Frequency Distributions

1
Frequency Distributions

• A frequency distribution is a table used to
  organize data. The left column (called classes
  or groups) includes numerical intervals on a
  variable being studied. The right column is a
  list of the frequencies, or number of
  observations, for each class. Intervals are
  normally of equal size, must cover the range of
  the sample observations, and be non-overlapping.

2
Construction of a Frequency Distribution

• Rule 1 Intervals (classes) must be inclusive
  and non-overlapping
• Rule 2 Determine k, the number of classes
• Rule 3 Intervals should be the same width, w
  the width is determined by the following
• Both k and w should be rounded upward, possibly
  to the next largest integer.

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Construction of a Frequency Distribution

• Quick Guide to Number of Classes for a Frequency
  Distribution
• Sample Size Number of Classes
• Fewer than 50 5 6 classes
• 50 to 100 6 8 classes
• over 100 8 10 classes

4
Cumulative Frequency Distributions

• A cumulative frequency distribution contains the
  number of observations whose values are less than
  the upper limit of each interval. It is
  constructed by adding the frequencies of all
  frequency distribution intervals up to and
  including the present interval.

5
Relative Cumulative Frequency Distributions

• A relative cumulative frequency distribution
  converts all cumulative frequencies to cumulative
  percentages

6
Histograms and Ogives

• A histogram is a bar graph that consists of
  vertical bars constructed on a horizontal line
  that is marked off with intervals for the
  variable being displayed. The intervals
  correspond to those in a frequency distribution
  table. The height of each bar is proportional to
  the number of observations in that interval.

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Histograms and Ogives

• An ogive, sometimes called a cumulative line
  graph, is a line that connects points that are
  the cumulative percentage of observations below
  the upper limit of each class in a cumulative
  frequency distribution.

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Histogram and Ogive for Example 2.1
9
Stem-and-Leaf Display

• A stem-and-leaf display is an exploratory data
  analysis graph that is an alternative to the
  histogram. Data are grouped according to their
  leading digits (called the stem) while listing
  the final digits (called leaves) separately for
  each member of a class. The leaves are displayed
  individually in ascending order after each of the
  stems.

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Stem-and-Leaf Display
Stem-and-Leaf Display for Gilottis Deli Example
11
Tables- Bar and Pie Charts -
Frequency and Relative Frequency Distribution for
Top Company Employers Example
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Tables- Bar and Pie Charts -
Figure 2.9 Bar Chart for Top Company Employers
Example
13
Tables- Bar and Pie Charts -
Figure 2.10 Pie Chart for Top Company Employers
Example
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Pareto Diagrams

• A Pareto diagram is a bar chart that displays the
  frequency of defect causes. The bar at the left
  indicates the most frequent cause and bars to the
  right indicate causes in decreasing frequency. A
  Pareto diagram is use to separate the vital few
  from the trivial many.

15
Line Charts

• A line chart, also called a time plot, is a
  series of data plotted at various time intervals.
  Measuring time along the horizontal axis and the
  numerical quantity of interest along the vertical
  axis yields a point on the graph for each
  observation. Joining points adjacent in time by
  straight lines produces a time plot.

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Line Charts