The mean and variance of n observations x1, x2, x3, ..., xn are 5 and 0 respectively. If displaystyle ∑i=1n x2i=400, then the value of n is equal to

Question

The mean and variance of n observations x1, x2, x3, ..., xn are 5 and 0 respectively. If displaystyle ∑i=1n x2i=400, then the value of n is equal to (A) 80 (B) 25 (C) 20 (D) 16

Tardigrade Admin · Accepted Answer

Variance =σ2 ⇒ (1/n) displaystyle ∑i=1n x2i-((1/n)∑ xi)2=σ2 ⇒ 0=(1/n)(400)-(5)2 ⇒ (400/n)=25 ⇒ n=16

Q. The mean and variance of $n$ observations $x_{1}$ , $x_{2}$ , $x_{3}$ , ..., $x_{n}$ are $5$ and $0$ respectively. If $i = 1 \sum n x_{i}^{2} = 400$ , then the value of $n$ is equal to

$80$

$25$

$20$

$16$

Variance $= σ^{2}$
$\Rightarrow \frac{1}{n}$ $i = 1 \sum n x_{i}^{2}$ $- (\frac{1}{n} \sum x_{i})^{2} = σ^{2}$
$\Rightarrow 0 = \frac{1}{n} (400) - (5)^{2}$
$\Rightarrow \frac{400}{n} = 25$
$\Rightarrow n = 16$

Q. The mean and variance of n observations x1​, x2​, x3​, ..., xn​ are 5 and 0 respectively. If i=1∑n​xi2​=400, then the value of n is equal to

80

25

20

16