Big Ideas Math Integrated I, 2016
BI
Big Ideas Math Integrated I, 2016 View details
4. Two-Way Tables
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Exercise 2 Page 357

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.

  1. Construct an empty table with the appropriate column and row headers.
  2. Find the joint frequencies.
  3. Find the marginal frequencies.

Let's do these three things one at a time.

Constructing the Table

We are told that male and female students are surveyed as to whether or not they are getting a summer job. This information is enough to determine the appropriate column and row headers for our table.

Are You Getting a Summer Job?
Gender Yes No Total
Female
Male
Total

Finding the Joint Frequencies

Each entry in the table is called a joint frequency. We are told that of the surveyed males, responded no. Of the surveyed females, responded yes. With this information, we can find the number of males that are getting a summer job and the number of females that are not getting a summer job.
Let's write the given and the newly obtained information in our table.
Are You Getting a Summer Job?
Gender Yes No Total
Female
Male
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.
Finally, we have two ways of calculating the grand total. We can add the number of to the number of or we can add the students who responded to the students who responded These two numbers must be the same!
Finally, we can complete our table!
Are You Getting a Summer Job?
Gender Yes No Total
Female
Male
Total