DESCRIBING DATA BY
TABLES AND GRAPHS
[JOHNSON &
BHATTACHARYYA (1992), WEISS (1999) AND FREUND (2001)]
QUALITATIVE
VARIABLE
The
number of observations that fall into particular class (or category) of the
qualitative
variable is called the frequency (or count) of that class. A table listing all
classes and their frequencies is called a frequency distribution. In addition
of the frequencies, we are often interested in the percentage of a class. We
find the percentage by dividing the frequency of the class by the total number
of observations and multiplying the result by 100. The percentage of the class,
expressed as a decimal, is usually referred to as the relative frequency of the
class.
Relative frequency of
the class =Frequency in the class
Total number of observation
A
table listing all classes and their relative frequencies is called a relative
frequency
distribution. The relative frequencies provide the most relevant information as
to the pattern of the data. One should also state the sample size, which serves
as an indicator of the credit-ability of the relative frequencies.
Relative frequencies sum to 1 (100%).
A
cumulative frequency (cumulative relative frequency) is obtained by summing the
frequencies (relative frequencies) of all classes up to the specific class. In
a case of qualitative variables, a cumulative frequency makes sense only for
ordinal variables, not for nominal variables. The qualitative data are
presented graphically either as
·
A Pie Chart Or As A
·
Horizontal Or Vertical Bar Graph.
A
pie chart is a disk divided into pie-shaped pieces proportional to the relative
Frequencies
of the classes. To obtain angle for any class, we
multiply the
Relative
frequencies by 360 degrees, which
corresponds to the complete circle.
A
horizontal bar graph displays the classes on the horizontal axis and the frequencies
(or relative frequencies) of the classes on the vertical axis. The
frequency
(or relative frequency) of each class is represented by vertical bar
whose
height is equal to the frequency (or relative frequency) of the class. In a bar
graph, its bars do not touch each other. At vertical bar graph, the classes are
displayed on the vertical axis and the frequencies of the classes on the
horizontal axis. Nominal data is best displayed by pie chart and ordinal data
by horizontal
or
vertical bar graph.
Example
3.1. Let the blood types of 40 persons are as follows:
O
O A B A O A A A O B O B O O A O O A A A A AB A B A A O O A
O
O A A A O A O O AB
Summarizing
data in a frequency table by using SPSS:
Analyze -> Descriptive Statistics -> Frequencies,
Analyze -> Custom Tables -> Tables of Frequencies
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