If the mean and variance of 8 observations are $10$ and $16$ respectively, and each observation is multiplied by $2$, then the new mean and new variance are respectively:

Solution

1. Given the original mean $\bar{x}=10$, variance ${\sigma }^2=16$, and the multiplier $k=2$.
2. The new mean is calculated as $$\begin{array}{rl}{\bar{x}}_{new}& =k\times \bar{x}\\ & =2\times 10\\ & =20\end{array}$$.
3. The new variance is calculated as $$\begin{array}{rl}{\sigma }_{new}^2& =k^2\times {\sigma }^2\\ & =2^2\times 16\\ & =4\times 16\\ & =64\end{array}$$.
4. Hence the answer is (B).