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Chapter 2: Q17 (page 49)

Constructing Frequency Distributions. In Exercises 11鈥�18, use the indicated data to construct the frequency distribution. (The data for Exercises 13鈥�16 can be downloaded at TriolaStats.com.)

Analysis of Last Digits Heights of statistics students were obtained by the author as part of an experiment conducted for class. The last digits of those heights are listed below. Construct a frequency distribution with 10 classes. Based on the distribution, do the heights appear to be reported or actually measured? What do you know about the accuracy of the results?

0 0 0 0 0 0 0 0 0 1 1 2 3 3 3 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 8 8 8 9

Short Answer

Expert verified

The following frequency distribution is constructed for the last digits of the heights:

Last digits of heights

Frequency

0

9

1

2

2

1

3

3

4

1

5

15

6

2

7

0

8

3

9

1

The majority of the values of heights have a 0 or 5 as their last digit. This explains that most students have not correctly measured their heights and have simply rounded them.

Thus, the given data on heights cannot be considered accurate.

Step by step solution

01

Given information

Data are given on the last digits of the heights of statistics students.

02

Frequency distribution

A frequency distribution is an ordered arrangement of frequencies of data values in the form of class intervals. It is used to depict numerical data.

03

Construction

Here, as the data contains only a few discrete values, and the question demands to create exactly 10 classes (as10 digits are available), it can be said that there is no need for closed class intervals.

By counting the number of times each discrete value appears in the data, the following information is obtained:

0 appears 9times.

1 appears 2times.

2 appears1 time.

3 appears 3times.

4 appears1time.

5 appears 15 times.

6 appears2 times.

7 appear 0 times.

8 appears3 times.

9 times 1 time.

Thus, the following frequency distribution is constructed:

Last digits of heights

Frequency

0

9

1

2

2

1

3

3

4

1

5

15

6

2

7

0

8

3

9

1

As the majority of values contain either 0 or 5, this suggests that the heights have been reported and not correctly measured.

Therefore, it can be said that the heights of the students are not very accurate.

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Most popular questions from this chapter

Normal Distributions. In Exercises 9 and 10, using a loose interpretation of the criteria for determining whether a frequency distribution is approximately a normal distribution, determine whether the given frequency distribution is approximately a normal distribution. Give a brief explanation.

Best Actors Refer to the frequency distribution from Exercise 6

Deceptive Graphs. In Exercises 17鈥�20, identify how the graph is deceptive.

Subway Fare In 1986, the New York City subway fare cost \(1, and as of this writing, the current cost is \)2.50, so the 1986 price was multiplied by 2.5. In the accompanying graph, the large bill is 2.5 times as tall and 2.5 times as wide as the smaller bill.

Heights Heights of adult males are normally distributed. If a large sample of heights of adult males is randomly selected and the heights are illustrated in a histogram, what is the shape of that histogram?

Deceptive Graphs. In Exercises 17鈥�20, identify how the graph is deceptive.

Cost of Giving Birth According to the Agency for Healthcare Research and Quality Healthcare Cost and Utilization Project, the typical cost of a C-section baby delivery is \(4500, and the typical cost of a vaginal delivery is \)2600. See the following illustration.

In Exercises 5鈥�8, identify the class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. The frequency distributions are based on real data from Appendix B.

Age (yr) of Best Actress When Oscar Was Won

Frequency

20-29

29

30-39

34

40-49

14

50-59

3

60-69

5

70-79

1

80-89

1
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