Recall that we can use both two-way frequency tables and a two-way relative frequency tables to show relationships between sets of paired data. Let's compare these types of tables.

Two-Way Frequency Table	Two-Way Relative Frequency Table
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.

Exercise