IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions
The ordered sample of nine premium amounts (in ₹ thousand) is 12, 15, 18, 21, 25, 30, 34, 41, 60. Using the definition in which the p-quantile is the value at position (n+1)p with linear interpolation, what is the lower quartile?
The lower quartile is 16.5 thousand rupees. The position is (n+1)/4 = 2.5, halfway between the second value 15 and the third value 18, so interpolation gives 16.5.
- A15
- B16.5Correct
- C18
- D21
- 17.5
Explanation
Position is (9+1)×0.25 = 2.5. This lies halfway between the 2nd value (15) and the 3rd value (18), so the quartile is 15 + 0.5×3 = 16.5. The value 18 would come from rounding position up to 3.
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