(a) Prove algebraically that adding a constant to every observation of a data set…
MATHEMATICS · Subjective · AP · AP Statistics · Exploring One-Variable Data · Exploring One-Variable Data
Problem
(a) Prove algebraically that adding a constant c to every observation of a data set does not change its variance or standard deviation.
(b) Show that if every observation of a data set is multiplied by a non-zero constant k, the variance is multiplied by k2 and the standard deviation by ∣k∣.
(c) Explain how your results in (a) and (b) can be combined to obtain the effect on variance and standard deviation when each observation is subjected to the linear transformation y=kx+c.
(d) Verify parts (a)–(c) numerically for the data set 3, 5, 7, 9.