IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis
For 20 policies, the sum of claim amounts is Rs 400 thousand and the sum of squares of claims is 8,500 (Rs thousand squared). What is the sample variance, to 1 decimal place?
The sample variance is 26.3. The mean is 20, Sxx = 8,500 - 20 x 400 = 500, and dividing by n-1 = 19 gives 26.3. Using n = 20 would give 25.0, which is the incorrect divisor for a sample variance.
- A25.0
- B26.3Correct
- C25.5
- D23.7
- 42.5
Explanation
Mean = 400/20 = 20. Sxx = 8,500 - 20*20^2 = 8,500 - 8,000 = 500. Variance = 500/19 = 26.3. Dividing by 20 gives 25.0, the wrong-divisor distractor.
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