If the variance of the following frequency distribution is 50, then x is equal to Class10-2020-3030-40Frequency2x2

If the variance of the following frequency distribution is 50, then x is equal to 

Class10-2020-3030-40
Frequency2x2

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    Solution:

    Computation of Variance

    Class

    MId-

    Values xi

    Frequencies 

    fi

    ui=xi-2510fiuifiui2
    10-20152-1-22
    20-3025x000
    30-40352122
      N=4+ x Σfiui=0Σfiui2=4

    X¯=25+1014+x×0=25   Using X¯=a+h1NΣfiui

    Now,

    Variance = 50

     h21NΣfiui21NΣfiui2=50 10044+x0=508=4+xx=4

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