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Chapter 1: Introduction and Graphical Displays
Quantitative Frequency Distributions – Grouped
In the case when we have quantitative data and the range of values is large,
it may not be practical to use an ungrouped frequency distribution. Such use
may result in a large table which may not be very informative. In such
cases, it may be best to create classes with groups for the data. Here we will
discuss the idea of
grouped frequency distributions
.
Definition: Grouped Frequency Distribution
A grouped frequency distribution is obtained by constructing classes (or
intervals) for the data, and then listing the corresponding number of values
(frequency count) in each class (interval).
Note:
There are several procedures which one can use to construct a grouped
frequency distribution. However, because of the many technologies (such as
statistical software) available today, it is not necessary to try to construct
such distributions using pencil and paper. Later in the chapter, we will
encounter a graphical display called the
histogram
. We will use this
graphical display to help construct grouped frequency distributions.
What is a histogram? A histogram is a graphical display of a frequency or
relative frequency distribution that uses classes and vertical (horizontal) bars
(rectangles) of various heights to represent the frequencies.
Note:
Choosing the number of classes for a group frequency distribution is
arbitrary and depends on the number of data values. Generally, a group
frequency distribution should have a minimum of five classes and a
maximum of twenty. For “small” data sets, one may use between five and
ten classes. For “large” data sets, one may use up to twenty classes.