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	9
36 - 38	21
39 - 41	30
42 - 44	22
45 - 47	18

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

Answer 1

Let A = 40

Diameter (in mm)	Class Mark      (X)	d =  X - A	no. of screws	f d
33 - 35	34	-6	9	-54
36 - 38	37	-3	21	-63
39 - 41	40	0	30	0
42 - 44	43	3	22	66
45 - 47	46	6	18	108
			∑ f =100	∑fd = 57

`bar"d" = (∑"f""d")/(∑ "f") = 57/100=0.57`

Mean by Assumed Mean Method

`bar"x" = "A" + bar"d"`
    =40 + 0.57
    =  40.57  mm 

Answer 2

Let A = 40

Diameter (in mm)	Class Mark      (X)	d =  X - A	no. of screws	f d
33 - 35	34	-6	9	-54
36 - 38	37	-3	21	-63
39 - 41	40	0	30	0
42 - 44	43	3	22	66
45 - 47	46	6	18	108
			∑ f =100	∑fd = 57

`bar"d" = (∑"f""d")/(∑ "f") = 57/100=0.57`

Mean by Assumed Mean Method

`bar"x" = "A" + bar"d"`
    =40 + 0.57
    =  40.57  mm