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Chapter 2: Q18 (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 Weights of respondents were recorded as part of the California Health Interview Survey. The last digits of weights from 50 randomly selected respondents are listed below. Construct a frequency distribution with 10 classes. Based on the distribution, do the weights appear to be reported or actually measured? What do you know about the accuracy of the results?

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

Short Answer

Expert verified

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

Last digits of weights

Frequency

0

26

1

1

2

1

3

2

4

2

5

12

6

1

7

0

8

4

9

1

Most of the values of weights have a 0 or 5 as their last digits. This explains that most students have reported their weights and not measured them.

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

Step by step solution

01

Given information

Data are given on the last digits of the weights 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 requirement of closed class intervals.

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

0 appears 26 times.

1 appears 1 time.

2 appears 1 time.

3 appears 2 times.

4 appears 2 times.

5 appears 12 times.

6 appears 1 time.

7 appear 0 times.

8 appears 4 times.

9 appears 1 time.

Thus, the following frequency distribution is constructed:

Last digits of weights

Frequency

0

26

1

1

2

1

3

2

4

2

5

12

6

1

7

0

8

4

9

1

Almost all values contain either 0 or 5.

This implies that the weights have not been measured and are reported as rounded values.

Thus, the weights do not appear to be very accurate.

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Most popular questions from this chapter

Interpreting a Histogram. In Exercises 5鈥�8, answer the questions by referring to the following Minitab-generated histogram, which depicts the weights (grams) of all quarters listed in Data Set 29 鈥淐oin Weights鈥� in Appendix B. (Grams are actually units of mass and the values shown on the horizontal scale are rounded.)

Relative Frequency Histogram How would the shape of the histogram change if the vertical scale uses relative frequencies expressed in percentages instead of the actual frequency counts as shown here?

Interpreting a Histogram. In Exercises 5鈥�8, answer the questions by referring to the following Minitab-generated histogram, which depicts the weights (grams) of all quarters listed in Data Set 29 鈥淐oin Weights鈥� in Appendix B. (Grams are actually units of mass and the values shown on the horizontal scale are rounded.)

Class Width and Class Limits Give the approximate values of the class width, and the lower and upper class limits of the class depicted in the bar farthest to the left.

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Chocolate Chips

Frequency

18-20

6

21-23

11

24-26

18

27-29

4

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1

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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

Frequency Distribution For the frequency distribution from Exercise 1, find the following.

a. Class limits of the first class

b. Class boundaries of the first class

c. Class midpoint of the first class
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