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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

Cookies Using the same frequency distribution from Exercise 1, identify the class boundaries of the first class and identify the class limits of the first class.

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Frequency

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4

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1

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a. What type of data is presented in the first column of the table ?

b. What type of data is presented in the second column of the table ?

c. What type of data is presented in the third column of the table ?

d. What type of data is provided by the information that Death Valley is in the United States?

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236 237 238 239 241 241 242 245 245 245 246 247 247 248 248 249 250 250 250 251 252 252 253 253 258 258 258 260 262 264

Data Type

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Frequency Distribution of Body Temperatures Construct a frequency distribution of the 20 body temperatures (oF) listed below. (These data are from Data Set 3 鈥楤ody Temperatures鈥� in Appendix B.) Use a class width of 0.5oF and a starting value of 97.0oF.

97.1 97.2 97.5 97.6 97.6 97.8 98.0 98.0 98.2 98.2 98.2 98.3 98.4 98.6 98.6 98.7 98.7 98.9 99.1 99.4.
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