why is the average of a set of numbers alway smaller than the largest number in the set?

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- Oct 20th 2008, 04:20 PMm3clubracerwhy is the average of a set of numbers alway smaller than the largest number in the s
why is the average of a set of numbers alway smaller than the largest number in the set?

- Oct 20th 2008, 05:54 PMterr13
Not true, take the set 5,5,5. The average is 5, which is not greater than the largest element 5.

- Oct 22nd 2008, 04:45 PMThePerfectHacker
I assume smaller is in the weak sense rather than in a strict sense.

Let us do it with three elements so you can see the idea. Say $\displaystyle \{a_1\leq a_2\leq a_3\}$.

The average $\displaystyle a_1=\tfrac{a_1+a_1+a_1}{3}\leq \tfrac{a_1+a_2+a_3}{3} \leq \tfrac{a_3+a_3+a_3}{3} = a_3$