Question

The mean and the variance of $10$ observations are given to be $4$ and $2$ respectively. If every observation is multiplied by $2$, the mean and the variance of the new series will be respectively.

• A. $8$ and $20$
• B. $8$ and $4$
• C. $8$ and $8$
• D. $80$ and $40$

Answer 1

Answer: (C)

$8$ and $8$

Mean is summation of all observations divided by number of observation and hence, would be multiplied by $2$ due to linearity. Hence, the new mean is $8$.

Variance is sum of squares of each observation subtracted by the mean. Hence, due to squared dependence, it will be quadrupled to get $8$.

Hence, both mean and variance are $8$.