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Graphs of Frequency Distributions

- The Frequency Polygon
- The Histogram
- The Bar Graph
- The Stem-and-Leaf Plot

The Frequency Polygon

- To convert a frequencydistribution table into a frequency polygon:
- Put your X values on the X axis (the abscissa).
- Find the highest frequency and use it to determine the highest value for the Y axis.
- For each X value go up and make a dot at the corresponding frequency.
- Connect the dots.

The Histogram

- Follow the same steps for creating a frequency polygon.
- Instead of connecting the dots, draw a bar extending from each dot down to the X axis.
- A histogram is not the same as a bar graph, there should be no gaps between the bars in a histogram (there should be no gaps in the data).

Grouped Frequency Distributions

- We can group the previous data into a smaller number of categories and produce simpler graphs
- Use the midpoint of the category for your dot

Relative Frequency Polygon

- Use the following formula to find out what percentage of scores falls in each category:
- Use the percentage on your Y axis instead of the frequency.

So what’s the point?

- Graphs of relative frequency allow us to compare groups (samples) of unequal size.
- Much of statistical analysis involves comparing groups, so this is a useful transformation.

Activity #1

A researcher is interested in seeing if college graduates are less satisfied with a ditch-digging job than non-graduates. Because of the small number of college graduates digging ditches, the researcher could not get as many college graduate participants. Below are the scores on a job satisfaction survey for each group (possible values are 0 – 30, 30 being the most satisfied):

College: 11, 3, 5, 12, 18, 6, 4, 1, 2, 6, 2, 17, 12, 10, 8, 3, 9, 9

No College: 19, 3, 15, 11, 13, 12, 12, 9, 2, 6, 21, 15, 11, 8, 6, 25, 17, 1, 14, 15, 9, 7, 20, 4, 2, 19, 7, 12

Activity #1

College: 11, 3, 5, 12, 18, 6, 4, 1, 2, 6, 2, 17, 12, 10, 8, 3, 9, 9

No College: 19, 3, 15, 11, 13, 12, 12, 9, 2, 6, 21, 15, 11, 8, 6, 25, 17, 1, 14, 15, 9, 7, 20, 4, 2, 19, 7, 12

- Create a frequency distribution table with about 10 categories (for each group)
- Convert the frequency to relative frequency (percentage)
- Construct a relative frequency polygon for each group on the same graph (see p. 43 for an example)
- Put your name on your paper.

Cumulative Frequency Polygon

- Create a column for cumulative frequency and make the Cum f value equal to the frequency plus the previous Cum fvalue (see ch. 3 for a review)
- Plot the resulting values just as you did for a frequency distribution polygon

Cumulative Percentage Polygon

- Using cumulative frequency data, calculate the cumulative percentage data.
- Make your Y axis go to 100%
- Plot the data as normal.

Bar Graph

- Used when you have nominal data.
- Just like a frequency distribution diagram, it displays the frequency of occurrences in each category.
- But the category order is arbitrary.

Example

- The number of each of 5 different kinds of soda sold by a vendor at a football stadium.

Line Graphs

- Line graphs are useful for plotting data across sessions (very common in behavior analysis).
- The mean or some other summary measure from each session is sometimes used instead of raw scores (X).
- The line between points implies continuity, so make sure that your data can be interpreted in this way.

Example

Rats are trained to perform a chain of behavior and then divided into two groups: drug and placebo. The average number of chains performed each minute is plotted across sessions.

Venn Diagrams

Not in your book, but make sure you understand the basics.

Activity #2

Work with a group and fix these 3 graphs:

Homework

- Prepare for Quiz 4
- Read Chapter 5
- Finish Chapter 4 Homework (check WebCT/website)

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