Question

The daily wages of 40 workers of a factory are given in the following table.

Wages in Rs.	30 – 34	34 – 38	38 – 42	42 – 46	46 – 50	50 – 54
No. of workers	4	7	9	11	6	3

Calculate (i) Mean (ii) Variance and (iii) Standard Deviation of wages and also interpret the findings.

Answer 1

Table of calculation
Class Interval (in Rs)	Frequency f	Mid-point X	fX	Deviation	Square of Deviation D2	f.D2
30 – 34	4	32	128	– 9.7	94.09	376.36
34 – 38	7	36	252	–5.7	32.49	227.43
38 – 42	9	40	360	–1.7	2.89	26.01
42 – 46	11	44	484	2.3	5.29	58.19
46 – 50	6	48	288	6.3	39.69	238.14
50 – 54	3	52	156	10.3	106.09	318.27
	= 40		1668			=1244.4

Sum of the frequencies = N = = 40

1668, = 1244.4

(i) Mean = = = 41.7

(ii) = = 31.11

(iii)

The average daily wage of the workers is Rs 41.7 and the wages deviate from the mean wage by approximately Rs 5.58.