IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis
A histogram of monthly claim amounts (in ₹ thousand) uses unequal class widths. The class 10–20 has frequency 30 and the class 20–40 has frequency 36. To draw the histogram correctly, the heights of these two bars (frequency density) should be:
The heights are 3 and 1.8. In a histogram with unequal class widths the bar height is frequency divided by class width, so 30/10 = 3 and 36/20 = 1.8, ensuring that area, not height, represents frequency.
- A30 and 36
- B3 and 1.8Correct
- C3 and 3.6
- D0.3 and 0.18
- 1.5 and 1.8
Explanation
Frequency density = frequency / class width. For 10–20: 30/10 = 3. For 20–40: 36/20 = 1.8. Using raw frequencies (30 and 36) would wrongly make the wider class look larger in area terms.
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