Question

The following table gives the wages of worker in a factory:

Wages in ₹	45 - 50	50 - 55	55 - 60	60 - 65	65 - 70	70 - 75	75 - 80
No. of Worker's	5	8	30	25	14	12	6

Calculate the mean by the short cut method.

Answer 1

Class Interval	Frequency `f_i`	Observation (mid value) `x_i`	`d_i = x_i - A`	`f_id_i`
45 - 50	5	47·5	-15	-75
50 - 55	8	52·5	-10	-80
55 - 60	30	57·5	-5	-150
60 - 65	25	62·5 = A	0	0
65 - 70	14	67·5	5	70
70 - 75	12	72·5	10	120
75 - 80	6	77·5	15	90
	`sumf_i` = 100			`sum f_i d_i` = -25

Mean `bar"X" = "A" + (sumf_i d_i)/(sumf_i)`
= `62·5 + (-25)/(100)` = 62·25.