Question 69

The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On rechecking, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is

n = 20, mean = 10, σ = 2, so σ² = 4.

Σxᵢ = 200. Σxᵢ² = n(σ² + mean²) = 20(4 + 100) = 2080.

Corrected: Σxᵢ(new) = 200 - 8 + 12 = 204. Mean(new) = 204/20 = 10.2.

Σxᵢ²(new) = 2080 - 64 + 144 = 2160.

σ²(new) = 2160/20 - (10.2)² = 108 - 104.04 = 3.96.

σ(new) = √3.96.

The correct answer is Option (3): √3.96.

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