The following table gives the weekly wages of workers in a factory.
Weekly wages (₹) No. of workers
50 - 55 5
55 - 60 20
60 - 65 10
65 - 70 10
70 - 75 9
75 - 80 6
80 - 85 12
85 - 90 8
Calculate the mean, by using :
(i) Direct method
(ii) Short-Cut method.
Measures of Central Tendency
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Question

The following table gives the weekly wages of workers in a factory.
Weekly wages (₹) No. of workers
50 - 55 5
55 - 60 20
60 - 65 10
65 - 70 10
70 - 75 9
75 - 80 6
80 - 85 12
85 - 90 8
Calculate the mean, by using :
(i) Direct method
(ii) Short-Cut method.

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KnowledgeBoat · Accepted Answer

(i) Mean by Direct method

Weekly wages (₹)	Mid value (x)	No. of workers (f)	fx
50 - 55	52.5	5	262.5
55 - 60	57.5	20	1150
60 - 65	62.5	10	625
65 - 70	67.5	10	675
70 - 75	72.5	9	652.5
75 - 80	77.5	6	465
80 - 85	82.5	12	990
85 - 90	87.5	8	700
Total		Σf = 80	Σfx = 5520

By formula,

Mean = $\dfrac{Σfx}{Σf} = \dfrac{5520}{80}$ = 69.

Hence, mean = 69.

(ii) Mean by Short-Cut method

Let assumed mean (A) be 67.5

Weekly wages	Mid value (x)	No. of workers (f)	d = x - A	fd
50 - 55	52.5	5	52.5 - 67.5 = -15	-75
55 - 60	57.5	20	57.5 - 67.5 = -10	-200
60 - 65	62.5	10	62.5 - 67.5 = -5	-50
65 - 70	A = 67.5	10	67.5 - 67.5 = 0	0
70 - 75	72.5	9	72.5 - 67.5 = 5	45
75 - 80	77.5	6	77.5 - 67.5 = 10	60
80 - 85	82.5	12	82.5 - 67.5 = 15	180
85 - 90	87.5	8	87.5 - 67.5 = 20	160
Total		Σf = 80		Σfd = 120

n = Σf = 80.

By formula,

Mean = A + $\dfrac{Σfd}{n} = 67.5 + \dfrac{120}{80}$ = 1.5

= 67.5 + 1.5 = 69.

Hence, mean = 69.