Given distinct positive integers 1, 11, 4, x, 2, and 9, which of the following could be the median?
Choose the most appropriate option.
A) 2  B) 3  C) 6  D) 8  E) 9
The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.   Arrange numbers in ascending order: 1, 2, 4, 9, 11, and x.   Now, x can not possibly be less than 4 as given that all integers are positive and distinct (and we already have 1, 2, and 4).   Next, if x is 4&lt;x&lt;9 then the median will be the average of 4 and x. As all answers for the median are integers, then try odd values for x:   If x=5, then median=(4+5)/2= 
<gadget id="calculator">(4+5)/2</gadget>
<output>9/2 = around 4.5</output>
4.5 --&gt; not among answer choices;   If x=8, then median=(4+8)/2= 
<gadget id="calculator">(4+8)/2</gadget>
<output>6</output>
6 --&gt; OK;   Answer: 6
<result>C</result>
Given distinct positive integers 1, 11, 4, x, 2, and 9, which of the following could be the median?