Question

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

Conclusion I: Equal number of data point(s) lie before and after the median(s).

Conclusion II: The data point(s) belong(s) to the left of median(s) is/are less than the median, whereas the data point(s) belong(s) to the right of the median is/are greater than the median.

• A. Only conclusion I is correct.
• B. Only conclusion II is correct.
• C. Both conclusions are correct.
• D. These conclusions cannot be generalized.

Answer 1

The correct option is C Both conclusions are correct.

We 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

4

6

9

Here, 4 lies exactly at the middle position.

Hence, median = 4

We observe that 2 and 3 lie left of the median, and 6 and 9 lies right of the median.

Also, 2 and 3 are smaller than the median, i.e., 4, whereas 6 and 9 are greater than the median.

$\therefore$ Both the conclusions are correct.