The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is

Solution

Maths sir · 4 steps

Rebuild the sum and the sum of squares from the wrong data, fix one value, then recompute.

1. Recover the totals. Mean 10 with n = 20 gives Σ x = 200. Then use the variance formula below to recover Σ x².

   σ² = (Σ x²)/n - x̄² ⇒ 4 = (Σ x²)/20 - 100 ⇒ Σ x² = 2080

2. Swap 9 for 11. Correct Σ x = 200 - 9 + 11 = 202, so the correct mean is 10.1. Correct Σ x² = 2080 - 81 + 121 = 2120.
3. New variance. σ² = 2120/20 - (10.1)² = 106 - 102.01 = 3.99.
4. So. The correct variance is 3.99, option (b).

The idea to keep. For a corrected observation, never patch the variance directly. Get Σ x and Σ x² back, replace the wrong value in both, then use the new mean in (Σ x²)/n - x̄².

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