Four Numbers Have A Mean Of 10 And A Median Of 10, But None Of The Numbers Is 10 What Could The Four Numbers Be?


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Vin Ginge answered
When there are an even number of values in a set then the median is found by taking the mean of the middle two values.  If the median is 10 then the two values must be 9 and 11, 8 and 12, 7 and 13 ......and so on. These two numbers can be represented by 10 + n and 10 - n.

If the mean is 10 then the second pair of numbers must also be of equal value greater or less than 10.
Therefore, the four numbers in the set can be represented  as :-
10 + n,10 - n, 10 + p and 10 - p where n and p are positive integers with p>n.(p is greater than n)
A typical set of numbers is 7,9,11,13 or 4,8,12,16.

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