Question

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

Diameter (in $mm$)	No. of Screws
$30-35$	$9$
$36-38$	$21$
$39-41$	$30$
$42-44$	$20$
$45-47$	$18$

Calculate mean diameter of head of a screw by 'Assumed Mean Method'

Answer 1

Diameter (in $mm$) C.I.	Class Mark $\left(x_i\right)$	$x_i-A=x_i-40=d_i$	No. of Screws $\left(f_i\right)$	$f_i{d}_i$
$33-35$	$34$	$-6$	$9$	$-54$
$36-38$	$37$	$-3$	$21$	$-63$
$39-41$	$40\to A$	$0$	$30$	$0$
$42-44$	$43$	$3$	$20$	$60$
$45-47$	$46$	$6$	$18$	$108$
			$\sum f_i=98$	$\sum f_i{d}_i=51$

$\overline{d}=\frac{\sum f_i{d}_i}{\sum f_i}$
$=\frac{51}{98}$
$=0.52$
$\overline{x}=A+\overline{d}$
$=40+0.52$
$\overline{x}=40.52$
$\therefore$ Mean diameter of head of a screw is $40.52$.