The measurments ( in mm) of the diameters of the head of the screws are given below :

Calculate the mean diameter of the screw by ' Assumed Mean Method' .
Steps to calculate mean by this method :
(1) Assume mean A. In this example , A = 40. (Generally, the class mark of the class having the maximum frequency or the class mark of the middle class is chosen as the assumed mean.)
(2) In column 1, write the class intervals,(Here, diameter).
(3) In column 2, write the corresponding class marks.
(4) In column 3, write the value of `d_(i), " where " d_(i) = x_(i) - A`.
A is the assumed mean.
(5) In column 4, write the frequencies `(f_(i))`. Write `Sigma f_(i) ` at the bottom of this column.
(6) In column 5, write the product `(f_(i) xx d_(i))` and their sum `Sigma f_(i) d_(i)`.
Calculate `bar d " and " bar X ` using the following formulae :
` bard = (Sigma f_(i)d_(i))/(Sigma f_(i))." Mean" barX = A + bar d`.
[d : mean of deviations.]

Answer

The mean diameter of the head of the screw is `41.08` mm.

Explanation

Let us take 40 as the assumed mean. Then A = 40 and deviation ` d_(i) = x_(i) - A = x_(i) - 40 `.

Here, `Sigma f_(i) d_(i) = 108 , Sigma f_(i) = 100`.
` bard = (Sigmaf_(i)d_(i))/(Sigmaf_(i)). = 108/100 . = 1.08`
`barX = A + bard`
` = 40 + 1.08`
` = 41.08`