1. If a fixed number c is added to all measurements in a data set, the deviations (x - ) remain unchanged (see Exercise 2.52). Consequently, s2 and s remain unchanged.
2. If all measurements in a data set are multiplied by a fixed number d, the deviations (x - ) get multiplied by d. Consequently, s2 gets multiplied by d2, and s by |d|. (The standard deviation is never negative.)
Verify these properties for the data set

taking c = 4 in property (1) and d = 2 in (2).

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