Hi Shibsriz,
if X =4 then set will be 2,4,5,9.
Median = (4+5)/2 =4.5
how you got 3 ?

Regards,
Uva.

[email protected] wrote:In this question, im not clear why we cant take 4 as X in that case wont the median be 3?

Thanks

Eliminate the four answer choices that COULD be the median.

2, 2, 5, 9 --> median = (2+5)/2 = 3.5.
Eliminate B.

2, 3, 5, 9 --> median = (3+5)/2 = 4.
Eliminate C.

2, 5, 5, 9 --> median = (5+5)/2 = 5.
Eliminate D.

2, 5, 8, 9 --> median = (5+8)/2 = 6.5.
Eliminate E.

The correct answer is A.

Of the 3 given values -- 2, 5, and 9 -- the average of the two smallest = (2+5)/2 = 3.5.
Implication:
The median cannot be less than 3.5.
To illustrate:
The least possible value for X is 1.
If X = 1, then the set becomes {1, 2, 5, 9}, in which case the median = (2+5)/2 = 3.5.

[email protected] wrote:In this question, im not clear why we cant take 4 as X in that case wont the median be 3?

Thanks

Median is 3.0 if the sum of two middle integers is 6, and X, 2, 5, 9 may be the order if X = 1 or 2, median is not 3.0. Further, 2, X, 5, 9 may be the order if X = 3, 4 or 5, median is not 3.0.Continue, 2, 5, X, 9 may be the order if X = 5, 6, 7, 8, or 9, median is not 3.0. Finally, 2, 5, 9, X may be the order if X = 9 or more, median is not 3.0, because median cannot be 3.0 in the given scenario. Not interested in testing remaining choices because I love A.

If X = 4, order is 2, 4, 5, 9 and the median is 4.5, not 3.0.

Revision: To determine median, we must list the numbers in order first, next count them, if they are 5 (means odd), the median will be ½ (5 + 1)th i.e. 3rd term from left or right, and if they are 4 (means even), there occur two medians, one is 4/2th i.e. 2nd term and the other is the next, means the 3rd term. The absolute median in this case is the average (arithmetic mean) of the two medians.

(x,2,5,9)

For Even number of array, Median = (Middle 1 + Middle 2)/2

Since, "5" will always be there so.. (5+Middle2)/2

{A} 3.0 ==> 3.0 = (5+Middle2)/2 ==> Middle2 = 1 ==> NOT POSSIBLE
{B} 3.5 ==> 3.5 = (5+Middle2)/2 ==> Middle2 = 2 ==> POSSIBLE
{C} 4.0 ==> 4.0 = (5+Middle2)/2 ==> Middle2 = 3 ==> POSSIBLE
{D} 5.0 ==> 5.0 = (5+Middle2)/2 ==> Middle2 = 5 ==> POSSIBLE
{E} 6.5 ==> 6.5 = (5+Middle2)/2 ==> Middle2 = 8 ==> POSSIBLE

[spoiler]{A}[/spoiler]