Question

Mean of 5 observations is 3. If four of these observations are 4, 5, 1, 3 and one is missing, then variance of all five observations is

• A. 4
• B. 2
• C. 2.5
• D. 3

Answer 1

The correct option is B 2

Givne $\frac{4+5+1+3+x}{5}=3$
$\Rightarrow 13+x=15\Rightarrow x=2$
$\therefore$ Observation are 1, 2, 3, 4, 5
Variance of first n natural numbers =$\frac{n^2-1}{12}$, by taking n =5
variance =$\frac{25-1}{12}=2$