Question

The mean and variance of $n$ observations $x_1$, $x_2$, $x_3$, ..., $x_n$ are $5$ and $0$ respectively. If $ \displaystyle \sum_{i=1}^n x^2_i=400$, then the value of $n$ is equal to

• A. $80$
• B. $25$
• C. $20$
• D. $16$

Answer 1

Answer: (D)

Variance $=\sigma^{2}$
$\Rightarrow \frac{1}{n} $$ \displaystyle \sum_{i=1}^n x^2_i$$-\left(\frac{1}{n}\sum x_{i}\right)^{2}=\sigma^{2}$
$\Rightarrow 0=\frac{1}{n}\left(400\right)-\left(5\right)^{2}$
$\Rightarrow \frac{400}{n}=25$
$\Rightarrow n=16$