Answer to Question #156854 in Statistics and Probability for Teja

Question

A population consists of the four numbers 3,7,11,15,the variance of the population is

Answer 1

We know the formula for variance of population such as , $\sigma ^2=\frac{\sum_{i=1}^{N} (x_i-\mu)^2}{N}$

where $x_i=$ value of $i$ th element

$\mu =$ population mean

$N=$ population size

Here the given population data are $3,7,11,15$

Now $\mu =\frac{(3+7+11+15)}{4}=9$ , $N=4$

and $\sum_{i=1}^{N}(x_i-\mu)^2=(3-9)^2+(7-9)^2+(11-9)^2+(15-9)^2=80$

$\therefore \sigma^2=\frac {80}{4}=20$

Hence required variance of the population is $=20$