Distint Positive Numbers?

Question

Let a, b , and c be 3 distinct positive numbers. What can be said about the difference between the mean and the median of the three numbers?

1. It is always positive or zero.
2. It is less than one-third of the difference between the largest and smallest of the numbers.
3. It is always negative or zero.
4. none of the above.

Answer 1

The answer is: 2. It is less than one-third of the difference between the largest and smallest of the numbers.

To see why, let the numbers be a > b > c
Then:

mean(a,b,c) - median(a,b,c) =
(a+b+c)/3 - b = a/3 -2b/3 + c/3
< a/3 - c/3 (since b>c)

Answer 2

not 1 and not 3 because of the zero , ( and the nummebrs are positive )


remains is 2)
take 3 numbera, 1,2,300
median = 2
mean = 101
this is more than 1/3 so the answerr is none of the above

Answer 3

I think 4 is correct

Answer 4

sorry, not good in maths.