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Chapter 2: Q18E (page 82)

Question:A company is analysing the prices at which its items are sold. Graph the relative frequency histogram for the 600 items summarized in the accompanying relative frequency table.

Short Answer

Expert verified

A graph that displays frequencies using vertical columns. And there are no spaces among the bars.

Step by step solution

01

Frequency histogram

A frequency histogram is a graph of a frequency and percentage in which the width, as well as location of rectangles, represent the different classes, as well as the height of those rectangles, represents the regularity with which data fell into the corresponding class. A graph that displays frequencies using vertical columns. And there are no spaces among the bars.

02

Measurement classes

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Most popular questions from this chapter

Is honey a cough remedy?Refer to the Archives of Pediatrics and Adolescent Medicine(December 2007) study of honeyas a remedy for coughing, Exercise 2.31 (p. 86). The coughingimprovement scores (as determined by the children鈥檚 parents)for the patients in the over-the-counter cough medicinedosage (DM) group, honey dosage group, and control groupare reproduced in the accompanying table.

Honey Dosage

12, 11, 15, 11, 10, 13, 10, 4 ,15, 16, 9, 14, 10, 6, 10, 8, 11, 12, 12, 8, 12, 9, 11, 15, 10, 15, 9, 13, 8, 12, 10, 8, 9, 5, 12

DM Dosage

4, 6, 9, 4, 7, 7, 7, 9, 12 ,10, 11, 6, 3, 4, 9, 12, 7, 6, 8, 12, 12, 4, 12, 13, 7, 10

No Dosage
(Control)

13, 9, 4, 4, 10, 15, 9, 5, 8, 6, 1, 0, 8, 12, 8, 7, 7, 1, 6, 7, 7, 12, 7, 9, 7, 9, 5, 11, 9, 5, 6, 8, 8, 6, 7, 10, 9, 4, 8, 7, 3, 1, 4, 3

a.Find the standard deviation of the improvement scores for the honey dosage group.

b.Find the standard deviation of the improvement scores for the DM dosage group.

c.Find the standard deviation of the improvement scores for the control group.

d.Based on the results, parts a鈥揷, which group appears to have the most variability in coughing improvement scores? The least variability?

Consider the horizontal box plot shown below.


a.What is the median of the data set (approximately)?

b.What are the upper and lower quartiles of the data set (approximately)?

c.What is the interquartile range of the data set (approximately)?

d.Is the data set skewed to the left, skewed to the right, or symmetric?

e.What percentage of the measurements in the data set lie to the right of the median? To the left of the upper quartile?

f.Identify any outliers in the data.

Question: In his essay "Making Things Right," W. Edwards Deming considered the role of statistics in the quality control of industrial products. In one example, Deming examined the quality-control process for steel rods manufacturers. Rods produced with diameters smaller than 1 centimeter fit too loosely in their bearings and ultimately must be rejected (thrown out). To determine whether the diameter setting of the machine that produces the rods is correct, 500 rods are selected from the day's production, and their diameters are recorded. The distribution of the 500 diameters for one day's production is shown in the accompanying figure. Note that the symbol LSL in the figure represents the 1-centimeter lower specification limit of the steel rod diameters. There has been speculation that some of the inspectors are unaware of the trouble that an undersized rod diameter would cause later in the manufacturing process. Consequently, these inspectors may pass rods with diameters that are barely below the lower specification limit and record them in the intervalcenteredat 1.000 centimeters. According to the figure, is there any evidence to support this claim? Explain.

Explain how the relationship between the mean and median provides information about the symmetry or skewness of the data鈥檚 distribution.

Question: Given a data set with a largest value of 760 and a smallest value of 135, what would you estimate the standard deviation to be? Explain the logic behind the procedure you used to estimate the standard deviation. Suppose the standard deviation is reported to be 25. Is this feasible? Explain
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