M7MBA wrote:If the mean of the set S is 14 then find the Median of the set

1) Sets S = {2, 5, 14, 30, x, y}
2) Range of Set S = 28

The OA is E.

Why is not possible to find the Median of the set? May any expert help me? I am confused.

Statement 1: If the mean of a 6 element set is 14, we know the sum = 6*14 = 84.
So 2 + 5 + 14 + 30 + x + y = 84
51 + x + y = 84
x+ y = 33
Case 1: x = 15, y = 18. Our set ( 2, 5, 14, 15, 18, 30) Median = (14 + 15)/2 = 29/2
Case 2: x = 16, y = 17. Our set (2, 5, 14, 16, 17, 30) Median = (14 + 16)/2 = 30/2.
We can generate more than one value, so this statement alone is not sufficient.

Statement 2: if the range is 28, it just means that we know x and y are somewhere in between 2 and 30. We could reuse both cases from statement 1, so we can already see that together, we can generate more than value for the median of the set. The statement alone is not sufficient and the statements together are not sufficient.

The answer is E.