Question

List I: $3,6,8,19$
List II: $x,3,6,8,19$
If the median of the numbers in list I above is equal to the median of the numbers in list II above, what is the value of $x$?

• A. $6$
• B. $7$
• C. $8$
• D. $9$
• E. $10$

Answer 1

Answer: (B)

$7$

Median is the middle value of the data values after arranging the data values in the ascending or descending order.

If $n$ is odd, then the median is $(\frac{n+1}{2}{)}^{th}$ value.

If $n$ is even, then the median is ${\frac{(\frac{n}{2}{)}^{th}+(\frac{n}{2}+1)}{2}}^{th}$ value.

List $I:3,6,8,19$

Total number of values is $n=4$ (even) then

the median is ${\frac{(\frac{4}{2}{)}^{th}+(\frac{4}{2}+1)}{2}}^{th}$

$=\frac{(2{)}^{nd}+(3{)}^{rd}}{2}=\frac{6+8}{2}=7$

List $II:x,3,6,8,19$

Total number of values is $n=5$ (odd) then

the median is $(\frac{5+1}{2}{)}^{th}=3^{rd}$ value.

Given that median of List I is equal to the median of List II. Therefore, for List II, $x=7$ should be median value.