IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis
Twenty-one observations of claim size are ordered. Using the convention that the p-th quantile lies at position p(n+1), what is the lower quartile if the 5th and 6th ordered values are ₹40,000 and ₹48,000?
The lower quartile is ₹44,000. Under the p(n+1) rule the position is 0.25 times 22, which is 5.5, so it lies midway between the 5th and 6th ordered values of 40,000 and 48,000.
- A₹40,000
- B₹44,000Correct
- C₹48,000
- D₹45,000
- ₹43,000
Explanation
Position = 0.25 × 22 = 5.5. This lies halfway between the 5th and 6th values: (40,000+48,000)/2 = 44,000. Using position 5.25 would give 42,000, which is not the stated rule.
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