Question

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

• (A) 10 or 20
• (B) 5 or 10
• (C) 5 or 20
• (D) 5 or 15

Answer 1

The Correct Option is C

Explanation:
We know $SD=\sqrt{\frac{\sum x_i^2}{n}-{\left(\frac{\sum x_i}{n}\right)}^2}$$$\begin{array}{rl}2& =\sqrt{\frac{100}{n}-{\left(\frac{20}{n}\right)}^2}=\sqrt{\frac{100}{n}-\frac{400}{n^2}}\\ \Rightarrow 4& =\frac{100}{n}-\frac{400}{n^2}\end{array}$$