Question

The mean of four observations is $3$. If the sum of the squares of these observations is $48$ then their standard deviation is

• A. $\sqrt{7}$
• B. $\sqrt{2}$
• C. $\sqrt{3}$
• D. $\sqrt{5}$

Answer 1

Answer: (C)

$\sqrt{3}$

We have given, mean $\overline{x}=3$ and $\sum x_i^2=48$ and number of observation $n=4$

Thus standard deviation is, $\sigma =\sqrt{\frac{\sum x_i^2}{n}-{\overline{x}}^2}=\sqrt{12-9}=\sqrt{3}$