IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis
Ten policy sizes (₹ lakh) have mean 12 and sample standard deviation 4. A new policy of ₹12 lakh is added to the data. What is the new sample standard deviation, to 3 decimal places?
The new standard deviation is 3.795. The added value equals the mean, so the sum of squared deviations stays at 144, while the divisor rises from 9 to 10. The variance becomes 14.4, whose square root is 3.795.
- A3.795Correct
- B4.000
- C3.636
- D3.810
- 3.286
Explanation
Original Sxx = 9 × 16 = 144. Adding a value equal to the mean leaves the mean at 12 and adds 0 to Sxx. New variance = 144/10 = 14.4, so SD = 3.795. Option 4.000 ignores the larger divisor.
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