Question

Two datasets arranged in descending order are; {8, x, 4,1} and {9, y, 5,2}. If the medians of

the two given datasets are equal, what is the value of (y − x)
2
?

Answer 1

1

Explanation:

A data arranged in descending order is a data arranged from the biggest to the smallest. The medisn of the data sets is the value at the middle of the dataset after rearrangment.

For the dataset {8, x, 4,1}, the median will be x and 4. Since we have two median values, we will take their average as shown

Median(1) =
`(x+4)/(2)`... 1

Simialrly for dataset {9, y, 5,2}, the median will be y and 5.

Median(2) =
`(y+5)/(2)` ...2

Since the medians of the two given datasets are equal, we will equate equation 1 and 2 and calculate for y-x as shown;

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

`x+4 = y+5\\x-y = 5-4\\x-y = 1\\y-x = -1`

Therefore y-x = -1

(y-x)² = (-1)²

= 1