SOLUTION: In a set of five positive integers, the average (arithmetic mean), median and mode are all the same number, m. If the lowest number in the set is a and the highest number in the se

Question 1202598: In a set of five positive integers, the average (arithmetic mean), median and mode are all the same number, m. If the lowest number in the set is a and the highest number in the set is b, which of the following must be true?
(A) The average of a and b is m.
(B) a, b, and m are the only numbers in the set.
(C) b-m = m-a
(D) b>2a
(E) 3m > a+b
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i think selection C is the answer
selection C says that b-m = m-a.
when the mean and the median and the mode are the same value, then you have a normal distribution.
a normal distribution is symmetric about the mean.
this means the area under the normal distribution curve is the same below the mean as above the mean.
here's one of many references from the web regaring normal distribution.
https://statisticsbyjim.com/basics/normal-distribution/

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