Question

Constructing Frequency Distributions. In Exercises 11–18, use the indicated data to construct the frequency distribution. (The data for Exercises 13–16 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

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

Given information

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

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.

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.