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.