Statistics
Combined Variance of Two Sets
nta_pyq_2023_apr
Grade 11
Question:
The mean and variance of 15 numbers are 12 and 14. Another 15 numbers have mean 14 and variance $\sigma^2$. If the combined variance of all 30 is 13, then $\sigma^2$ is equal to
Step-by-Step Solution
Key Concept: Combined variance formula: $\sigma^2_{combined}=\frac{n_1(\sigma_1^2+d_1^2)+n_2(\sigma_2^2+d_2^2)}{n_1+n_2}$ where $d_i$ are deviations of group means from combined mean.
$\sigma^2=10$.
Correct Answer: 1