IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis
A histogram of monthly claim amounts (in ₹ thousand) uses these classes: 0-10 (frequency 40), 10-20 (frequency 30), 20-40 (frequency 20), 40-80 (frequency 10). If the first class bar is drawn with height 4 units, what height should the 20-40 bar have so that area is proportional to frequency?
The bar height should be 1.0. A histogram with unequal class widths plots frequency density, frequency divided by width. The 20-40 class has frequency 20 and width 20, giving 1.0, consistent with the first bar's density of 4.
- A1.0Correct
- B2.0
- C0.5
- D4.0
- 1.5
Explanation
Frequency density = frequency/width. For 0-10: 40/10 = 4, which matches the given height. For 20-40: 20/20 = 1.0. Using the raw frequency 20 as height (or 2.0 from dividing by 10) ignores the class width.
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