A is a 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.
- Find the .
- Find the .
Let's do these three things one at a time.
Constructing the Table
We are told that male and female students are surveyed as to whether or not they are getting a summer job. This information is enough to determine the appropriate column and row headers for our table.
|
Are You Getting a Summer Job?
|
Gender
|
Yes
|
No
|
Total
|
Female
|
|
|
|
Male
|
|
|
|
Total
|
|
|
|
Finding the Joint Frequencies
Each entry in the table is called a joint frequency. We are told that of the
75 surveyed males,
18 responded
no. Of the
57 surveyed females,
45 responded
yes. With this information, we can find the number of males that are getting a summer job and the number of females that are not getting a summer job.
Males who said yes:Females who said no:75−18=5757−45=12
Let's write the given and the newly obtained information in our table.
|
Are You Getting a Summer Job?
|
Gender
|
Yes
|
No
|
Total
|
Female
|
45
|
12
|
57
|
Male
|
57
|
18
|
75
|
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.
Students who said yes:Students who said no:45+57=10212+18=30
Finally, we have two ways of calculating the grand total. We can add the number of
females to the number of
males, or we can add the students who responded
yes to the students who responded
no. These two numbers must be the same!
Grand total 57+75 =132102+30=132 ✓
Finally, we can complete our table!
|
Are You Getting a Summer Job?
|
Gender
|
Yes
|
No
|
Total
|
Female
|
45
|
12
|
57
|
Male
|
57
|
18
|
75
|
Total
|
102
|
30
|
132
|