[EX02-042] A USA Snapshot titled “Nuns an aging order” reports that the median age of 94,022 Roman Catholic nuns in the United States is 65 years and the percentages of U.S. nuns by age group are as follows:

Under 50 51–70 Over 70 Refused to give age 16% 42% 37% 5%

This information is based on a survey of 1049 Roman Catholic nuns. Suppose the survey had resulted in the following frequency distribution (52 ages unknown):

Age 20–30 30–40 40–50 50–60 60–70 70–80 80–90 Frequency 34 58 76 187 254 241 147

(See the histogram drawn in Exercise 2.42, p. 69.)

a. Find the mean, median, mode, and midrange for this distribution of ages.

b. Find the variance and standard deviation.