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Statistical Inference: A Short Course by Michael J. Panik

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2.3 Tabular and Graphical Techniques: Grouped Data

The preceding set of descriptive techniques (tabular and graphical) was easily applied to discrete sets of data with a relatively small number of observations. (A small sample in statistics typically has about 30 observations (give or take a few data points) whereas a medium-sized sample has around 50 observations.) Much larger data sets, involving either discrete or continuous observations, can be handled in a much more efficient manner. That is, instead of listing each and every different value of some variable X (there may be hundreds of them) and then finding its associated absolute or relative frequency or percent, we can opt to group the values of X into specified classes.

Figure 2.1 (a) Absolute frequency function. (b) Relative frequency function. (c) Percent function.

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Paralleling the above development of tabular and graphical methods, let us first determine an absolute frequency distribution—it shows the absolute frequencies with which the various values of a variable X are distributed among chosen classes. Here an absolute frequency is now a class frequency—it is the number of items falling into a given class.

The process of constructing this distribution consists of the following steps:

1. Choose the classes into which the data are to be grouped. Here, we must do the following:
a. Determine the number of classes.

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