Question

Consider the following conclusions regarding the median of a data set.

Conclusion I : The number of data points lies before and after the median may or may not be equal.

Conclusion II : After arranging the data set in ascending order, the data points belong to the left of median are greater than the median, whereas the data points belong to the right of the median are less than the median.

• A. Only conclusion I is wrong.
• B. Only conclusion II is wrong.
• C. Both conclusions are wrong.
• D. Both conclusions are correct.

Answer 1

The correct option is C Both conclusions are wrong.

We can verify the conclusions with the help of an example.

Let's consider the following data set.

$4$

$6$

$9$

$3$

$2$

To determine the median, we arrange the data set in ascending order.

$2$

$3$

$\underset{–}{4}$

$6$

$9$

Here, the number $4$ lies exactly at the middle position. Hence, the median of the above data set is $4$.

We observe that $2$ and $3$ lie to the left of median, and $6$ and $9$ lie to the right of median. So, the number of data points lies to the left and right of median are always equal.

$\therefore$ Conclusion I is incorrect.

Also, the numbers ($2$ and $3$) belong to the left of median ($4$) are smaller than the median, whereas the numbers ($6$ and $9$) belong to the right of median ($4$) are larger than the median.

$\therefore$ Conclusion II is also incorrect.