We want to construct a two-way table that shows the joint and marginal relative frequencies. To do it, we will first construct a two-way table with the original joint and marginal frequencies.
Organizing the Information
A two-way table is a frequency table that displays data collected from one source that belongs to two different categories. One category of data is represented by rows and the other is represented by columns. We want to organize the given information in a two-way table. To do so, we will follow three steps.
Construct an empty table with the appropriate column and row headers.
Let's do these three things one at a time. Then we will interpret the marginal frequencies.
Constructing the Table
We are told that people who received a flu vaccine and people who did not receive it are surveyed on whether or not they got the flu that season. This information is enough to determine the appropriate column and row headers for our table.
Did They Get the Flu This Season?
Vaccinated?
Did
Did Not
Total
Yes
No
Total
Finding the Joint Frequencies
Each entry in the table is called a joint frequency. We are told that of the 49 people who received the flu vaccine, 16 got the flu. Of the 63 people who did not receive the flu vaccine, 17 got the flu. With this information, we can find the number of people did not get the flu.
Vaccinated And Flu-Free:&& 49- 16= 33
Not Vaccinated And Flu-Free:&& 63- 17= 46
Let's write the given and the newly obtained information in our table.
Did They Get the Flu This Season?
Vaccinated?
Did
Did Not
Total
Yes
16
33
49
No
17
46
63
Total
Finding the Marginal Frequencies
The sums of the rows and columns are called marginal frequencies. Let's calculate these sums to find the missing marginal frequencies.
Did Get the Flu:&& 17+ 16=33
Did Not Get the Flu:&& 46+ 33=79
Finally, we have two ways of calculating the grand total. We can add the number of people who were vaccinated to the number of people who were not vaccinated, or we can add the number of people who got the flu to the number of people who did not get the flu. These two numbers must be the same!
Grand total
l 49+ 63 =112 33+79=112 ✓
Finally, we can complete our table!
Did They Get the Flu This Season?
Vaccinated?
Did
Did Not
Total
Yes
16
33
49
No
17
46
63
Total
33
79
112
Finding Relative Frequencies
Now, we want to use this table to construct a two-way table that shows the joint and marginal relative frequencies. To do so, we will divide each joint frequency by the grand total to obtain the joint relative frequencies. Similarly, we will divide each marginal frequency by the grand total to obtain the marginal relative frequencies.
