Start by constructing an empty table with the appropriate column and row headers. Then use the given information to find the missing frequencies.
Table:
Wash Their Hands After Using the Public Rest Rooms
Gender
Do
Do Not
Total
Males
132
39
171
Females
151
29
180
Total
283
68
351
Interpretation of the Marginal Frequencies: See solution.
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 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.
Let's do these three things one at a time. Then we will interpret the marginal frequencies.
Constructing the Table
We are told that males and females were surveyed on whether they wash their hands after using the public rest rooms. This information is enough to determine the appropriate column and row headers for our table.
Wash Their Hands After Using the Public Rest Rooms
Gender
Do
Do Not
Total
Males
Females
Total
Finding the Joint Frequencies
Each entry in the table is called a joint frequency. We are told that of the 171 males surveyed, 132 do wash their hands after using the public rest rooms. Of the 180 females surveyed, 151 do it. With this information, we can find the number of males and females that do not wash their hands after using the public rest rooms.
Males Who Do Not:&& 171- 132&= 39
Females Who Do Not:&& 180- 151&= 29
Let's write the given and the newly obtained information in our table.
Wash Their Hands After Using the Public Rest Rooms
Gender
Do
Do Not
Total
Males
132
39
171
Females
151
29
180
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.
People Who Do It:&& 132+ 151&=283
People Who Do Not Do It:&& 39+ 29&=68
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 people who do it to the people who do not. These two numbers must be the same!
Grand total
l 180+ 171 =351 283+68=351 âś“
Finally, we can complete our table!
Wash Their Hands After Using the Public Rest Rooms
Gender
Do
Do Not
Total
Males
132
39
171
Females
151
29
180
Total
283
68
351
Interpreting the Marginal Frequencies
In the marginal frequencies, we can see that 180 females and 171 males were surveyed. Moreover, 283 people wash their hands after using the public rest rooms and 68 people do not wash their hands after using the public rest rooms. A total of 351 people were surveyed.
