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