Question

There are M positive numbers and the averages of each possible pair of these numbers is found.If the average of these number is N, what is the average of M numbers?

Answer 1

Given : There are M positive numbers and the averages of each possible pair of these numbers is found.

average of all these averages is N,

To Find :  What is the average of M numbers

Solution:

Take example    1 ,  5 , 6

3 numbers  

Average = (1 + 5 + 6)/3  = 4

Possible Pairs ( 1 , 5) , ( 1 , 6) , (  5, 6)

Average of Each  = 3 , 3.5 ,  5.5

Average of all average = ( 3 + 3.5 + 5.5)3  =  12/3 = 4

Hence Average is same.

average of all these averages is N

Hence  average of M numbers is N

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