Let X n denote the mean of first n natural numbers, then the mean of X 1 , X 2 , … , X 100 is

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Question: Answered & Verified by Expert

Let

X_{n}

denote the mean of first

n

natural numbers, then the mean of

X_{1}, X_{2}, \dots, X_{100}

is

MathematicsStatisticsJEE Main

Options:

A $25$
B $50$
C $25.5$
D $25.75$

Solution:

2176 Upvotes Verified Answer

The correct answer is:

25.75

X_{n} = \frac{\sum_{r = 1}^{n} r}{n} = \frac{n (n + 1)}{2 n} = \frac{n + 1}{2}

\frac{\sum_{n = 1}^{100} X_{n}}{n} = \frac{\frac{100 \times 101}{2} + 100}{200}

= \frac{101}{4} + \frac{1}{2} = 25.75

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