Two-Way Table-Relative Frequency

There are three different ways to compute the Relative Frequency for a Two-Way Table. All three methods use the same process to calculate the relative frequency, with the only difference being the total you use in the denominator of the fraction. To look at how this works a little closer take the following Two-Way Table, which is the results of a survey of how students get to school, and their gender.

Two-Way Table

The first method uses the total of all the categories. Which in the case of the above table, that value is 91. So, to find the relative frequency of the males who walk to school, you take that frequency, which is 9 and divide it by 91. This process is continued for every cell in the table. The Two-Way table with all of the relative frequencies calculated this way is shown below:

Two-Way Table - Relative Frequency - Total.png

The second method is to uses the total from each of the rows to compute the relative frequency. The main difference between this method and the first method is that while the first method used the same number in all of the calculations, this method the total changes based on what row we are looking at.

Two-Way Table - Relative Frequency - Row.png

Using the above Two-Way table as an example, when computing the relative frequency of the top row, we use 38 in the denominator, and when calculating the relative frequency of the bottom row, we will use 53 in the denominator. So, to calculate the number of males who bike to school you take the 5 and divide it by 38. But to find the relative frequency of the number of females who bike to school you take the 11 and divide it by 53. A completed table is shown below.

Two-Way Table - Relative Frequency - Column.png

The third and final method is very similar to the second method, with the only difference being that instead of using the total for each row, you use the total in each column to calculate the relative frequency. So, using the above table as an example to find the relative frequency of the males who drive with parents we take the 5 and divide it by 13, while to find the number of females who drive themselves we take the 11 and divide it by 16. A Two-Way table with all of the relative frequencies computed this way is as follows.