Given the set of n numbers, n>1, of which one is 1-1n and all the others are 1. The arithmetic mean of the n numbers is:

1962 AMC 12 Problem 8

Attempt Problem 8 of the 1962 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1962 AMC 12 solutions, or check the answer key.

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Given the set of

n

numbers,

n\gt1,

of which one is

1-\dfrac1n

and all the others are

1.

The arithmetic mean of the

n

numbers is:

1

n-\dfrac1n

n-\dfrac1{n^2}

1-\dfrac1{n^2}

1-\dfrac1n-\dfrac1{n^2}

There are

n-1

copies of

1

Add all

n

numbers, then divide the sum by

n

The sum is

(n-1)+\left(1-\frac1n\right)=n-\frac1n.

Dividing by

n

gives

1-\frac{1}{n^2}.

Thus, the correct answer is D.