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Question
The arithmetic mean of the set of observations 1, 2, 3, --------n is -----
n+1/2
(n/2+1)
n/2
1/2(n-1)
ANSWER : 1
Descrption
<p>The arithmetic mean of a set of numbers is equal to the sum of the numbers divided by the total number of numbers. In this case, we want to find the arithmetic mean of the set of observations from 1 to n.</p><p>The sum of the numbers from 1 to n can be found using the formula for the sum of an arithmetic series:</p><p>sum = (n/2)(first term + last term)</p><p>In this case, the first term is 1, the last term is n, and the common difference is 1. Therefore, we have:</p><p>sum = (n/2)(n+1)</p><p>The total number of numbers in the set is n, so the arithmetic mean is:</p><p>mean = sum/n</p><p>Substituting the expression for sum, we get:</p><p>mean = [(n/2)(n+1)]/n</p><p>Simplifying, we get:</p><p>mean = (n+1)/2</p><p>Therefore, the arithmetic mean of the set of observations 1, 2, 3, ..., n is (n+1)/2</p>
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