The arithmetic mean of the following frequency distribution: Variable (X)  :    0     1     2     3    ….      nFrequency (f) :    nC0     nC1     nC2     nC3     ….      nCnis

The arithmetic mean of the following frequency distribution: 

Variable (X)  :    0     1     2     3    .     n

Frequency (f) :    nC0     nC1     nC2     nC3     .     nCn

is

  1. A

    2nn

  2. B

    2nn+1

  3. C

    n2

  4. D

    2n

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    Solution:

    Let X¯ denote the required mean. Then,

    X¯=r=0nrnCrr=0nnCr=r=1nrnrn1Cr1r=0nrnCr=nr=1nn1Cr12n X¯=n×2n12n=n2 r=1nn1Cr1=2n1

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