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Standard 3 : Solve problems involving categorical data.
Cluster Standards

This cluster includes the following benchmarks.

Visit the specific benchmark webpage to find related instructional resources.

  • MA.912.DP.3.1 : Construct a two-way frequency table summarizing bivariate categorical data. Interpret joint and marginal frequencies and determine possible associations in terms of a real-world context.
  • MA.912.DP.3.2 : Given marginal and conditional relative frequencies, construct a two-way relative frequency table summarizing categorical bivariate data.
  • MA.912.DP.3.3 : Given a two-way relative frequency table or segmented bar graph summarizing categorical bivariate data, interpret joint, marginal and conditional relative frequencies in terms of a real-world context.
  • MA.912.DP.3.4 : Given a relative frequency table, construct and interpret a segmented bar graph.
  • MA.912.DP.3.5 : Solve real-world problems involving univariate and bivariate categorical data.
Cluster Information
Number:
MA.912.DP.3
Title:
Solve problems involving categorical data.
Type:
Standard
Subject:
Mathematics (B.E.S.T.)
Grade:
912
Strand
Data Analysis and Probability
Cluster Access Points

This cluster includes the following Access Points.

  • MA.912.DP.3.AP.1 : When given a two-way frequency table summarizing bivariate categorical data, identify joint and marginal frequencies.
  • MA.912.DP.3.AP.2 : Given the marginal relative frequencies and a partially completed two-way table, calculate one missing value per row and/or per column.
  • MA.912.DP.3.AP.3 : Given a segmented bar graph summarizing categorical bivariate data, select the interpretation in terms of a real-world context.
Cluster Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Original Student Tutorial
  • Data and Frequencies: Learn to define, calculate, and interpret marginal frequencies, joint frequencies, and conditional frequencies in the context of the data with this interactive tutorial.

Formative Assessments
  • Two-Way Relative Frequency Table: Students are asked to convert raw data to relative frequencies by both rows and columns given a two-way frequency table.

  • School Start Time: Students are asked to describe an association between two variables given a table of relative frequencies by column.

  • Music and Sports: Students are asked to construct a two-way frequency table given a set of raw data.

  • Marginal and Joint Frequency: Students are asked to use a two-way frequency table to interpret marginal and joint relative frequencies.

  • Who Is a Vegetarian?: Students are given a two-way frequency table and asked to determine if there is a relationship between the two variables.

  • Breakfast Drink Preference: Students are asked to use data from a survey to create a two-way frequency table.

  • Conditional Relative Frequency: Students are asked to use a two-way frequency table to interpret two different conditional relative frequencies.

  • Siblings and Pets: Students are asked to describe an association between two variables given a table of relative frequencies by row.

Lesson Plans
  • Taxes using Two-Way Frequency Tables: Students will construct a two-way frequency table of different levels of government and the imposed gasoline taxes in Florida. Students will learn about marginal and joint frequencies. This is lesson three of a 3-part integrated mathematics and civics mini-unit.

  • Investigating Relationships With Two-Way Frequency Tables: In this lesson, students are introduced to two-way frequency tables. They will calculate joint, marginal, and relative frequencies and draw conclusions about the relationship between two categorical variables.

  • Can You Walk in My Shoes?: Students use real-life data to create dot-plots and two-way tables. Students will collect data at the beginning of the lesson and use that data to create double dot plots and frequency tables, finding and interpreting relative frequencies.

    The assignment allows students to work collaboratively and cooperatively in groups. They will communicate within groups to compare shoes sizes and ages to acquire their data. From the collection of data they should be able to predict, analyze and organize the data into categories (two-way tables) or place on a number line (dot-plot).

    As the class assignment concludes, a discussion of the final class display should take place about the purchasing of shoes versus ages and the relationship that either exists or doesn't exist.

  • How Random is "Shuffle Mode"?: Today's teenager is a savvy consumer of digital music and the constantly-evolving technology that plays it. Ask a typical student what they know about iTunes versus Pandora versus Spotify—most of them will have an opinion on the "best" service for listening to songs. This lesson links students' existing interest in music with the mathematical topics of frequency and relative frequency.

