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If the arithmetic mean of the data given...

If the arithmetic mean of the data given below is 28 , find (a) the missing frequency , and (b) the median of the series :
`{:("Profit per Retail Shop (inRs.)",0-10,10-20,20-30,30-40,40-50,50-60),("Number of Retail Shops"," "12," "18," "27," "f," "17," "6):}`

Text Solution

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`overline(X) = (sumfm)/(sumf)`
`28=(2,100+35f)/(80+f)`
`28(80+f)=2,100+35f`
`2,240+28f=2,100+35f`
`35f-28f=2,240-2,100`
`7f=140`
`f=20`

M= Size of `((N)/(2))`th item
= Size of `((100)/(2))` th item
= Size of 50th item
Hence , median lies in the class 20-30.
`M=l_(1)+(N/(2)-c.f.)/(f) xxi`
`=20+(100/(2)-30)/(27)xx10`
`=20+(50-30)/(27)xx10`
`=20+(20)/(27)xx10`
`20+7.41=27.41`
`:.` value of missing frequency =20 and value of the median = Rs. 27.41.]
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