Question

The measurements (in mm) of the diameters of the heads of the screws are given below. Calculate the mean diameter of the head of the screws.

Diameter (in mm)	33-35	36-38	39-41	42-44
Number of screws $\left(f_1\right)$	17	19	23	21

Answer 1

Given Data

The measurements (in mm) of the diameters of the heads of the screws.

Diameter (in mm)	$33-35$	$36-38$	$39-41$	$42-44$
Number of screws	$17$	$19$	$23$	$21$

Diameter	(continuous) Diameter	Mid point $\left(x_i\right)$	No of screws $\left(f_i\right)$	$f_i{x}_i$
$33-35$	$32.5-35.5$	$34$	$17$	$578$
$36-38$	$35.5-38.5$	$37$	$19$	$703$
$39-41$	$38.5-41.5$	$40$	$23$	$920$
$42-44$	$41.5-44.5$	$43$	$21$	$903$
			$\sum f_i=80$	$\sum f_i{x}_i=310$

mean $\left(\overline{x}\right)=\frac{\sum f_i{x}_i}{\sum f_i}$

$=38.8$

$\therefore$ mean diameter of the head of the screws $=38.8$