Question

Mean of first 15 numbers is 12 and variance is 14. Mean of next 15 numbers is 14 and variance is a. If variance of all 30 numbers is 13, then a is equal to

• A. 12
• B. 14
• C. 10
• D. 3

Answer 1

Answer: (C)

10

Answer 2

The correct answer is option (C) : 10

$\sigma^2=\sum x_i^2-(\bar x)^2$

$13=\frac{(14+144)\times15+(a+196)\times15}{30}-(13)^2$

$\Rightarrow a=10$