We asked $25$ classmates the following.

Do they have a curfew?
Do they have assigned chores at home?

Here is a two-way table of the results. We want to interpret them.

	Curfew	No Curfew
Chores	$13$	$4$
No Chores	$2$	$6$

To interpret data in a two-way table, we usually find and then compare the relative frequencies. To do so, first we need to find the totals in each row and each column. This means adding the values in each row and column. Let's do it!

	Curfew	No Curfew	Total
Chores	$13$	$4$	$13 + 4 = 17$
No Chores	$2$	$6$	$2 + 6 = 8$
Total	$13 + 2 = 15$	$4 + 6 = 10$	$25$

Now, we can find the frequencies by row or by column. Looking at it by column, we will write the ratios of each value to the total in that column. We will then calculate the quotients. Take note that there are $15$ students with curfew and $10$ students without a curfew.

	Curfew	No Curfew	Total
Chores	$13; \frac{1 3}{1 5} \approx 0.87$	$4; \frac{4}{1 0} = 0.4$	$17$
No Chores	$2; \frac{2}{1 5} \approx 0.13$	$6; \frac{6}{1 0} = 0.6$	$8$
Total	$15$	$10$	$25$

As we divide each response of 'chores' and 'no chores' over the total number, respective of 'curfew' and 'no curfew,' we get the frequencies. Next, we need to interpret what the results mean. See that $0.87 = 87 %$ of the students who have a curfew also have chores assigned. What is more, $0.13$ or $13 %$ of the students who have a curfew do not have any chores assigned.

	Curfew	No Curfew	Total
Chores	$13; 0.87$	$7; 0.4$	$17$
No Chores	$2; 0.13$	$3; 0.6$	$8$
Total	$15$	$10$	$25$

Since $0.87 > 0.13,$ not even close, we can say that most of the students who have a curfew also have chores. For similar reasons, because $0.6 > 0.4,$ a student that does not have a curfew more likely does not have any chores assigned either. What a cool study.

Exercise