Exercise 2 Page 729

Have Been to Canada

Have Not Been to Canada

Total

Have Been to Mexico

6; 0.67

3; 0.33

9

Have Not Been to Mexico

5; 0.31

11; 0.69

16

Total

We are given a table with the results of a survey about whether students have been to Canada or Mexico.

	Have Been to Canada	Have Not Been to Canada
Have Been to Mexico	$6;$	$3;$
Have Not Been to Mexico	$5;$	$11;$
Total

We are asked to find and interpret the relative frequencies by row for this table. This means that we will need to find the sum of the values in each row. Notice that the sums of the columns are completely redundant to us this time, so we will not evaluate them. Let's find the sums of the rows!

	Have Been to Canada	Have Not Been to Canada	Total
Have Been to Mexico	$6;$	$3;$	$6 + 3 = 9$
Have Not Been to Mexico	$5;$	$11;$	$5 + 11 = 16$
Total

To find the relative frequencies by row, we will divide the numbers in each row by that row's total.

	Have Been to Canada	Have Not Been to Canada	Total
Have Been to Mexico	$6; \frac{6}{9} \approx 0.67$	$3; \frac{3}{9} \approx 0.33$	$9$
Have Not Been to Mexico	$5; \frac{5}{1 6} \approx 0.31$	$11; \frac{1 1}{1 6} \approx 0.69$	$16$
Total

We found all the relative frequencies by row. Now let's interpret them! We can start with the first cell.

	Have Been to Canada	Have Not Been to Canada	Total
Have Been to Mexico	$6; 0.67$	$3; 0.33$	$9$
Have Not Been to Mexico	$5; 0.31$	$11; 0.69$	$16$
Total

We can see that the relative frequency of the students that have been to Mexico and Canada is $0.67 .$ This means that most of the students that have been to Mexico have also been to Canada. Next, let's look at the last cell of the next row.

	Have Been to Canada	Have Not Been to Canada	Total
Have Been to Mexico	$6; 0.67$	$3; 0.33$	$9$
Have Not Been to Mexico	$5; 0.31$	$11; 0.69$	$16$
Total

The relative frequency of the students that have been to neither Mexico nor Canada is $0.69 .$ Therefore, we can conclude that most of the students that have not been to Mexico have also not been to Canada.

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