Algebra 1 Two-Way Frequency Tables

Use the table below to answer the following questions. 1.How many people chose cats as their preferred pet? 2.How many 9 th graders chose dogs as their preferred pet? 3.How many 10 th graders responded to this survey? 4.How many total people responded to this survey? 5.What percentage of all students chose fish as their favorite pet? GRADEPREFERRED PET BirdCatDogFish

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 9 th graders chose dogs as their preferred pet?” The answer to this question is considered the joint frequency because these respondents are both 9 th 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. GRADEPREFERRED PET BirdCatDogFish

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. GRADEPREFERRED PET BirdCatDogFish

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 10 th 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 9 th graders from this problem because the question has asked me about 10 th grade students. GRADEPREFERRED PET BirdCatDogFish

Example 2: Use the table to answer the following questions. 1.What is the marginal frequency for males? 2.What is the relative frequency for males that prefer the color red? 3. What is the joint frequency for female students who prefer the color green? 4. How many females prefer the color pink? 5. What percentage of male students chose pink as their favorite color? GenderFavorite Color BlueRedGreenPink Male51482 Female111051

Example 2: Use the table to answer the following questions. 6. What percentage of the students surveyed chose blue as their favorite color? 7. Given that the student is male, what is the conditional relative frequency for blue? 8. Given that the student prefers red, what is the conditional relative frequency for being female? GenderFavorite Color BlueRedGreenPink Male51482 Female111051