Start by constructing an empty table with the appropriate column and row headers. Then use the given information to find the missing frequencies.
Table:
Was the Conference Impactful?
Gender
Yes
No
Total
Men
200
20
220
Women
230
40
270
Total
430
60
490
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 220 men and 270 women are surveyed as to whether or not they agree that the conference was impactful. This information is enough to determine the appropriate column and row headers for our table.
Was the Conference Impactful?
Gender
Yes
No
Total
Men
Women
Total
Finding the Joint Frequencies
Each entry in the table is called a joint frequency. We are told that of the 220 men surveyed, 200 say the conference was impactful. Of the 270 women surveyed, 230 say the conference was impactful. With this information, we can find the number of men and women who did not agree that the conference was impactful.
Men who disagree:&& 220- 200= 20
Women who disagree:&& 270- 230= 40
Let's write the given and the newly obtained information in our table.
Was the Conference Impactful?
Gender
Yes
No
Total
Men
200
20
220
Women
230
40
270
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 agreed:&& 200+ 230&=430
People who disagreed:&& 20+ 40&=60
Finally, we have two ways of calculating the grand total. We can add the number of men to the number of women, or we can add the people who agreed to the people who disagreed. These two numbers must be the same!
Grand total
l 270+ 220 =490 430+60=490 ✓
Finally, we can complete our table!
Was the Conference Impactful?
Gender
Yes
No
Total
Men
200
20
220
Women
230
40
270
Total
430
60
490
Interpreting the Marginal Frequencies
In the marginal frequencies, we can see that 430 people agreed that the conference was impactful, whereas 60 did not agree. Moreover, we learned that a total of 490 people were surveyed.
