statistics

uptowngirl92 wrote:What is the median of set S = (a - b, b - a, a + b) ?

1. The mean of set S is equal to a + b
2. The range of set S is equal to 2b

Using Statement 1, we can find the mean of the set and set it equal to a+b:

(a - b + b - a + a + b)/3 = a + b
(a+b)/3 = a+b
a + b = 3a + 3b
2(a + b) = 0
a + b = 0

Now, we know the value of a+b, one of the elements in our set, so our set is

{a - b, b - a, 0}

Now, a - b = -(b - a), so if one of the two remaining elements is positive, the other must be negative, and 0 must be the median. If all the elements equal 0, again we find that 0 is the median. So Statement 1 is sufficient.

For Statement 2, it's certainly possible that a = b = 0, and that the median is 0. But we might have that a = 0, b = 1, and the elements in our set are {-1,1,1}, and the range is equal to 2b, but the median is not 0. So Statement 2 is not sufficient.