Given below are the dimaters of circles (in mm) drawn in a design.

Calculate the mean diameter of the circles, variance and standard deviation.

Explanation

Converting the given series into an exclusive series, we prepare the table given below.

`therefore" "A=42.5, h=4, N=Sigmaf_(i)=100, Sigmaf_(i)y_(i)=25 and Sigmaf_(i)y_(i)^(2)=199.`
`therefore" "barx(A+(Sigmaf_(i)y_(i))/(N)xxh)rArrbarx=(42.5+(25)/(100)xx4)=43.5.`
Thus, mean =43.5 mm.
`"Variance, "sigma^(2)=(h^(2))/(N^(2))cdot{N cdot Sigmaf_(i)y_(i)^(2)-(Sigmaf_(i)y_(i))^(2)}`
`=(16)/(10000)xx{100xx199-(25)^(2)}=(16)/(10000)xx(19900-625)`
`=((16)/(10000)xx19275)=(3084)/(100)=30.84.`
Standard deviation, `sigma=sqrt(30.84)=5.55.`
Hence, mean = 43.5 mm, variance = 30.84, and standard deviation =5.55.