Using Statistics in Argument: Frequency

A frequency statement says how many things in a class S have the property P; it tells us the frequency with which P occurs in that class.

An absolute frequency statement gives the actual number of Ss that are P.


2,149 students at Tiptop College are humanities majors.

A relative frequency statement gives the proportion of Ss that are P.


Thirty-six percent of the students at Tiptop College are humanities majors.

As you can see, an absolute frequency is a special sort of total, and a relative frequency is a special sort of ratio.

A frequency statement divides Ss into two subclasses: those that are P and those that are not P: humanities majors versus nonhumanities majors.

However, we can also do a more thorough classification, dividing Ss into those that are P, Q, R, and so forth, indicating the proportions that fall into each subclass. The result is called a frequency distribution.

From a logical standpoint, a distribution is simply a classification with numbers attached. Because a distribution involves a classification, the rules of classification apply. To have a meaningful distribution, we should use a single principle or a consistent set of principles--that is, a single variable or set of variables.

The subgroups should be mutually exclusive, so that we don't count individual things twice. If they are not mutually exclusive, the frequencies will add up to more than 100 percent.

The subgroups should also be jointly exhaustive, so that all the Ss are assigned to one species (value) or another. If they are not jointly exhaustive, the frequencies will add up to less than 100 percent.

Statements about frequencies and distributions also require that we define our terms carefully. If we are going to measure the proportions of Ss that are P, or the distribution of Ss into subgroups P, Q, and R, we need definitions of all these groups.

Unlike a definition used in ordinary reasoning, a definition used for statistical purposes can't have fuzzy borders; it must give us a clear criterion for deciding whether to include or exclude any given thing.

This usually involves an element of stipulation, and different researchers make different decisions.

One implication is that you cannot always compare statistics compiled by different researchers, even when they deal with the same subject.


Before you could draw any conclusions about whether illiteracy is widespread in this country, you would need to decide what a reasonable definition of illiteracy is. You cannot accept any particular number at face value without being able to defend the definition that produced it.

Totals | Ratios | Frequency | Averages
Using Statistics in Argument

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