When data undergoes a linear transformation yi = a + bxi: the new mean is a + b(old mean), the new variance is $b^2$(old variance), and the new SD is |b|(old SD). The constant 'a' shifts all values uniformly, affecting the mean but leaving variance unchanged ("shift is silent"). The constant 'b' scales all values, affecting both mean and variance ("scale is squared"). This property enables simplification: to find variance of {100, 102, 104, 106, 108}, transform to {0, 2, 4, 6, 8} (subtract 100), compute variance = 8, then note original variance is the same (8) since only a shift was applied. If you further divide by 2 to get {0,1,2,3,4}, variance becomes 2, and original variance = 2^2 * 2 = 8.