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Question

Find the median wages for the following frequency distribution: Wages per day61707180819091100101110111120(in Rs.)No. of women5152030208workers


Solution

The given series is of inclusive form. Converting it into exclusive form and preparing the cumulative frequency table, we get

Wages per day

(in Rs.)

Frequency fi C.F
60.5-70.5 5 5
70.5-80.5 15 20
80.5-90.5 20 40
90.5-100.5 30 70
100.5-110.5 20 90
110.5-120.5 8 98
  N=∑fi=98  

N =98

=> N/2 = 49

Now,

The cumulative frequency just greater than 49 is 70 and corresponding class is 90.5-100.5.

Thus, the median class is 90.5-100.5

I = 90.5, h = 10, f = 30, c = C.F. preceding median class = 40 and N/2 = 49

Median = I+[h×(N/2−cf)/f]
=90.5+[10×(49−40)/30]
 

= 90.5+3 = Rs. 93.5

Hence, median is Rs. 93.5

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