Effects of Linear Transformations on Mean, Median, sd, and Variance

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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