Two-Way Frequency Tables Lesson 4.2.1 Two-Way Frequency Tables MCC9-12.S.ID.5 MCC9-12.S.ID.6a MCC9-12.S.ID.6b MCC9-12.S.ID.6c

Use the table below to answer the following questions. How many people chose cats as their preferred pet? How many 9th graders chose dogs as their preferred pet? How many 10th graders responded to this survey? How many total people responded to this survey? What percentage of all students chose fish as their favorite pet? GRADE PREFERRED PET Bird Cat Dog Fish 9 3 49 53 22 10 7 36 64

Use the table below to answer the following questions. The table above is what we call a two-way frequency table. They can help us to see trends, or patterns, in the data. A joint frequency is the number of responses for a given characteristic. For example, question #2 stated “How many 9th graders chose dogs as their preferred pet?” The answer to this question is considered the joint frequency because these respondents are both 9th graders and they prefer cats. A marginal frequency is the total number of times a response was given, or the total number of respondents with a given characteristic. Question #1 asks you to give the marginal frequency because you are finding the total number of students that prefer cats. GRADE PREFERRED PET Bird Cat Dog Fish 9 3 49 53 22 10 7 36 64

Use the table below to answer the following questions. Finally, conditional relative frequency allows a comparison to be made for multiple responses. They are found by dividing the number of responses by either the total number of people who gave that response, the total number of people with a given characteristic, or the total number of respondents. In question #5, we have been asked to find the conditional relative frequency for fish for all students. We can find this by dividing: # of students who prefer fish total # of students This value can be left as a decimal or converted to a percentage for comparison purposes. GRADE PREFERRED PET Bird Cat Dog Fish 9 3 49 53 22 10 7 36 64

When finding conditional relative frequency, it is important to read the question very carefully. I could have easily changed question #5 to: 5) What percentage of 10th graders chose fish as their preferred pet? What would the fraction look like in order to solve this question correctly? Notice that I am completely excluding 9th graders from this problem because the question has asked me about 10th grade students. GRADE PREFERRED PET Bird Cat Dog Fish 9 3 49 53 22 10 7 36 64

Example 2: Use the table to answer the following questions. What is the joint frequency of males who sleep 6-8 hours? ____________ What is the marginal frequency of 8-10 hours of sleep? _____________ Of all the students surveyed, what is the conditional relative frequency for students who get 6-8 hours of sleep? Of all the females surveyed, what is the conditional relative frequency for 4-6 hours of sleep? Gender Hours of Sleep 4-6 6-8 8-10 10-12 Male 5 14 8 2 Female 11 10 1