# Conditional Relative Frequencies and Association

Video lessons with examples and solutions to help High School students learn to interpret conditional relative frequencies.

New York State Common Core Math Module 2, Algebra I, Lesson 11

Student Outcomes

Students calculate and interpret conditional relative frequencies from two-way frequency tables.

Students evaluate conditional relative frequencies as an indication of possible association between two variables.

Students explain why association does not imply causation.

Lesson 11 Summary

A conditional relative frequency compares a frequency count to the marginal total that represents the condition of interest.

The differences in conditional relative frequencies are used to assess whether or not there is an association between two categorical variables.

The greater the differences in the conditional relative frequencies, the stronger the evidence that an association exits.

An observed association between two variables does not necessarily mean that there is a cause-and-effect relationship between the two variables.

Example 1: Conditional Relative Frequencies

A conditional relative frequency compares a frequency count to the marginal total that represents the condition of interest. For example, the condition of interest in the first row is females.
The row conditional relative frequency of females responding “Invisibility” as the favorite superpower is 48/228 or approximately 0.211. This conditional relative frequency indicates that approximately 21.1% of females prefer “Invisibility” as their favorite superpower. Similarly, 27/222, or approximately 0.122 or 12.2%, of males prefer “Invisibility” as their favorite superpower.

Row Conditional Frequency - The relative frequency of female surveyed who chose super strength.

Column Conditional Frequency - The relative frequency of those who chose super strength who are female.

Example 3: Association and Cause-and-Effect

Students were given the opportunity to prepare for a college placement test in mathematics by taking a review course. Not all students took advantage of this opportunity. The following results were obtained from a random sample of students who took the placement test:

1. Construct a row conditional relative frequency table.

2. Construct a column conditional relative frequency table.

Lesson 11 Exit Ticket

Juniors and seniors were asked if they plan to attend college immediately after graduation, seek full-time employment, or choose some other option. A random sample of 100 students was selected from those who completed the survey.
Scott started to calculate the row conditional relative frequencies to the nearest thousandth.

1. Complete the calculations of the row conditional relative frequencies. Round your answers to the nearest thousandth.

2. Are the row conditional relative frequencies for juniors and seniors similar, or are they very different?

3. Do you think there is a possible association between grade level (junior or senior) and after high school plan? Explain your answer.

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