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

Answer: (C)

10

Answer 2

$\bar{x}$ = 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 = $\frac{\sum x_{i}^{2}\sum y_{i}^{2}}{30}-(\frac{15\bar{x}+15\bar{y}}{30})^{2}$
$\frac{2370+\sum y_{i}^{2}}{30}-(13)^{2}$
$\sum y_{i}^{2}=3090\Rightarrow \sigma _{2}^{2}=\frac{3090}{15}-(14)^{2}=10$