Question

The standard deviation of n observations $x_1,x_2,x_3,...,x_n$ is 2. If ${\sum }_{i=1}^n{x}_i=20$ and ${\sum }_{i=1}^n{x}_i^2=100$, then n is

• A. 10 or 20
• B. 5 or 10
• C. 5 or 20
• D. 5 or 15

Answer 1

Answer: (C)

Given $S.D.=2\Rightarrow S.D{.}^2=4$
$\Rightarrow \frac{{\sum }_{i=1}^n{x}_i^2}{n}-\frac{{\left({\sum }_{i=1}^n{x}_i\right)}^2}{n^2}=4$
$\Rightarrow \frac{100}{n}-\frac{{\left(20\right)}^2}{n^2}=4$
$\Rightarrow 4n^2-100n+400=0$
$\Rightarrow n^2-25n+100=0$
$\Rightarrow n=5,20.$