Interpretation of the Marginal Frequencies: 40 students are planning to attend a school dance and 36 students are not. 51 students are planning to attend a football game and 25 are not. A total of 76 students were surveyed.
Practice makes perfect
A two-way table is a frequency table that displays two categories of data collected from the same source. One category of data is represented by rows and the other is represented by columns. We want to find and interpret the marginal frequencies. Let's do these things one at a time.
Finding the Marginal Frequencies
We are given the following frequency table.
Football Game
Dance
Attend
Not Attend
Attend
35
5
Not Attend
16
20
The sums of the rows and columns are called marginal frequencies. Let's calculate these sums to find the marginal frequencies.
Students attending a school dance: 35+ 5= 40
Students not attending a school dance: 16+ 20= 36
Students attending a football game: 35+ 16=51
Students not attending a football game: 5+ 20=25
Finally, we have two ways of calculating the grand total. We can add the number of students attending a school dance to the number of students not attending a school dance, or we can add the students attending a football game to the students not attending a football game. These two numbers must be the same!
Grand total
l 40+ 36 =76 51+25=76 ✓
Finally, we can complete our table!
Football Game
Dance
Attend
Not Attend
Total
Attend
35
5
40
Not Attend
16
20
36
Total
51
25
76
Interpreting the Marginal Frequencies
In the marginal frequencies, we can see that 40 students are planning to attend a school dance and 36 students are not. Moreover, 51 students are planning to attend a football game and 25 are not. A total of 76 students were surveyed.
