The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is :

Solution

Maths sir · 4 steps

Get the total and the sum of squares for all 7, remove the two known values, then rebuild the variance.

1. Total of all 7. Mean 8 for 7 observations gives Σ x = 7 × 8 = 56.
2. Sum of squares. Use variance = (Σ x²)/n - x̄². Then 16 = (Σ x²)/7 - 64, so Σ x² = 7 × 80 = 560.
3. Remove 6 and 8. The remaining 5 have sum 56 - 6 - 8 = 42 and sum of squares 560 - 36 - 64 = 460.

   σ² = 460/5 - (42/5)² = 92 - 1764/25 = (2300 - 1764)/25 = 536/25

4. So. The variance of the remaining 5 observations is 536/25, which is option (c).

The idea to keep. Variance cannot be split directly, but Σ x and Σ x² can. Recover both totals, add or remove observations, then rebuild the variance with the new mean.

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