If a variable takes values 0, 1, 2, …………. n with respective frequencies $n_{0}^{C}, n_{1}^{C}, n_{2}^{C} . . . . . . n_{n}^{C}$ then the A.M is

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$\frac{2^{n}}{n}$

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n+1

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$\frac{n}{2}$

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Solution

The correct option is D
$\frac{n}{2}$

$N = \sum f_{i} = 1 + n_{c_{1}} + n_{c_{1}} + . . . . . + n_{c_{n}} = 2^{n}$

$\sum f_{i} x_{i} = 1 \times 0 + n_{c_{1}} \times n_{c_{2}} \times 2 + . . . . + n_{c_{n}} = n$

$= n [n - 1_{c_{0}} + n - 1_{c_{1}} + . . . . n - 1_{c_{n - 1}}]$

$= n {.2}^{n - 1} A . M = \frac{\sum f_{i} x_{i}}{N} = \frac{n {.2}^{n - 1}}{2^{n}} = \frac{n}{2}$

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