Question

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

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

Calculate mean diameter of head of a screw by ‘Assumed Mean Method’.

Answer 1

Let A be the assumed mean.
A is taken as the class mark of the middle class.
Hence, let us take 40 as the assumed mean.
Then A = 40 and deviation d_i = x_i – A = x_i – 40

Diameter	Class	Deviations	Number of	fidi
(in mm)	marks	di=xi-A	Screws	-
-	xi	di=xi-40	fi	-
33-35	34	-6	10	-60
36-38	37	-3	19	-57
39-41	40=A	0	23	0
42-44	43	3	21	63
45-47	46	6	27	162
Total	-	-	∑fi=100	∑fidi=108

Here,∑f_id_i=108, ∑f_i=100

`bard=(Sigmaf_id_i)/(Sigmaf_i)=108/100=1.08`

`barx=A+bard`

   =40+1.08

   =41.08

Thus, the mean diameter of the screw heads is 41.08 mm.