How would you explain...
x is the standard deviation of the set of numbers (a,b,c,d,e). For each of the following sets, indicate which sets must have a standard deviation equal to x.
(a+2, b+2, c+2, d+2, e+2)
(a-2, b-2, c-2, d-2, e-2)
(2a, 2b, 2c, 2d, 2e)
(a/2, b/2, c/2, d/2, e/2)
Standard deviation measures spread about the mean. Adding 2 to each value also increases the mean by 2 so difference between each value and the mean does'nt change. Hence standard deviation doesn't change. Similarly when subtracting 2.