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Section 2.1: Grouped Frequency Distributions
Definitions: class width:
Class boundaries:
Class midpoint:
Rules to Follow in the Construction of Classes
- There should be between 5 and 20 classes.
- Class width should be an odd number.
- Classes must be mutually exclusive.
- Classes must be continuous.
- Classes must be exhaustive.
- Classes must be equal in width.
Steps in the Construction of a Grouped Frequency Distribution
- Find the range of the data (highest value – lowest value).
- Divide the range by the number of classes desired and round up to the nearest whole number. This is the class width.
- Select a starting point for lower class limit (usually the smallest data value).
- Add the class width to get the lower limit of the NEXT class!!!
- Continue to add the class width until the desired number of classes is obtained.
- Find the upper class limits.
- Find the boundaries.
- Tally the data.
- Find the numerical frequencies from the tallies and find the cumulative frequencies.
Example: Construct a grouped frequency distribution for the following data for the hours spent studying statistics for 22 students. Use five classes.
3 5 6 6 7 10 4 5 6 6 7 11 4 6 6 7 7 15 5 10 15 11
Example: The data shown here represent the gas mileage that 30 selected SUVs obtained in city driving. Construct a frequency distribution.
12 17 12 14 16 18 16 18 12 16 17 15 15 16 12 15 16 16 12 14 15 12 15 15 19 13 16 18 16 14
Section 2.2: Histograms, Frequency Polygons, Ogives
Definitions: Histogram:
Definition: The frequency polygon is a graph
Example: Construct a frequency polygon for the stats data.
Definition: The ogive is a graph
Example: Construct an ogive for the stats data.
Section 2.3 Other Types of Graphs
Definition: A Pareto chart
Example: Construct a Pareto chart for the following data.
Level of Spirituality Number of Respondents Highly 761 Moderately 880 Nominally 1162 Trace 899 Agnostic 299
Definition: A time series graph
Definition: A stem and leaf plot
Example: Construct a stem and leaf plot for the following data.
