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Chapter 2: 139 SE (page 142)

Construct a relative frequency histogram for the data summarized in the accompanying table.

Short Answer

Expert verified

The graph is given below:

Step by step solution

01

Defining the relative frequency

Relative frequency shows how often something happens compared to others. It is calculated as the number of times something happens divided by the total outcomes. The heights of all bar in the relative frequency histogram must add up to 1.

02

Construct the relative frequency histogram 

Plot measurement class on the x-axis and the relative frequency on the y-axis. Then draw vertical bars with heights matching the value of relative frequency.

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Most popular questions from this chapter

A qualitative variable is measured for 20 companies randomly sampled and the data are classified into three classes, small (S), medium (M), and large (L), based on the number of employees in each company. The data (observed class for each company) are listed below. ______________________________________ SSL M SM M S M S L M S SSS M L S L ----------------------------------------------------------------

a. Compute the frequency for each of the three classes.

b. Compute the relative frequency for each of the three classes.

c. Display the results, part a, in a frequency bar graph.

d. Display the results, part b, in a pie chart.

Cable TV subscriptions and “cord cutters.” Has the increasing popularity of smartphones and video streaming over the Internet affected cable and satellite TV subscriptions? This was one of the questions of interest in a recent Pew Research Center survey (December 2015). Telephone (both landline and cell phone) interviews were conducted on a representative sample of 2,001 adults living in the United States. For this sample, 1,521 adults reported that they currently receive cable or satellite TV service at home, 180 revealed that they have never subscribed to cable/satellite TV service at home, and the remainder (300 adults) admitted that they are “cord cutters,” i.e., they canceled the cable/satellite TV service. The results are summarized in the Minitab pie chart shown.

a. According to the pie chart, what proportion of the adults in the sample currently have a cable/satellite TV subscription at home? Verify the accuracy of this proportion using the survey results.

b. Now consider only the 1,821 adults in the sample that have at one time or another subscribed to cable/satellite TV service. Create a graph that compares the proportions of adults who currently subscribe to cable/satellite TV service with the proportion who are “cord cutters.”

Suppose a data set consisting of exam scores has a lower quartile QL = 60, a median QM = 75, and an upper quartile QU = 85. The scores on the exam range from 18 to 100. Without having the actual scores available to you, construct as much of the box plot as possible.

Monitoring weights of flour bags.When it is working properly, a machine that fills 25-pound bags of flour dispenses an average of 25 pounds per fill; the standard deviation of the amount of fill is .1 pound. To monitor the performance of the machine, an inspector weighs the contents of a bag coming off the machine’s conveyor belt every half hour during the day. If the contents of two consecutive bags fall more than 2 standard deviations from the mean (using the mean and standard deviation given above), the filling process is said to be out of control, and the machine is shut down briefly for adjustments. The data

given in the following table are the weights measured by the inspector yesterday. Assume the machine is never shut down for more than 15 minutes at a time. At what times yesterday was the process shut down for adjustment? Justify your answer.

Time

Weight (pounds)

8:00 a.m

25.10

8:30

25.15

9:00

24.81

9:30

24.75

10:00

25.00

10:30

25.05

11:00

25.23

11:30

25.25

12:00

25.01

12:30 p.m

25.06

1:00

24.95

1:30

24.80

2:00

24.95

2:30

25.21

3:00

24.90

3:30

24.71

4:00

25.31

4:30

25.15

5:00

25.20

Question: The output from a statistical software package indicates that the mean and standard deviation of a data set consisting of 200 measurements are \(1,500 and \)300, respectively.

a.What are the units of measurement of the variable of interest? Based on the units, what type of data is this: quantitative or qualitative?

b.What can be said about the number of measurements between \(900 and \)2,100? Between \(600 and \)2,400? Between \(1,200 and \)1,800? Between \(1,500 and \)2,100?
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