Organizing Qualitative Data

1
Lesson 2 - 1

• Organizing Qualitative Data

2
Objectives

• Organize qualitative data in tables
• Construct bar graphs
• Construct pie charts

3
Vocabulary

• Frequency Distribution lists each category of
  data and the number of occurrences for each
  category of data
• Relative Frequency Distribution is the
  proportion (or percentage) of observations within
  a category
• Bar Graph a graph showing frequency or relative
  frequency on the y-axis and categories on the
  x-axis
• Pareto chart bar graph whose bars are drawn in
  decreasing order of frequency or relative
  frequency
• Side-by-Side bar graphs use relative frequency
  since sample or population sizes may be different
• Pie Charts circle divided into sectors each
  sector represents a category of data area is
  proportional to the frequency of the category
  all data must be represented

4
Different Views
5
Frequency Distributions Histograms

• There are no hard and fast rules for constructing
  frequency distributions and histograms for
  continuous data since there are no natural
  categories. The way out of this dilemma is to
  define our own categories. One drawback is that
  individuals working with the same set of data,
  may construct distributions with different
  appearances. The reason for this variation lies
  in the choice of the number of classes to use and
  the choice of the width of the classes. Using too
  few classes gives an inaccurate picture by
  smoothing out too many details. Too many classes
  present too much detail and the overall view can
  be lost (forest and trees analogy).
• Another problem is the adverse effect on
  histograms of outliers in the data. When outliers
  are present some artistic modification is
  required. Although somewhat arbitrary, the
  following rule is presented to allow for some
  uniformity in constructing frequency
  distributions and histograms.
• The number of classes k to be constructed can be
  roughly approximated by
•  
• k ?number of observations
•  
• To determine the width of a class use w (max
  min) / k and always round up to the same
  decimal units as the original data.

6
Example 1

• Construct a frequency distribution and a
  histogram.
• Below are the net weight (in ounces) of 30 cans
  of peas from the Grumpy Blue Midget Company.
•  
• 16.2 15.8 15.8 15.8 16.3 15.6
• 15.7 16.0 16.2 16.1 16.8 16.0
• 16.4 15.2 15.9 15.9 15.9 16.8
• 15.4 15.7 15.9 16.0 16.3 16.0
• 16.4 16.6 15.6 15.6 16.9 16.3

7
Example 1 Graph
8
Summary and Homework

• Summary
• Charts help to display data more visually with
  fewer words
• Homework
• pg 67 73 6-8, 11, 13, 15, 22, 30