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?

1

Step-by-step explanation:

Median of a dataset is the value at the centre of the dataset after rearrangement.

Given the data {8, x, 4,1}, the median of the set will be two values (x and 4). Since we have two values as the median, we will take their average.

Median of the first data set = x+4/2 ... (1)

For the second dataset {9, y, 5,2}, the median will be y+5/2

Since we are told that the medians of both datasets are equal, we will equate the value of the medians of both datasets as given below;

x+4/2 = y+5/2

cross multiplying;

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

Dividing both sides by 2 will give;

x+4 = y+5

From the resulting equation;

y-x = 4-5

y-x = - 1

(y-x) ² = (-1) ² = 1