Find the mean and variance for each of the data : First 10 multiples of 3.

Explanation

First 10 multiples of `3=3,6,9,…………30`
Their sum `=sumx_(i)=3+6+9+…….+30`
`=3(1+2+3+..+10)`
`=3xx(10xx11)/2=165`
Their mean `=(sumx_(i))/n=165/10=16.5`
Sum of their squares
`sumx_(i)^(2)=3^(2)+6^(2)+9^(2)+……+30^(2)`
`=3^(2)(1^(2)+2^(2)+3^(2)+.....+10^(2))`
`=9xx(10xx11xx21)/6=3465`
Now variance `sigma^(2)=(sumx_(i)^(2))/n-((sumx_(i))/n)^(2)`
`=3465/10-(16.5)^(2)`
`=346.5-272.25=74.25`