Question

Which data set has a median of $16$?

• A. $16,21,26,29,32$
• B. $0,4,7,10,16,16$
• C. $0,9,31,17,18,22$
• D. $25,14,7,16,21$

Answer 1

The correct option is D $25,14,7,16,21$

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.

For option A:

data set is $16,21,26,29,32$

Ascending order of the data values $16,21,26,29,32$.

total number of values $=n=5$ (odd)

Median = $(\frac{n+1}{2}{)}^{th}=(\frac{5+1}{2}{)}^{th}=3^{rd}\text{value}=26$ FALSE

For option B:

data set is $0,4,7,10,16,16$

Ascending order of the data values $0,4,7,10,16,16$.

total number of values $=n=6$ (even)

Median = ${\frac{(\frac{n}{2}+\frac{n+1}{2})}{2}}^{th}$ value = ${\frac{(\frac{6}{2}{)}^{th}+(\frac{6}{2}+1)}{2}}^{th}$ value= ${\frac{(3{)}^{rd}+(4)}{2}}^{th}$ value =$\frac{7+10}{2}=\frac{17}{2}=8.5$ FALSE

For option C:

data set is $0,9,31,17,18,22$

Ascending order of the data values $0,9,17,18,22,31$.

total number of values $=n=6$ (even)

Median = ${\frac{(\frac{n}{2}+\frac{n+1}{2})}{2}}^{th}$ value = ${\frac{(\frac{6}{2}{)}^{th}+(\frac{6}{2}+1)}{2}}^{th}$ value= ${\frac{(3{)}^{rd}+(4)}{2}}^{th}$ value =$\frac{17+18}{2}=\frac{35}{2}=17.5$ FALSE

For option D:

data set is $25,14,7,16,21$

Ascending order of the data values $7,14,16,21,25$.

total number of values $=n=5$ (odd)

Median = $(\frac{n+1}{2}{)}^{th}=(\frac{5+1}{2}{)}^{th}=3^{rd}\text{value}=16$ TRUE