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

• October 20th 2008, 04:20 PM
m3clubracer
why 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?
• October 20th 2008, 05:54 PM
terr13
Not true, take the set 5,5,5. The average is 5, which is not greater than the largest element 5.
• October 22nd 2008, 04:45 PM
ThePerfectHacker
Quote:

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