Introduction to Detailed Notes
This 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 tendancy 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. For example, the section below represents commentary on the Chapter 0 material in the book. However, for this class, there is additional material on descriptive statistics. There is additional material, originally prepared for the Math 179 class, that we should look at. The material in Chapter 0 of your text is important. 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. Please be aware of the fact that this is material we are borrowing from another course. It has not yet been tuned for the Math 169 class. The web material can be found at the Descriptive Statistics page.
Textbook Chapter 0: Statistics: Measures of Central Tendency
Chapter 0, Section 1: The Mean, Median, and Mode
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.)
For those students using a TI-85, please see both
the Mean, Median, and Mode on the TI-85 page,
and the Basic Statistics on the TI-85 page.
For those students using a TI-86, please see both
the Mean, Median, and Mode on the TI-86 page,
and the Basic Statistics on the TI-86 page.
For those students using a TI-89, please see
the Mean, Median, and Mode on the TI-89 page.
On page ii, 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 ii, 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 iii, 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 iv, 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 probably a good time to return to the
Beginning Statistics on the TI-83 page and
the COLLATE program for the TI-83 calculator.
It is clear that we should expand on the beginning statistics to show students how to use the TI-83 to obtain an actual frequency plot and a frequency polygon on the calculator. I will try to create this page.
©Roger M. Palay
Saline, MI 48176
September, 1999