For a sample with mean , adding a constant c to each observation changes the mean to Â and the standard deviation Â is unchanged. Multiplying each observation by Â changes the mean to and the standard deviation to
(a) Scores on a difficult exam have a mean of 57 and a standard deviation of 20. The teacher boosts all the scores by 20 points before awarding grades. Report the mean and standard deviation of the boosted scores.
(b) Suppose that annual income of Canadian lawyers has a mean of Â and a standard deviation of $30,000. Values are converted to British pounds for presentation to a British audience. If one British pound equals , report the mean and standard deviation in British currency.
(c) Observations from a survey that asks about the number of miles traveled each day on mass transit are to be converted to kilometer units (1 mile = 1.6 kilometers). Explain how to find the mean and standard deviation of the converted observations.