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Q.

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

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a

2nn

b

2nn+1

c

n2

d

2n

answer is C.

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Detailed Solution

Let X¯ denote the required mean. Then,X¯=∑r=0n r⋅nCr∑r=0n nCr=∑r=1n r⋅nrn−1Cr−1∑r=0n rnCr=n∑r=1n n−1Cr−12n⇒ X¯=n×2n−12n=n2 ∵∑r=1n n−1Cr−1=2n−1
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The arithmetic mean of the following frequency distribution: Variable (X)  :    0     1     2     3    ….      nFrequency (f) :    nC0     nC1     nC2     nC3     ….      nCnis