Question

Which number can be included in the given data set such that the median remains unchanged?

• A. $0$
• B. $2$
• C. $4$
• D. It is not possible to determine as there are multiple answers.

Answer 1

The correct option is C $4$

The data set in ascending order is as follows:
$\{1,2,2,3,4,7,8,9,10\}$

It is an odd-numbered data set.
Hence, the median is the central value of the data set, i.e., $4.$

Let's include $4$ in the data set.

$\{1,2,2,3,4,\underset{–}{4},7,8,9,10\}$

Now, this is an even-numbered data set.
Median = Average of fifth and sixth data points
$\Rightarrow$ Median $=\frac{4+4}{2}=4$

Hence, the median is the same as before, i.e., $4.$
$\therefore$ The required answer is $4.$