Exercise 1 Page 692

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. Fill in the table with the given values.
3. Find the rest of values.

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

Constructing the Table

We are told that boys and girls are surveyed as to whether or not they agree with new rules in the cafeteria. This information is enough to determine the appropriate column and row headers for our table.

	Agree with Rules	Do not Agree with Rules	Total
Males
Females
Total

Filling in the Table

We are told that $38$ males agree with the new rules and $70$ do not. Of the $92$ females surveyed, $41$ agree with rules. Let's write the given information in our table.

	Agree with Rules	Do Not Agree with Rules	Total
Males	$38$	$70$
Females	$41$		$92$
Total

Finding the Missing Values

To calculate the number of surveyed males, we add the number of males who agree with rules and who do not. The number of females who do not agree with new rules is the number of females who agree with rules subtracted from the total number of females. Let's complete the table with new information.

	Agree with Rules	Do Not Agree with Rules	Total
Males	$38$	$70$	$108$
Females	$41$	$51$	$92$
Total

Let's calculate the sums of each column to find the missing values. Finally, we have two ways of calculating the grand total. We can add the number of $\text{females}$ to the number of $\text{males},$ or we can add the students who agree with rules to the students who do not. These two numbers must be the same! Finally, we can complete our table!

	Agree with Rules	Do Not Agree with Rules	Total
Males	$38$	$70$	$108$
Females	$41$	$51$	$92$
Total	$79$	$121$	$200$