Lesson #3

Purpose:  To study Stem and Leaf plots and begin to understand mean deviation.

Stem and Leaf plots are useful.  You can see all of the data and it also looks like a bar graph.

I will use the same example I used in Lesson # 2.  These are the scores of my students on a recent Algebra test.

 54 67 72 72 75 78 81 84 86 86 88 92 95 98 100
I can arrange this data in a display called a Stem and Leaf plot.   The stems are the tens digit of each of the numbers.  The stems are located in the first column.

 5 4 6 7 7 2 2 5 8 8 1 4 6 6 8 9 2 5 8 10 0
The leaves are the unit's digits. There is usually a key given with this display to make sure that everyone who uses the display knows what the data means.
The key might look like this;        8 |6       = 86

With a Stem and Leaf plot, you can see which sort of data occurs most frequently.  The mean and median are not very easy to see.  You must calculate and count to arrive at those averages.  The mode is pretty easy to see.

If you do't understand this explanation visit Jenn's Stem and Leaf plot instructions to get a better idea.  Then download your assignment and see what you can make.

Jenn's stem and leaf intructions

Assignment # 3     President's ages.doc

Concept: To examine one more data descriptor.

If you can't see all of the data ... it is too large a set or the actual data is just not listed ... it is helpful to know information about the data.  The data's mean, median, mode, and range are some descriptors but here is a new one.

One descriptor that you probably haven't understood before is called the MAD = Mean Absolute Deviation.

Different sets of data may have the same mean but, when examined, are actually very different lists of data.

Here is an example of what I mean.  I asked 9 of my students to count the number of people in their immediate family ( the family that lives in their home),  Their responses looked like this;
 Thomas 5 Rachel 6 Jorge 3 Latrisha 5 Jon 7 Vivian 3 Nathan 2 Jillian 9 Maria 5
The average (mean) of these nine student's family sizes is 5 people per family.  But, their family sizes are very different.
Here's another set of family sizes from another 9 students that I interviewed.

 Jesse 5 Madge 5 George 5 Patty 5 Sam 5 Lucy 5 Nick 5 Lois 5 Maddy 5
The average (mean) of these nine student's family sizes is also 5 people per family.  But, this data looks very different from the previous 9 student's data.

One way to look at the data is to see how far all of the elements are from the mean.  This is called the absolute (since the distance is always written as positive) mean deviation.

 family size deviation from mean positive deviation from mean Thomas 5 0 0 Rachel 6 1 1 Jorge 3 -2 2 Latrisha 5 0 0 Jon 7 2 2 Vivian 3 -2 2 Nathan 2 -3 3 Jillian 9 4 4 Maria 5 0 0 total= 0 14
To find the Mean Absolute Deviation (MAD) you find the sum of the positive deviations from the mean and then find the average (mean) of those numbers.

You can see that it would be important to make all of the deviations positive so that you would be able to average distance from the mean and not just get 0 as your average deviation.

The MAD of my data, then, is 14/9 = 1.5555555...