Some properties of the standard deviation.

1. If a fixed number c is added to all measurements in a data set, the deviations remain unchanged (see Exercise 2.52). Consequently, and s remain unchanged.

2. If all measurements in a data set are multiplied by a fixed number

d, the deviations get multiplied by

d. Consequently, gets multiplied by , and s by

 d . (Note: The standard deviation is never negative.)

Verify these properties for the data set 5 9 9 8 10 7 taking in property (1) and in

(2).