One-Way Tables in Statistics

A one-way table is the tabular equivalent of a bar chart. Like a bar chart, a one-way table displays categorical data in the form of frequency counts and/or relative frequencies.

A one-way table is distinguished from a two-way table (described in the next lesson); because the data entries in a one-way table refer to one variable, whereas the data entries in a two-way table refer to two variables.

Frequency Tables

When a one-way table shows frequency counts for a particular category of a categorical variable, it is called a frequency table.

Below, the bar chart and the frequency table display the same data. Both show frequency counts, representing travel choices of 10 travel agency clients.

Bar chart showing travel choices
Choice USA Europe Asia
Frequency 5 3 2

Relative Frequency Tables

When a one-way table shows relative frequencies (i.e., percentages or proportions) for particular categories of a categorical variable, it is called a relative frequency table.

Each of the tables below summarizes data from the bar chart above. Both tables are relative frequency tables. The table on the left shows relative frequencies as a proportion, and the table on the right shows relative frequencies as a percentage.

Choice USA Europe Asia
Proportion 0.5 0.3 0.2
Choice USA Europe Asia
Percentage 50 30 20

Test Your Understanding of This Lesson

Problem

Twenty first graders were asked which color they liked best - red, green, or blue. Their responses appear below.

red, green, green, blue, red, blue, red, red, blue, red
red, blue, red, red, blue, red, blue, green, green, red

Which of the following one-way tables correctly summarizes responses from the first graders?

Choice Red Green Blue
Frequency 0.5 0.2 0.3

I

Choice Red Green Blue
Proportion 50 20 30

II

Choice Red Green Blue
Percentage 10 4 6

III

(A) I only
(B) II only
(C) III only
(D) None of the above.
(E) All of the above.

Solution

The correct answer is (D). None of the frequency tables is labeled correctly. Option I shows proportions, but the label says "Frequency". Option II shows percentages, but the label says "Proportion". And finally, Option III shows frequencies, but the label says "Percentage".