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 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

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

Given information

Data are given on the last digits of the heights 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 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.