Question

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?

Answer 1

We have been given that two datasets arranged in descending order are:
`\{8, x, 4,1\}` and
`\{9, y, 5,2\}`. We are asked to find the value of
`(y-x)^2`, if the medians of the two given datasets are equal.

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

`\{1,4,x,8\}` and
`\{2,5,y,9\}`

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

`(4+x)/(2)` and
`(5+y)/(2)`

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

`(5+y)/(2)=(4+x)/(2)`

Cross multiply:

`2(5+y)=2(4+x)`

Divide both sides by 2:

`(2(5+y))/(2)=(2(4+x))/(2)`

`5+y=4+x`

`5-5+y-x=4-5+x-x`

`y-x=-1`

Let us square both sides of our equation.

`(y-x)^2=(-1)^2`

`(y-x)^2=1`

Therefore, the value of
`(y-x)^2` would be 1.