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Question -

Consider the following distribution of daily wages of 50 workers of afactory.



Answer -

Daily wages (in Rs.)

100-120

120-140

140-160

160-180

180-200

Number of workers

12

14

8

6

10

Find the mean daily wages of the workers of the factory by using anappropriate method.


Solution:

Find the midpoint ofthe given interval using the formula.

Midpoint (xi) = (upper limit + lower limit)/2

In this case, thevalue of mid-point (xi) is very large, so let us assume the meanvalue, A = 150 and class interval is h = 20.

So, u= (xi – A)/h = ui  = (xi – 150)/20

Substitute and findthe values as follows:

Daily wages

(Class interval)

Number of workers

frequency (fi)

Mid-point (xi)

u= (xi – 150)/20

fiui

100-120

12

110

-2

-24

120-140

14

130

-1

-14

140-160

8

150

0

0

160-180

6

170

1

6

180-200

10

190

2

20

Total

Sum f= 50

Sum fiui = -12

So, the formula tofind out the mean is:

Mean = x̄ = A + h∑fiui /∑f=150+ (20 × -12/50) = 150 – 4.8 = 145.20

Thus, mean daily wageof the workers = Rs. 145.20

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