Several adults in a school building were asked about their highest degree completed and whether they were a teacher.

What do you notice? What do you wonder? 

The next table shows what percentage of the 200 total people are represented by each combination of categories. The segmented bar graph represents the same information graphically.

	urban	rural
cat	27%	21%
dog	40%	12%

The next table is a column relative frequency table and shows the percentage of people represented in each column that have a certain pet preference. The segmented bar graph represents the same information graphically.

	urban	rural
cat	40%	64%
dog	60%	36%

The last table is a row relative frequency table and shows the percentage of people represented in each row that live in a certain area. The segmented bar graph represents the same information graphically. 

	urban	rural
cat	56%	44%
dog	77%	23%

1. For each relative frequency table, select a percentage, and explain how numbers from the original table were used to get the percentage.
2. What percentage of those surveyed live in an urban area and prefer dogs?
3. Among the people surveyed who prefer dogs, what percentage of them live in an urban setting?
4. What percentage of people surveyed who live in an urban setting prefer dogs?
5. How many of the people responded that they prefer dogs and live in an urban setting?
6. Among the people surveyed, are there more people who prefer dogs or cats?
7. Your pet food company has access to a billboard in a rural setting. Would you recommend advertising dog food or cat food on this billboard? Which table did you use to make this decision? Explain your reasoning.

In an experiment to test the effectiveness of vitamin C on the length of colds, two groups of people with colds are given a pill to take once a day. The pill for one of the groups contains 1,000 mg of vitamin C, while the other group takes a placebo pill. The researchers record the results in a table.

1. First, the researchers want to know what percentage (to the nearest whole percent) of people are in each combination of categories. 14% of all the participants had a cold that lasted less than a week and were in group A. What percentage of all the participants had a cold that lasted less than a week and were in group B? Complete the rest of the relative frequency table with the corresponding percentages. 
    

   	group A	group B
   cold lasts less than a week	14%
   cold lasts a week or more

2. Next, the researchers notice that among participants who had colds that lasted less than a week, 37% were in group A. Among participants who had colds that lasted a week or more, what percentage were in group B? Complete the table with the corresponding percentages.
    

   	group A	group B
   cold lasts less than a week	37%
   cold lasts a week or more

3. Finally, the researchers notice that among the participants in group A, 48% had colds that lasted less than one week. Among the participants in group B, how many had colds that lasted a week or more? Complete the table with the corresponding percentages. 
    

   	group A	group B
   cold lasts less than a week	48%
   cold lasts a week or more

4. To understand the results, the researchers want to know the following: Among people whose colds lasted less than a week, what percentage are in group B? Explain your reasoning. 
5. If the researchers believe that vitamin C has a small effect on the length of a cold, which group most likely got the pills containing vitamin C? Explain your reasoning.