Find the mean, standard deviation and variance of first 10 multiples of 3.

Explanation

First 10 multiples of 3 are 3,6,9,12,30.
This is an AP with a=3, n=10 and l=30.
`therefore" sum"=(n)/(2)(a+l)=(10)/(2)cdot(3+30)=165.`
`therefore" mean," barx=(165)/(10)=16.5.`
`"Variance, "sigma^(2)=(Sigmax_(i)^(2))/(n)-(barx)^(2)`
`={(3^(2)+6^(2)+9^(2)+...+30^(2))/(10)-(16.5)^(2)}`
`=(3^(2)xx{1^(2)+2^(2)+3^(2)+...+10^(2)})/(10)-(16.5)^(2)`
`=(9xx10xx(10+1)(2xx10+1))/(6xx10)-(16.5)^(2)" "[because Sigman^(2)=(n(n+1)(2n+1))/(6)]`
`=((9xx10xx11xx21)/(6xx10)-272.25)=((693)/(2)-272.25)`
`=(346.5-272.25)=74.25.`
`therefore" variance, "sigma^(2)=74.25.`
Standard deviation, `sigma=sqrt(74.25)=8.61.`