Tables

Frequency Distribution

- Sorted collection of observations showing the number of times (frequency) each observation occurs
- ungrouped
- grouped

- If you have a large number of values that cover a wide range, the UNGROUPED FREQUENCY DISTRIBUTION is not appropriate.

Trade-off between ease of viewing and detail of data (individual vs grouped).

How to construct a GROUPED FREQUENCY DISTRIBUTION

- Relative Frequency Distribution
- A frequency distribution consisting of proportions of observations for each class
- Useful for comparing two distributions with different numbers of observations.
- Constructing a Relative Frequency Distribution
- Sum the tallies for each class in a standard frequency distribution
- Divide the tally for each class by the sum

- Cumulative Frequency Distribution
- A frequency distribution showing the sum of the observations for each class and all classes below
- Useful for showing relative standing within the group of observations.
- Constructing a Cumulative Frequency Distribution
- Take a standard frequency distribution and start at the bottom class
- For each class, add the tally of the class that you're at with all class tallies below it.
- Bottom class will remain unchanged

- Cumulative Proportions or Cumulative Percents
- Just like a cumulative frequency distribution except using proportions
- Useful for showing relative standing among groups with different numbers of observations.
- Cumulative Relative Frequency Distribution
- Take a relative frequency distribution and apply steps for constructing a cumulative frequency distribution.
- Cumulative proportions = Percentile ranks

- Outliers
- Extreme values in a frequency distribution
- e.g., if you have 100 observations and 99 of these observations range from 1 to 100, an observation of 32,000 would be an outlier
- Why is it there?
- Is it a mistake or coding error?
- Is something interesting going on?
- You may exclude the value from your table, BUT you must make sure that it is clear that the value has been excluded

- A graph of a frequency distribution in which a rectangular bar is drawn over each value on the x axis
- Classes are plotted on the x axis
- Frequency is plotted on the y axis
- x axis: horizontal; y axis: vertical

- A line graph of a frequency distribution in which classes are plotted on the x axis and frequencies are plotted on the y axis
- A line graph version of a histogram
- How to graph a frequency polygon

- 1. Take a histogram
- 2. Place a dot at the top and middle of each bar
- 3. Connect the dots
- 4. Attach endpoints to the x axis

- 1. Normal distribution
- familiar bell-shaped curve
- symmetrical
- describes many naturally occurring phenomena
- 2. Bimodal distribution
- distribution with two modes or "humps"
- most observations fall in or around one of two classes
- 3. Skewed distribution
- Distribution with a few extreme values
- Positively skewed: extreme values are large
- Negatively skewed: extreme values are small

- A type of histogram used to graph qualitative data
- Each bar is separated from its neighbors

Graphs

- Help summarize data in a visual form
- “A picture is worth a thousand words.”
- Once you can “see” all the data the fun can begin...
- Are graphs good for everything?
- At least one variable must be quantitative...
- Plotting things other than frequency of occurrence.
- Independent variable is on the x-axis.
- Dependent variable is on the y-axis.