Histogram
To recover frequencies from a histogram: frequency = frequency density × class width.
Example: A bar from 20 to 30 has frequency density 4.5. Frequency $= 4.5 \times 10 = 45$.
Estimating within a class: Bar from 10–20, freq density 3. Frequency in 15–20 $= 3 \times 5 = 15$ (assuming uniform spread within the class).
Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
Interactive Demonstration — Histograms
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Interactive demonstration available in the Calculator tab!
📊 Histogram Tool
Enter class intervals and frequencies to calculate frequency densities.