The standard deviation of $n$ observations $x_{1},x_{2},\ldots..,x_{n}\$ is 2. If $\ \ \sum_{i = 1}^{n}{x_{i} = 20}$ and $\sum_{i = 1}^{n}{x_{i}^{2} = 100}$, then $n$ is

Question

Dr. Abubacker · Accepted Answer

(c)
Given, SD$= 2 = \sqrt{\frac{100}{n} - \left( \frac{20}{n} \right)^{2}}$
$\Rightarrow 4 = \frac{100}{n} - \frac{400}{n^{2}}$
$\Rightarrow \ \ n^{2} - 25n + 100 = 0$
$\Rightarrow \ \ \ n = 20,5$

Q. The standard deviation of $n$ observations $x_{1},x_{2},\ldots..,x_{n}\$ is 2. If $\ \ \sum_{i = 1}^{n}{x_{i} = 20}$ and $\sum_{i = 1}^{n}{x_{i}^{2} = 100}$, then $n$ is

Explanation

Reviewed by Dr. Abubacker

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