Answer:
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
