wo way frequency tables
Two-way frequency tables show how many data points fit in each category.
Here's an example:
Preference Male Female
Prefers dogs 363636 222222
Prefers cats 888 262626
No preference 222 666
The columns of the table tell us whether the student is a male or a female. The rows of the table tell us whether the student prefers dogs, cats, or doesn't have a preference.
Each cell tells us the number (or frequency) of students. For example, the 363636 is in the male column and the prefers dogs row. This tells us that there are 363636 males who preferred dogs in this dataset.
Notice that there are two variables—gender and preference—this is where the two in two-way frequency table comes from.
Want a review of making two-way frequency tables? Check out this video.
Want to practice making frequency tables? Check out this exercise.
Want to practice reading frequency tables? Check out this exercise
Two way relative frequency tables
Two-way relative frequency tables show what percent of data points fit in each category. We can use row relative frequencies or column relative frequencies, it just depends on the context of the problem.
For example, here's how we would make column relative frequencies:
Step 1: Find the totals for each column.
Preference Male Female
Prefers dogs 363636 222222
Prefers cats 888 262626
No preference 222 666
Total 464646 545454
Step 2: Divide each cell count by its column total and convert to a percentage.
Preference Male Female
Prefers dogs \dfrac{36}{46}\approx78\%
46
36
≈78%start fraction, 36, divided by, 46, end fraction, approximately equals, 78, percent \dfrac{22}{54}\approx41\%
54
22
≈41%start fraction, 22, divided by, 54, end fraction, approximately equals, 41, percent
Prefers cats \dfrac{8}{46}\approx17\%
46
8
≈17%start fraction, 8, divided by, 46, end fraction, approximately equals, 17, percent \dfrac{26}{54}\approx48\%
54
26
≈48%start fraction, 26, divided by, 54, end fraction, approximately equals, 48, percent
No preference \dfrac{2}{46}\approx4\%
46
2
≈4%start fraction, 2, divided by, 46, end fraction, approximately equals, 4, percent \dfrac{6}{54}\approx11\%
54
6
≈11%start fraction, 6, divided by, 54, end fraction, approximately equals, 11, percent
Total \dfrac{46}{46}=100\%
46
46
=100%start fraction, 46, divided by, 46, end fraction, equals, 100, percent \dfrac{54}{54}=100\%
54
54
=100%start fraction, 54, divided by, 54, end fraction, equals, 100, percent
Notice that sometimes your percentages won't add up to 100\%100%100, percent even though we rounded properly. This is called round-off error, and we don't worry about it too much.
Two-way relative frequency tables are useful when there are different sample sizes in a dataset. In this example, more females were surveyed than males, so using percentages makes it easier to compare the preferences of males and females. From the relative frequencies, we can see that a large majority of males preferred dogs (78\%)(78%)left parenthesis, 78, percent, right parenthesis compared to a minority of females (41\%)(41%)left parenthesis, 41, percent, right parenthesis.