Add a new row and a new column called Total to the given two-way table. To fill in the missing entries, find the sum all of the entries situated in the corresponding rows or columns.
Marginal Frequencies:
Recycle
Gender
Yes
No
Total
Female
28
9
37
Male
24
14
38
Total
52
23
75
Interpretation: See solution.
Practice makes perfect
The results of a survey about whether students recycle are given in a two-way table. In this exercise, we want to find and interpret the marginal frequencies. We will start by adding a new row and column called Total to the given table. Let's do it!
Recycle
Gender
Yes
No
Total
Female
28
9
Male
24
14
Total
We fill in the empty entries by adding up all of the values in each row and column. Let's do it!.
Recycle
Gender
Yes
No
Total
Female
28
9
28+9= 37
Male
24
14
24+14= 38
Total
28+24= 52
9+14= 23
The last entry can be calculated by either adding up all the entries in the Total row or by adding up all the entries in the Total column. Let's do it both ways to see if we get the same result.
Total:& 37+ 38 = 75
Total:& 52 + 23 = 75
We have got the same result, so let's fill in the last entry.
Recycle
Gender
Yes
No
Total
Female
28
9
37
Male
24
14
38
Total
52
23
75
We can get a lot of information from the marginal frequencies. A total of 75 students were surveyed, 37 female and 38 male. Of them, 52 students recycle and 23 students do not.
