60 males and 70 females were surveyed. 104 students liked the recent school play and 26 did not. A total of 130 students were surveyed.
Practice makes perfect
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 find and interpret the marginal frequencies.
Finding the Marginal Frequencies
We are told that boys and girls are surveyed about whether they liked a recent school play.
Student
Gender
Liked
Did Not Like
Male
48
12
Female
56
14
The sums of the rows and columns are called marginal frequencies. Let's calculate the sums of the rows.
Males:& 48 + 12 = 60
Females:& 56 + 14 = 70
Now, let's do the same for columns.
Liked a Play:& 48 + 56 = 104
Did Not Like a Play:& 12 + 14 = 26
We can create new column and new row for the sums.
Student
Gender
Liked
Did Not Liked
Total
Male
48
12
60
Female
56
14
70
Total
104
26
Finally, we have two ways of calculating the grand total. We can add the number of males to the number of females, or we can add the students who liked a play to the students who did not. These two numbers must be the same!
Grand total
l 60+ 70 = 130 104+ 26= 130 ✓
Finally, we can complete our table!
Student
Gender
Liked
Did Not Like
Total
Male
48
12
60
Female
56
14
70
Total
104
26
130
Interpreting the Marginal Frequencies
In the marginal frequencies, we can see that 60 males and 70 females were surveyed. Moreover, 104 students liked the recent school play and 26 did not. A total of 130 students were surveyed.
