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Calculate median of the following series...

Calculate median of the following series :
`{:("Wage Rate (Rs.) (less than)",10,20,30,40,50,60,70,80),("Number of Waorkers",15,35,60,84,96,127,198,250):}`

Text Solution

Verified by Experts

As a first step the cumulative frequency of 'less than ' type is converted into a simple frequency distribution as under :

M= size of N/2th item or 250/2 = 125th item which lies in 127 th cummulative frequency of the series. The corresponding calss interval , 50-60 is , therefore , the median class interval. the actual value the median is determined using the standard formula, viz.
`M=+l_(1)+((N)/(2)-c.f.)/(f)xxi`
Imputing the values,
`l_(1)=50,c.f=96,f=31,i=10`
`M=50+((250)/(2)-96)/(31)xx10`
`M=50+(125-96)/(31)xx10`
`=50+(29)/(31)xx10`
`=50+9.35=59.35`
Median Wage Rate = Rs. 59.35.
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