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

  1. #1
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    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?
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  2. #2
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    Not true, take the set 5,5,5. The average is 5, which is not greater than the largest element 5.
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    Quote Originally Posted by m3clubracer View Post
    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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