Assume that Y is a linear transformation of X. Then,

Y = bX + A

What is the relationship between the mean, median, standard deviation, and variance of X and the mean, median, standard deviation, and variance of Y?

Mean of Y = b(mean of X) +A

Median of Y = b(median of X) + A

sd of Y = b(sd of X)

Variance of Y = b² (variance of X)

For example, let b = 2 and A = 3

X Y 1 5 2 7 3 9

X Y Mean 2 (2)(2)+3 = 7 Median 2 (2)(2)+3 = 7 sd 1 (2)(1) = 2 variance 1 (2²)(1) =4