1. Displaying Categorical Data
Frequency tables, the Area Principle and Bar Graphs

2. The Three Rules of Data Analysis
Draw Pictures!
T. Serino
The Three Rules of Data Analysis
The three rules of data analysis won’t be difficult to remember:
Make a picture—things may be revealed that are not obvious in the raw data. These will be things to think about.
Make a picture—important features of and patterns in the data will show up. You may also see things that you did not expect.
Make a picture—the best way to tell others about your data is with a well-chosen picture.

3. Frequency Tables Frequency Tables
T. Serino
The picture we will concentrate on in this lesson is a bar graph. To create a bar graph, first we must understand how to read a frequency table.
Frequency Tables
Tables that show how many or how often (frequent) something happens.

4. Frequency Tables
T. Serino
The frequency table below shows some data about the passengers and crew aboard the Titanic.
Class Count
First Class
325
Second Class
285
Third Class
706
Crew
885
Calculate the total number of people on the Titanic.
There were 325 first class passengers aboard the Titanic.
There were 285 second class passengers aboard the Titanic.
There were 706 third class passengers aboard the Titanic.
There were 885 crew members aboard the Titanic.

5. Frequency Tables
T. Serino
A relative frequency table may give a better picture of the class of people aboard the Titanic.
To Create a relative frequency table, simply change each number to a percent.
Class Count
(Relative Frequency)
First Class
Second Class
Third Class
Crew
0.147=14.7%
14.7%≈15%
Therefore, approximately 15% of passengers were first class passengers.
Total
For First Class Passengers:
To change to percents first remember:
15%

6. Frequency Tables
T. Serino
A relative frequency table may give a better picture of the class of people aboard the Titanic.
To Create a relative frequency table, simply change each number to a percent.
Class Count
(Relative Frequency)
First Class
Second Class
Third Class
Crew
Total
For Second Class Passengers:
0.129=12.9%
12.9%≈13%
Therefore, approximately 13% of passengers were 2nd class passengers.
15%
13%

7. Frequency Tables
T. Serino
A relative frequency table may give a better picture of the class of people aboard the Titanic.
To Create a relative frequency table, simply change each number to a percent.
Class Count
(Relative Frequency)
First Class
Second Class
Third Class
Crew
Total
Use a calculator to complete the table.
15%
13%

8. Area Principle The Area Principle This is an example of a BAD display!
T. Serino
The Area Principle
Good data displays observe the area principle.
Area Principle: The area occupied by a part of the graph should correspond to the magnitude of the value it represents
This is an example of a BAD display!

9. Area Principle
T. Serino
Although the lengths of these ships seem to correspond to the number of people each ship represents, the area of each ship is misleading.
885
706
285
325

10. Area Principle 885 ÷ 285 ≈ 3 This graph violates the area principle!
T. Serino
885
To see this, let’s consider only the number of crew members compared to the number of second class passengers.
Crew members
885 ÷ 285 ≈ 3
Yet, this picture makes it seem like there were more than 8 times as many crew members as second class passengers.
So there were approximately 3 times as many crew members as there were second class passengers.
Second
Class
285
This graph violates the area principle!

11. Area Principle
T. Serino
Pictographs like the one describing the passengers of the Titanic can often violate the area principle, but when drawn correctly like the graph below, pictographs can be used to accurately display categorical data.
Notice that this pictograph closely resembles a horizontal bar graph.

12. Bar Graphs
T. Serino
Bar Graphs
Bar graphs display the distribution of a categorical variable, showing the counts for each category next to each other for easy comparison.
Number of People (Frequency)
Class (Category)
People on the Titanic by Ticket Class
The question is, does a bar graph observe the area principle?

13. Bar Graphs
T. Serino
If we were to isolate the bars representing crew members and second class passengers, we can see that the bar graph stays true to the area principle.
885 ÷ 285 ≈ 3
Both the area and the height of the bar representing crew members is approximately 3 times as big as the bar representing second class passengers.
885
285

14. Bar Graphs Additional information about bar graphs
T. Serino
Additional information about bar graphs
Frequency
Category
People on the Titanic by Ticket Class
The frequency axis of a bar graph is typically drawn as the vertical axis and the category axis is typically drawn as the horizontal axis.

15. Bar Graphs Additional information about bar graphs
T. Serino
Additional information about bar graphs
Category
Frequency
People on the Titanic by Ticket Class
It is not unusual to see a horizontal bar graph where the frequency axis is the horizontal axis and the category axis is the vertical axis.

16. Bar Graphs Additional information about bar graphs
T. Serino
Additional information about bar graphs
Bar graphs can also contain negative values.
A bar graph with positive and negative frequency values would look like the following.
Bars representing negative values start at the zero axis and project downward to indicate negative values.

17. Bar Graphs Additional information about bar graphs
T. Serino
Additional information about bar graphs
A bar graph showing data from a frequency table will look identical to a bar graph showing the same data from a relative frequency table.

18. athematical M D
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