The mean of the data set {9, 5, y, 2, x } is twice the data set {8, x, 4, 1, 3}. What is (y-x) ^2?

256

Step-by-step explanation:

To calculate the mean, we simply divide the sum of the values by the count.

For the first set, the mean is as follows;

(9 + 5 + 2 + y + x) / 5 = (x + y + 16) / 5

For the second set;

(8 + x + 4 + 1 + 3) / 5 = (16 + x) / 5

Since both are divided by 5, we can eliminate it

Mean of first set is twice the second

This means that;

x + y + 16 = 2 (16 + x)

x + y + 16 = 32 + 2x

y = 32-16+2x-x

y = 16 + x

Now we want to calculate

(y-x) ^2

substitute the value of y here

(16+x-x) ^2

= 16^2 = 256