**Displaying and Describing**

Categorical Data

Categorical Data

**AP Stats - Chapter 3**

The first 3 rules of statistics:

1. Make a picture.

2. Make a picture.

3. Make a picture.

Types of Tables

Frequency & Relative Frequency Tables

Contengency Tables

Conditional Distributions

Categorical Displays

Bar Charts

Pie Charts

Segmented Bar Charts

The Area Principle

Why is making a picture so important?

Here's an example of the same set of data shown 3 different ways.

Sentence Form: A survey of 100 students at MHS shows that 38 students arrive to school by car (20 male & 18 female). Also that 30 males and 20 females arrive by bus and that 5 males and 7 females walk to school.

As a table:

As a picture:

Hopefully you can tell that pictures organize the data in such a way that makes them easier to draw conclusions from. Seeing the graphs in the following video are much nicer than just presenting the same data in paragraph form.

A Marginal Distribution is when you focus on the totals of one variable in a contengency table. The distribution is made up of the values in the margins, hence the name "marginal distribution.

For example, the marginal distribution for the gender variable in our example woulsd be males 43 and females 37.

While the marginal distribution for the eye color variable would be blue 20, brown 45, and green/other 15.

We all know how to make bar graphs, but when is it appropriate to make a bar chart?

A bar chart is appropriate when you want to DISPLAY the distribution of a categorica variable.

Once again, we all know how to make pie graph, but when is it appropriate to make a pie chart?

When you want to show the whole group of cases as a circle. Each pie piece is proportional to the fraction of the entire group.

Take a look at the doctors in the graph. It appears that the doctor on the left is nearly 3 times as large as the doctor on the far right. But when you look at the frequencies underneath each doctor, there is a difference of about 2000 (8023-6212).

Last time I checked, 3 times 6000 is not 8000.

This is a violation of "The Area Principle". This usually comes up when you use pictures instead of bars for a graph or a pictograph. A pictograph looks nicer and can be more interesting, but the area occupied by each part of the graph should correspond to the magnitude of the value it represents.

A segmented bar braph shows each subgroup of a variable as a separate bar. Each bar shows each gender and divides it up proportionally into seegments corresponding to the relative frequency in each group.

**Independent Variables**

When we compare two variables it is very important to know if they are independent of each other.

One way to check is to see if the distribution of one variable is the same for all categories of the other variable. If the distributions are nearly the same, then the variables are independent of each other.

If the distributions are a lot different, then they are NOT independent.

Let's take a look at our eye color example. Are the variables gender and eye color independent variables?

Can you make a decision yet? Looking at the pieces of the segmented bar graph might give you a clue.

After looking at the numbers in the table and looking at the segmented bar graph, I would say that the distributions are close enought to say that eye color and gender are independent variables.

**Wrap Up . . .**

That's all for the flipped lecture.

Make sure you read about the following in your textbook:

"What can go wrong?"

Simpson's Paradox

Know your vocabulary