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out contradicting information. If the concept of relative frequency does not come up during the conversation, ask students “what does the 44% represent?” (44% of the teachers interviewed have a master degree or higher)
Display the actual values used to get relative frequency table in the task for all to see.
teacher
not a teacher
associate degree
2
4
bachelor degree
26
16
master degree or higher
22
5
Point out that, although there are more teachers with bachelor degrees than non-teachers with bachelor degrees, the percentage is lower. This is because there are more teachers who responded to this survey overall and the table shows the relative percentage of adults for each group. That is, the 26 teachers with bachelor degrees are considered among the 50 teachers while the 16 non-teachers with bachelor degrees are only considered among the 25 non-teachers.
Ask students,
• “What is the categorical variable for the categories that label the rows?” (It is the type of degree earned. It likely resulted from a survey question like ‘What is the highest degree that you hold.)
• “What is the categorical variable for ‘teacher’ and ‘not a teacher’?” (It is the person’s occupation.)
2.2 City Cat, Country Cat
10 minutes
The mathematical purpose of this activity is for students to gain an understanding of the relationship between a two-way frequency table and a two-way relative frequency table. Students will be given the same information in a two-way table and a segmented bar graph, then asked to interpret the information given in context.
Launch
Arrange students in groups of 2.
Help orient students by having them notice:
• The sum of all 4 percentages in the second table is 100%.
• For each of the next two tables, ask students to nd percentages that sum to 100%. (The third
table has columns that sum to 100% and the fourth table has rows that sum to 100%.)
Unit 3 Lesson 2: Relative Frequency Tables 19