A two-way table is a frequency table that displays data collected from one source that belongs to two different categories.
See solution.
Practice makes perfect
We want to know if a greater percentage of males or females volunteer at the animal shelter. To do so, we will first identify the number of males who volunteer at the animal shelter and the number of females who volunteer at the animal shelter in the two-way table. Let's do it!
Males
Females
Animal Shelter
26
21
Hospital
13
17
Library
9
14
We can see in the two-way table that there are 26 males and 21 females that volunteer at the shelter. Now we will calculate the total number of male volunteers and the total number of female volunteers.
Male Volunteers: 26+13+9= 48
Female Volunteers: 21+17+14= 52
We can add this information to the table.
Males
Females
Animal Shelter
26
21
Hospital
13
17
Library
9
14
Total
48
52
Finally, we can find the the relative frequencies by colummns to compare the percentages. To do so, we can calculate the ratio of each value to the total in that column.
Males
Females
Animal Shelter
26; 26/48 ≈ 0.54
21; 21/52 ≈ 0.40
Hospital
13; 13/48 ≈ 0.27
17; 17/52 ≈ 0.33
Library
9; 9/48 ≈ 0.19
14; 14/52 ≈ 0.27
Total
48; 48/48 = 1.00
52; 52/52 = 1.00
We can use the calculated joint relative frequencies to compare the percentages.
Out of 48 male volunteers, about 54 % of them volunteered at the animal shelter.
Out of 52 female volunteers, about 40 % of them volunteered at the animal shelter.
We know that 54 % is greater than 40 %. This means that the percentage of males who volunteered at the animal shelter is greater than the percentage of females who volunteered at the animal shelter.
