Relative Frequency Tables

5 min

Narrative

The purpose of this Warm-up is to elicit the idea that two-way tables can be used to think about relative frequency, which will be useful when students create relative frequency tables in a later activity. While students may notice and wonder many things about these images, the ways in which the values in the two-way tables relate to the totals are the important discussion points.

Launch

Arrange students in groups of 2. Display the two-way table for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time and then 1 minute to discuss with their partner the things they notice and wonder.

Student Task

Several adults in a school building were asked about their highest degree completed and whether they were a teacher.

What do you notice? What do you wonder? 

teacher not a teacher
associate degree 4% 16%
bachelor’s degree 52% 64%
master’s degree or higher 44% 20%

Sample Response

Things students may notice:

  • The columns sum to 100%.
  • Most teachers have a bachelor’s degree or higher.
  • 20% of the adults who are not teachers have a master’s degree or higher.

Things students may wonder:

  • Why does the bachelor’s degree row sum to greater than 100%?
  • How many people were asked these questions?
  • Are there more nonteachers with bachelor’s degrees or teachers with bachelor’s degrees?
Activity Synthesis (Teacher Notes)

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the table. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.

It is not important to answer the questions that students are wondering about at this time. Many of their questions will be addressed later in the lesson. 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’s degree or higher.)

Display the actual values used in the relative frequency table in the task for all to see. 

teacher not a teacher
associate degree 2 4
bachelor’s degree 26 16
master’s degree or higher 22 5

Point out that, although there are more teachers with bachelor’s degrees than nonteachers with bachelor’s 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’s degrees are considered among the 50 teachers, while the 16 nonteachers with bachelor’s degrees are only considered among the 25 nonteachers.

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.)
Standards
Addressing
  • HSS-ID.B.5·Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
  • S-ID.5·Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
  • S-ID.5·Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
  • S-ID.5·Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

15 min

15 min