Exercise 3 Page 693

We want to find relative frequencies by row. To do so, we will start by completing the given table.

	Text Message	Instant Message	Total
7th graders	$59;$	$25;$
8th graders	$59;$	$41;$
Total

Let's find the sums of each row and column. Let's write the newly obtained information in our table.

	Text Message	Instant Message	Total
7th graders	$59;$	$25;$	$84$
8th graders	$59;$	$41;$	$100$
Total	$118$	$66$

We have two ways of calculating the grand total. We can add the number of $7\text{th graders}$ to the number of $8\text{th graders},$ or we can add the students who $\text{text message}$ to the students who $\text{instant message}.$ These two numbers must be the same! Now, we can complete our table!

	Text Message	Instant Message	Total
7th graders	$59;$	$25;$	$84$
8th graders	$59;$	$41;$	$100$
Total	$118$	$66$	$184$

To find the relative frequencies by row, we calculate the ratios of each value and the total in that row. We will round the results to the nearest hundredth.

	Text Message	Instant Message	Total
7th graders	$59;$ $\frac{59}{84}\approx 0.70$	$25;$ $\frac{25}{84}\approx 0.30$	$84;$ $\frac{84}{84}=1.00$
8th graders	$59;$ $\frac{59}{100}=0.59$	$41;$ $\frac{41}{100}=0.41$	$100;$ $\frac{100}{100}=1.00$
Total	$118$	$66$	$184$

Looking at the relative frequencies, we can say that many more $7^{\text{th}}$ graders text message than instant message. The $8^{th}$ graders split more evenly.