Displays the frequency of each category, as well as row and column totals. In other words, shows how many data items are in each category.
Presents the ratio of the number of data in each category and the total number of data items. These ratios are usually expressed as percents.
We can see that the difference between a two-way frequency table and a two-way relative frequency table is that in relative frequency table, we have percentages, not counts. Let's consider an example to see why this is an advantage of relative tables.
Do You Often Do Physical Exercises?
Gender
Yes
No
Total
Boys
8
2
10
Girls
16
24
40
Total
24
26
50
It looks like 2 times more girls than boys answered that they often exercise, so we might suspect that girls are more active than boys. However, if we look at the two-way relative frequency table by rows, then we can see that actually 80 % of boys often do physical exercises and only 40 % of girls do the same. This suggests that boys are actually more active.
Do You Often Do Physical Exercises?
Gender
Yes
No
Total
Boys
80 %
20 %
100 %
Girls
40 %
60 %
100 %
Total
48 %
52 %
100 %
Notice that the number of boys surveyed was much smaller than the number of girls surveyed. If one category has much fewer data items than others, we can wrongly identify the relationship between data based only on the frequency table. In the case of two-way relative frequency tables, we do not have this problem because we express values as ratios.
