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

**m3clubracer** · October 20th 2008, 04:20 PM

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

**terr13** · October 20th 2008, 05:54 PM

Not true, take the set 5,5,5. The average is 5, which is not greater than the largest element 5.

**ThePerfectHacker** · October 22nd 2008, 04:45 PM

Originally Posted by m3clubracer

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

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 $\{a_1\leq a_2\leq a_3\}$ .

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

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