Find the median of the following data.

Wages ( in rupees ) : More than 150 , More than 140 , More than 130 , More than 120 , More than 110 , More than 100 , More than 90 . More than 80.

No.of workers : NIL ,12,27,60,105,124,141,150.

By selecting classes for the given data as:80 - 90, 90 - 100, 100 - 110, 110 - 120, 120 - 130, 130 - 140, 140 - 150We write the frequency distribution as below:
 
Class interval (C.I) Frequency (f) Cumulative Frequency (c f)
80 - 90 150 - 141 = 9 9
90 - 100 141 - 124 = 17 26
100 - 110 124 - 105 = 19 45
110 - 120 105 - 60 = 45 90
120 - 130 60 - 27 = 33 123
130 - 140 27 - 12 = 15 138
140 - 150 12 - 0 = 12 150

Hence, n = 150
 n2 = 75Now, 110 - 120 is the class whose cumulative frequency 90 is greater than 75.Hence, median class is 110 - 120.Thus, l = 110,   n2 = 75,   cf = 45,   f = 45  and   h = 10Therefore,  Median = l + n2 - cff × h                             = 110 + 75 - 4545 × 10                             = 110 + 3045 × 10                             = 110 + 23 × 10                             = 110 + 203 = 110 + 6.67 = 116.67  

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