Chapter 0 Introduction to Detailed Notes

his is a set of notes that is being constructed during the term. Some of these notes are based on notes that were started in Fall, 1999. However, that earlier effort was essentially rough drafts, placed on the WEB to get some reaction and possibly to benefit the students. Please note that these WEB notes contain commentary on the material in the textbook, and material that is supplementary to the material that is in the book.

After writing out the notes for the first few sections, it has become clear that there is a tendency to make this a "teaching" document. As much as possible, efforts will be made to not do this. Rather, if there is teaching material to be presented then that will be done in separate pages, with pointers inserted here.

There is additional material, prepared for the Math 179 class, that we should look at. The material in the supplement, Measure of Central Tendency, is important, and I have added notes about it here. However, there is more that I want you to read and learn. That extra material has been placed on the web. You will need to go to those web pages to read that material. The web material can be found at the Descriptive Statistics page.

Supplement Chapter 0: Statistics: Measures of Central Tendency

Chapter 0, Section 1: The Mean, Median, and Mode

The web page Basic Statistics on the TI-86 walks students through the use of the TI-86 to do some, if not all, of the work in Chapter 0. The web page Basic Statistics on the TI-85 walks students through the use of the TI-85 to do some, if not all, of the work in Chapter 0. On the other hand, the web pages Mean, Median, and Mode on the TI-85, Mean, Median, and Mode on the TI-86, and Mean, Median, and Mode on the TI-89 give a more complete treatment of the steps needed for this entire chapter. A similar page is beign developed for the TI-86. The web page Beginning Statistics on the TI-83 walks students through the use of the TI-83 to do some, if not all, of the work in Chapter 0. (This page also contains references to and examples of the COLLATE program for the TI-83. That program will be useful in looking at the material in Section 2 of this chapter of the textbook.) I will have to add more pages to demonstrate the COLLATE program, and to demonstrate the creation of frequency plots, frequency polygons, and histograms on the TI-86 (and the TI-85).

On page 2, item 2, Example 1, the question of finding the mode of 3, 5, 7, 2, 9, 8, 4, 6 is posed. The solution that is given is that there is "NO MODE". In fact the preceding text in the book states that there is no mode if every number occurs once. We could just accept that rule, or we could have not made this a special case. We could say that this is a multimodal instance and that there are 8 modes. For the most part, with large sets of data, this situation (each number occurs just once) just does not happen. As long as it does not happen we do not need to worry about our exact interpretation.

Page 2, item 3, presents the concept of the median. The text should point out the situations where the median is appropriately used and where it should not to be used. Unfortunately, the text does not do this. You will need to read the web pages, under Descriptive Statistics, to learn that concept.

Page 3, item 4, presents the rule for finding the median when we have an even number of values in the data set. The example demonstrates generating a median by finding the value that is half way between the two middle values. In the example in the book, that means that we add 6 and 8 to get 14 and then we divide 14 by 2 to give the answer as 7. First, note that in this case the median is not one of the original values. And, second, you need to understand that this is a rule the pops up on lots of "math" tests and quizes. However, in real life, with large data sets having many repeated values, this rarely happens. For large data set real life situations with an even number of values, usually the two middle values will be identical. In that case the median is just that same value. Again, the web pages cover this in more detail.

Page 4, item 6, starts a discussion about the appropriateness of each of the measures, the mode, the median, and the mean. This is covered in much more detail in the web pages.

Chapter 0, Section 2: Frequency Tables and Frequency Polygons

This section begins with a discussion of how one constructs a frequency table. This is also covered in my web pages. What remains to be done is to crete additional web pages to demonstrate the COLLATE program, and the creation of frequency plots, polygons, and historgrams on the TI-86 (and 85).