One-Way Tables
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.
| Choice | Frequency |
|---|---|
| USA | 5 |
| Europe | 3 |
| Asia | 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. One table shows relative frequencies as a proportion, and the other table shows relative frequencies as a percentage.
| Choice | Proportion |
|---|---|
| USA | 0.5 |
| Europe | 0.3 |
| Asia | 0.2 |
| Choice | Percentage |
|---|---|
| USA | 50 |
| Europe | 30 |
| Asia | 20 |
Test Your Understanding
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?
Table I
| Choice | Frequency |
|---|---|
| Red | 0.5 |
| Green | 0.2 |
| Blue | 0.3 |
Table II
| Choice | Proportion |
|---|---|
| Red | 50 |
| Green | 20 |
| Blue | 30 |
Table III
| Choice | Percentage |
|---|---|
| Red | 10 |
| Green | 4 |
| Blue | 6 |
(A) Table I only
(B) Table II only
(C) Table 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. Table I shows proportions, but the label says "Frequency". Table II shows percentages, but the label says "Proportion". And finally, Table III shows frequencies, but the label says "Percentage".