Calculate mean, variance and standard deviation for the following frequency distribution:

Explanation

Here h=30. Let the assumed mean be A=105. Now, we prepare the table given below.

`therefore" "A=105, h=30, N=Sigmaf_(i) =30, Sigma f_(i)y_(i)=2 and Sigmaf_(i)y_(i)^(2)=76.`
`therefore" "barx=(A+(Sigmaf_(i)y_(i))/(N)xxh)rArrbarx=(105+(2)/(30)xx30)=(105+2)=107.`
Thus, mean =107.
`"Variance, "sigma^(2)=(h^(2))/(N^(2))cdot{N cdot Sigmaf_(i)f_(i)^(2)-(Sigmaf_(i)y_(i))^(2)}`
`=((30)^(2))/((30)^(2))cdot{30xx76-(2)^(2)}=(2280-4)=2276.`
Standard deviation, `sigma=sqrt(22763)=47.71.`