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Chapter 3: Q 3.4. (page 100)
True of False: The mean, median and mode can all be used with quantitative data. Explain your answer.
The given statement "The mean, median and mode can all be used with quantitative data" is true.
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Weekly Salaries. 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 99 and 108, 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 thexf- values, that is, classmark 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. (Hint: What does xf represent for each class?)
(d) Construct a table similar to the one in part (b) but with columns for .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.
Consider the data set: .
a) Obtain the mean and median of the data.
b) Replace the in the data set by and again compare the mean and median. Decide which measure of the center works better here and explain your answer.
c) For the data set in part b) the mean is neither central nor typical for the data. The lack of what property of the mean accounts for this result.
Age of U.S. Residents. The U.S. Census Bureau collects information about the ages of people in the United States. Results are published in Current Population Reports
a. Identify the variable and population under consideration.
b. A sample of six U.S. residents yielded the following data on ages (in years). Determine the median of these age data. Decide whether this descriptive measure is a parameter or a statistic, and use statistical notation to express the result.
c. By consulting the most recent census data, we found that the median age of all US residents is . Decide whether that descriptive measure is a parameter or a statistic and use statistical notation to express the result
We have provided simple data sets for you to practice finding the descriptive measures discussed in this section. For each data set.
Obtain the quartiles, determine the inter quartile range, find the five-number summary.
A company produces cans of stewed tomatoes with an advertised weight of 14oz. The standard deviation of the weights is known to be 0.4oz. A quality - control engineer selects a can of stewed tomatoes at random and finds its net weight to be 17.28oz.
Part (a): Estimate the relative standing of that can of stewed tomatoes, assuming the true mean weight is 14oz. Use the z-score and Chebyshev's rule.
Part (b): Does the quality - control engineer have reason to suspect that the true mean weight of all cans of stewed tomatoes being produced is not 14oz? Explain your answer.
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