1. Tardigrade
  2. Question
  3. Mathematics
  4. The standard deviation of n observations x1, x2, x3, ... , xn is 2. If ∑ni = 1 xi = 20 and ∑ni=1 xi2 = 100, then n is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Statistics

Solution:

Given $S.D.= 2 \Rightarrow S.D.^{2} =4$
$ \Rightarrow \frac{\sum^{n}_{i=1} x_{i}^{2}}{n} - \frac{\left(\sum^{n}_{i=1}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.$