Question

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

Diameter (in mm)	33 - 35	36 - 38	39 - 41	42 - 44	45 - 47
No. of screw	10	19	23	21	27

• A. $38.08$ mm
• B. $40.08$ mm
• C. $41.08$ mm
• D. $45.08$ mm

Answer 1

Answer: (C)

$41.08$ mm

Consider the following table, to calculate mean:

$ci$	$f_i$	$x_i$	$f_i{x}_i$
32.5-35.5	10	34	340
35.5-38.5	19	37	703
38.5-41.5	23	40	920
41.5-44.5	21	43	903
44.5-47.5	27	46	1242

$N=\Sigma f_i=100$

$\Sigma f_i{x}_i=4108$

Mean $\overline{x}=\frac{\Sigma f_i{x}_i}{N}$

$\therefore \overline{x}=\frac{4108}{100}=41.08$

Mean diameter of head of a screw is $41.08$mm

Hence, option $C$ is correct.