1. The Table Categorization
Unit 4 – Bivariate Data
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Algebra 1 Institute

2. Select your Favorite Color
Red
Orange
Yellow
Green
Blue
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Algebra 1 Institute

3. Display Data Bar Chart Frequency one-way table 1/1/2019
Algebra 1 Institute

4. Relative Frequency Table
Includes proportions or percentages
Convert the frequency table to a relative frequency table
What statistical question could be answered with this data?
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Algebra 1 Institute

5. Two-Way Tables Joint Frequency Marginal Frequency 1/1/2019
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6. Relative Frequency Tables
The relative frequencies in the body of the table are called conditional frequencies or the conditional distribution.
It can show:
Relative Frequencies for the whole table
Relative Frequencies for rows
Relative Frequencies for columns
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Algebra 1 Institute

7. Relative Frequency Tables
For rows
For columns
What information can be draw from these tables?
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Algebra 1 Institute

8. Possible Association
For what activity would you say that the conditional relative frequencies for females and males are very different?
For what activities are the conditional relative frequencies nearly equal for males and females?
Suppose a person is selected at random from the people who completed the survey. If you had to predict which activity this person selected, would it be helpful to know the person’s gender? Why?
Is there evidence of an association between gender and favorite activity? Explain.
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Algebra 1 Institute

9. Association - Cause and Effect
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Algebra 1 Institute

10. Reflect
Is there an association between taking the review course and a student’s placement in a math class?
If you knew that a student took a review course, would it make a difference in what you predicted for which math course they were placed in?
Do you think taking a course caused a student to place higher in a math placement?
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Algebra 1 Institute

11. Conditional Relative Frequency Table
Based on the conditional relative frequencies, is there evidence of association between whether a student takes the review course and the math course in which the student was placed? Explain your answer.
Looking at the conditional relative frequencies, the proportion of students who placed into Math 200 is much higher for those who took the review course than for those who did not.
One possible explanation is that taking the review course caused improvement in placement test scores.
What is another possible explanation?
Is this is an example of a cause-and-effect relationship?
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Algebra 1 Institute

12. Sugar Consumption and Exercise Level
Is there evidence of association between sugar consumption category and exercise level? Support your answer using conditional relative frequencies.
Do you think it is reasonable to conclude that high sugar consumption is the cause of the observed differences in the conditional relative frequencies? What other explanations could explain a difference in the conditional relative frequencies? Explain your answer.
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Algebra 1 Institute

13. Sugar Consumption and Exercise Level
It is possible that students in the above study who are more health conscious tend to be in the low sugar consumption category and also tend to be in the high exercise level category.
It is not possible to determine if the difference in the conditional relative frequencies is due to a cause-and-effect relationship.
The data summarized in this study were collected in an observational study. With an observational study,
Any observed differences in conditional relative frequencies might be explained by some factor other than the variables examined in the study.
Evidence of association may exist, but it is not possible to imply that there is a cause-and-effect relationship.
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Algebra 1 Institute