Lecture Notes
Chapter Two: Methods for Describing Sets of Data
Randall Miller
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P a g e
1.
Describing Qualitative Data
Definition 2.1
A
class
is one of the categories into which qualitative data can be classified.
Definition 2.2
The
class frequency
is the number of observations in the data set that fall into a particular class.
Definition 2.3
The
class relative frequency
is the class frequency divided by the total number of observations
in the data set; that is,
class frequency
class relative frequency
n
=
Definition 2.4
The
class percentage
is the class relative frequency multiplied by 100; that is,
(
)
class percentage
class relative frequency
*100
=
Summary of Graphical Descriptive Methods for Qualitative Data
Bar Graph
:
The categories (classes) of the qualitative variable are represented by bars, where
the height of each bar is either the class frequency, class relative frequency, or class percentage.
Pie Chart
:
The categories (classes) of the qualitative variable are represented by slices of a pie
(circle).
The size of each slice is proportional to the class relative frequency.
Pareto Diagram
:
A bar graph with the categories (classes) of the qualitative variable (i.e., the
bars) arranged by height in descending order from left to right.
2.
Graphical Methods for Describing Quantitative Data
Determining the Number of Classes in a Histogram
Number of Observations in Data Set
Number of Classes
Fewer than 25
5 – 6
25 - 50
7 – 14
More than 50
15 - 20
Summary of Graphical Descriptive Methods for Quantitative Data
Dot Plot
: The numerical value of each quantitative measurement in the data set is represented by
a dot on a horizontal scale.
Then data values repeat, the dots are placed above one another
vertically.

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