The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is _____________.

Solution

Maths sir · 3 steps

Rebuild the wrong sums, swap 25 for 15 in both, and only then recompute the mean and variance.

1. Wrong totals. Mean 15 for 10 observations gives Σ x = 150. Variance = (Σ x²)/10 - 15² = 15, so Σ x² = 10 × 240 = 2400.
2. Correct the totals. Take out 25 and put in 15. Then Σ x = 150 - 25 + 15 = 140 and Σ x² = 2400 - 625 + 225 = 2000.

   σ² = 2000/10 - (140/10)² = 200 - 196 = 4

3. So. The correct variance is 4, so the correct standard deviation is √4 = 2.

The common slip: 4. Stopping at the variance gives 4, not 2. The question asks for the standard deviation, so take the square root.

The idea to keep. When an observation is misread, do not patch the mean or variance directly. Go back to Σ x and Σ x², correct both, then recompute.

Answer from the NTA final answer key. Solution by PrepWiser.