# Question: In the following table we repeat the salary data in

In the following table, we repeat the salary data in Data Set II from Example 3.1.

a. Use Definitions 3.4 and 3.6 on pages 95 and 105, respectively, to obtain the sample mean and sample standard deviation of this (ungrouped) data set.

b. A frequency distribution for Data Set II, using single-value grouping, is presented in the first two columns of the following table. The third column of the table is for the xf -values, that is, class mark or midpoint (which here is the same as the class) times class frequency. Complete the missing entries in the table and then use the grouped-data formula to obtain the sample mean.

c. Compare the answers that you obtained for the sample mean in parts (a) and (b). Explain why the grouped-data formula always yields the actual sample mean when the data are grouped by using single-value grouping.

d. Construct a table similar to the one in part (b) but with columns for x, f, x - x-bar, (x − ¯x)2, and (x − x-bar)2f. Use the table and the grouped-data formula to obtain the sample standard deviation.

e. Compare your answers for the sample standard deviation in parts (a) and (d). Explain why the grouped-data formula always yields the actual sample standard deviation when the data are grouped by using single-value grouping.

a. Use Definitions 3.4 and 3.6 on pages 95 and 105, respectively, to obtain the sample mean and sample standard deviation of this (ungrouped) data set.

b. A frequency distribution for Data Set II, using single-value grouping, is presented in the first two columns of the following table. The third column of the table is for the xf -values, that is, class mark or midpoint (which here is the same as the class) times class frequency. Complete the missing entries in the table and then use the grouped-data formula to obtain the sample mean.

c. Compare the answers that you obtained for the sample mean in parts (a) and (b). Explain why the grouped-data formula always yields the actual sample mean when the data are grouped by using single-value grouping.

d. Construct a table similar to the one in part (b) but with columns for x, f, x - x-bar, (x − ¯x)2, and (x − x-bar)2f. Use the table and the grouped-data formula to obtain the sample standard deviation.

e. Compare your answers for the sample standard deviation in parts (a) and (d). Explain why the grouped-data formula always yields the actual sample standard deviation when the data are grouped by using single-value grouping.

**View Solution:**## Answer to relevant Questions

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. ...Define a. Descriptive measures. b. Measures of center. c. Measures of variation. Dr. Thomas Stanley of Georgia State University has collected information on millionaires, including their ages, since 1973. A sample of 36 millionaires has a mean age of 58.5 years and a standard deviation of 13.4 years. a. ...The U.S. Department of Agriculture collects data pertaining to the value of agricultural exports and publishes its findings in U.S. Agricultural Trade Update. For one year, the values of these exports, by state, are provided ...The data for shell thickness and concentration of PCBs for 60 Anacapa pelican eggs from Exercise 4.70 are on the WeissStats CD. In exercise Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be a great ...Post your question