Two datasets arranged in descending order are; {8, , 4,1} and {9, , 5,2}. If the medians of the two given datasets are equal, what is the value of ( − )2?

We have been given that two datasets arranged in descending order are: and . We are asked to find the value of , if the medians of the two given datasets are equal.

First of all, we will arrange our given data sets in ascending order.

and

Since our data sets have 4 data points, so median will be average of middle two terms.

and

Now we will equate both median as we are told that median of both data sets are equal.

Cross multiply:

Divide both sides by 2:

Let us square both sides of our equation.

Therefore, the value of would be 1.