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) ?

Answer

Legon fo)

Step-by-step explanation:

Dataset 1 (in increasing order)

{1, 4, x, 8}

Dataset 2 (in increasing order)

{2, 5, y, 9}

Median of dataset 1

[4 + x] / [2]

Median of dataset 2

[5 + y] / [2]

since the medians of the two given sets of data are the same,

=> [4 + x] / [2] = [5 + y] / [2]

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

=> 10 + 2y = 8 + 2x

=> 2y - 2x = 8 - 10

=> 2y - 2x = - 2

=> 2 (y - x) = - 2

=> [2 (y - x) ] / [2] = [ - 2] / [2]

denominators and numerators cancel out

=> (y - x) = - 1

Therefore, (y - x) ² = (-1) ²

=> (y - x) ² = 1