62 Chapter 2 Graphical Summaries of Data g. Repeat parts (b)–(d), using the frequency distribution constructed in part (f). h. Do you think that five and nine classes are both reasonably good choices for these data, or do you think that one choice is much better than the other? Explain your reasoning. 28. Technology salaries: The following table presents the annual salaries for the employees of a small technology firm. 91,808 118,625 131,092 60,763 36,463 37,187 45,870 50,594 98,302 123,973 182,255 59,186 44,889 164,861 71,082 69,695 28,098 157,110 50,461 98,132 49,742 25,339 24,164 107,878 136,690 129,514 99,254 57,468 a. Construct a frequency distribution with approximately nine classes. b. Construct a frequency histogram from this frequency distribution. c. Construct a relative frequency distribution using the same classes. d. Construct a relative frequency histogram from this relative frequency distribution. e. Are the histograms skewed to the left, skewed to the right, or approximately symmetric? f. Construct a frequency distribution with approximately four classes. g. Repeat parts (b)–(d), using the frequency distribution constructed in part (f). h. Do you think that four and nine classes are both reasonably good choices for these data, or do you think that one choice is much better than the other? Explain your reasoning. 29. Brothers and sisters: Thirty students in a first-grade class were asked how many siblings they have. Following are the results. 1 1 2 1 2 3 7 1 1 5 1 1 3 0 1 1 1 2 5 0 0 1 2 2 4 2 2 3 3 4 a. Construct a frequency histogram. b. Construct a relative frequency histogram. c. Are the histograms skewed to the left, skewed to the right, or approximately symmetric? 30. Pets: Thirty students in a second-grade class were asked how many pets their family has. Following are the results. 1 0 0 1 1 2 0 1 2 1 1 2 2 0 1 0 1 1 3 1 1 5 2 1 1 4 0 1 1 2 a. Construct a frequency histogram. b. Construct a relative frequency histogram. c. Are the histograms skewed to the left, skewed to the right, or approximately symmetric? 31. No histogram possible: A company surveyed 100 employees to find out how far they travel in their commute to work. The results are presented in the following frequency distribution. Distance in Miles Frequency 0.0 – 4.9 18 5.0 – 9.9 26 10.0 – 14.9 15 15.0 – 19.9 13 20.0 – 24.9 12 25.0 – 29.9 9 30 or more 7 Explain why it is not possible to construct a histogram for this data set. 32. Histogram possible? Refer to Exercise 31. Suppose you found out that none of the employees traveled more than 34 miles. Would it be possible to construct a histogram? If so, construct a histogram. If not, explain why not. Extending the Concepts 33. Silver ore: The following histogram presents the amounts of silver (in parts per million) found in a sample of rocks. One rectangle from the histogram is missing. What is its height? 0 1 2 3 4 5 6 0.3 0.2 0.1 0 Silver (parts per million) Relative Frequency 34. Classes of differing widths: Consider the following relative frequency distribution for the data in Table 2.7, in which the classes have differing widths. Class Frequency Relative Frequency 0.00–0.99 9 0.138 1.00–1.49 19 0.292 1.50–1.99 7 0.108 2.00–2.99 11 0.169 3.00–3.99 13 0.200 4.00–6.99 6 0.092 a. Compute the class width for each of the classes. b. Construct a relative frequency histogram. Compare it to the relative frequency histogram in Figure 2.6, in which the classes all have the same width. Explain why using differing widths gives a distorted picture of the data. c. The density of a class is the relative frequency divided by the class width. For each class, divide the relative frequency by the class width to obtain the density. d. Construct a histogram in which the height of each rectangle is equal to the density of the class. This is called a density histogram. e. Compare the density histogram to the relative frequency histogram in Figure 2.6, in which the classes all have the same width. Explain why differing class widths in a density histogram do not distort the data.
navidi_monk_essential_statistics_1e_ch1_3
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