Multiple choice

The arithmetic mean of the set of observations $1, 2, 3, ..., n$ is

  1. $\displaystyle \frac{n+1}{2}$
  2. $\displaystyle \left ( \frac{n}{2}+1 \right )$
  3. $\displaystyle \frac{n}{2}$
  4. $\displaystyle \frac{1}{2}\left ( n-1 \right )$
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A Correct answer
Explanation

The sum of the first n natural numbers is n(n+1)/2. The mean is the sum divided by n, which is (n(n+1)/2) / n = (n+1)/2.

AI explanation

The sum of the first n natural numbers is given by the formula n(n+1)/2. To find the arithmetic mean, divide this sum by the number of observations, n. This yields n(n+1)/2n, which simplifies to (n+1)/2.

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