Question

For two groups of 15 sizes each, mean and variance of first group is 12, 14 respectively, and second group has mean 14 and variance of σ². If combined variance is 13 then find variance of second group?

• A. 9
• B. 11
• C. 10
• D. 12

Answer 1

The Correct Option is C

\(\bar{x}\) = 12, \(\sigma _{1}^{2}\) = 14, \(\bar{y}\) = 12, \(\sigma _{2}^{2}\) = \(\sigma ^{2}\), n₁ = n₂ = 15
\(\sigma _{1}^{2}\) = 14 = \(\sum \frac{x_{i}^{2}}{15}-(12)^{2}\Rightarrow \sum x_{i}^{2}=2370, \sum x_{i}=180\)
\(\sigma _{2}^{2}=\sum \frac{y_{i}^{2}}{15}-(14)^{2}, \sum y_{i}=210\)
13 = \(\frac{\sum x_{i}^{2}\sum y_{i}^{2}}{30}-(\frac{15\bar{x}+15\bar{y}}{30})^{2}\)
\(\frac{2370+\sum y_{i}^{2}}{30}-(13)^{2}\)
\(\sum y_{i}^{2}=3090\Rightarrow \sigma _{2}^{2}=\frac{3090}{15}-(14)^{2}=10\)