Question

Find the mean and variance of first 10 multiples of 3.

Answer 1

Given: x = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

$\sum x$ = 3+ 6+ 9 + 12+ 15+ 18 + 21+24 +27 + 30 = 165

And $\sum x^2=(3{)}^2+(6{)}^2+(9{)}^2\dots \dots .+(30{)}^2=3465$

Mean = (165/10) = 16.5

Now, Variance=$\left({\sigma }^2\right)=\frac{N\sum x^2-(\sum x{)}^2}{N^2}=\frac{10\times 3465-27225}{N^2}=7425/100=74.25$