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

Answer:

1

Step-by-step 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) = $\frac{x+4}{2}$... 1

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

Median(2) = $\frac{y+5}{2}$ ...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;

$\frac{x+4}{2} = \frac{y+5}{2}$

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

Therefore y-x = -1

(y-x)² = (-1)²

= 1