The first two columns of the following table provide a frequency distribution, using limit grouping, for the days to maturity of 40 short-term investments, as found in BARRON€™S. The third column shows the class marks.

a. Use the grouped-data formulas to estimate the sample mean and sample standard deviation of the days-to-maturity data. Round your final answers to one decimal place.
b. The following table gives the raw days-to-maturity data.

Using Definitions 3.4 and 3.6 on pages 95 and 105, respectively, gives the true sample mean and sample standard deviation of the days-to-maturity data as 68.3 and 16.7, respectively, rounded to one decimal place. Compare these actual values of ¯ x and s to the estimates from part (a). Explain why the grouped-data formulas generally yield only approximations to the sample mean and sample standard deviation for non€“single-value grouping.

Days to Frequency Class mark maturity f 30-39 40-49 50-59 60-69 70-79 80-89 90-99 34.5 44.5 54.5 64.5 74.5 84.5 94.5 10 59680 63897 78503 87988 99819 86687 64 60 955 50-06 57556 97173 96746 8636 3553 02571 76755