    The activity assumes that students know what Shuffle Mode does when they listen to digital music. Shuffle Mode is a function on digital music players that "shuffles" or randomly rearranges the order of a list of songs. Each time a person presses Shuffle Mode, the playlist is rearranged. If we assume a music player's Shuffle Mode is truly random, the chances of any particular song being played would equal 1 divided by the total number of songs (1/total #). This is analogous to rolling a fair die; each number on the die has an equal probability of being rolled (1/6 or 16.7%).

  • Dropping Out or Staying In: Two-Way Table Analysis: This lesson will require students to calculate relative frequencies and determine if an association exists within a two-way table. The students will analyze the frequencies and write a response justifying the associations and trends found within the table.

  • How tall is an 8th grader?: Ever wonder about the differences in heights between students in grade 8? In this lesson, students will use data they collect to create and analyze multiple box plots using 5-number summaries. Students will make inferences about how height and another category may or may not be related.

  • Plane Statistics: This lesson starts with an activity to gather data using paper airplanes then progresses to using appropriate statistics to compare the center and spread of the data. Box plots are used in this application lesson of concepts and skills previously acquired.

  • What's your preference?: In this lesson, students will collect data and construct two-way frequency tables. They will analyze the two-way frequency table by calculating relative conditional frequencies.

  • What's Your Story?: Exploring Marginal and Conditional Distributions Through Social Networks: In this interactive lesson, students explore marginal and conditional distributions. Students will calculate the relative frequency of data collected about cell phone use and social media access. These categories can be adjusted as necessary.

  • Relative Frequency Tables... with extra cheese!: Have students get colorful in defining marginal, joint and conditional frequencies of two-way frequency tables. Students will take charge in justifying the associations they find in the tables.

  • High School Dropouts: Students will examine dropout rates in the United States in 2012 by gender and race using data provided by the National Center for Education Statistics. Students will create conditional relative frequency tables to interpret the data and identify associations between genders, races, and dropout rates.

  • It's Your Choice: In groups, students will analyze associations between categorical data by constructing two-way frequency tables and two-way relative frequency tables. Students will analyze and interpret the results and present their findings to their classmates.

  • Breakfast for Champions?: Students will create and interpret two-way frequency tables using joint, marginal, and conditional frequencies in context. They will investigate whether breakfast is for champions.

  • Using Two-Way Frequency Tables to Analyze Data: The television program, 60 Minutes reports that parents are intentionally holding their children back in kindergarten to give them a competitive advantage in sports later on in life. The students will use data collected to decide if this is truly a trend in the United States.

  • Comedy vs. Action Movies Frequency Interpretation: Using a completed survey of male and female student interest in comedy vs. action movies, the students will create a two-way frequency table using actual data results, fraction results, and percent results. The students will then act as the movie producer and interpret the data to determine if it is in their best interest to make a comedy or action movie. As the Summative Assessment, the student will take on the job/role of an actor/actress and interpret the data to support their decision.

  • Show Me the Money: Students will create a statistical question and collect and analyze data using relative frequency tables. They will present their argument in hopes of earning a cash prize for their philanthropy. An iterative process of critique and refinement will take place. A student packet is included that guides all parts of the lesson.

  • Quantitative or Qualitative?: This lesson examines the differences between quantitative and qualitative data and guides students through displaying quantitative data on a scatter plot and then separating the data into qualitative categories to be displayed and interpreted in a two-way frequency table.

  • Are you a CrimiNole or Gatorbait? Two rivalries in one table!: This is an introduction to two-way frequency tables. The lesson will be delivered using a PowerPoint presentation. The teacher will introduce and define joint and marginal frequency, demonstrate how two-way frequency tables are constructed from a given set of data, calculate relative frequencies, and draw conclusions based on the information in the table. Students will practice these skills through guided practice with the teacher, independent practice, and complete a summative assessment to measure student learning. All resources, including the PowerPoint, have been provided.

  • Two-Way Math Survey: In this lesson, students will construct a two-way table based on data given. They will interpret the data to find if there is a correlation between the two variables from the same subject. As the lesson progresses, students will create their own testable questions that they will collect data on using the survey method. Students will show their mastery of this math concept with the presentation of the data in a two-way table and interpretation of the data to draw inferences.

  • Tackling 2 Way Tables: This highly engaging and interactive lesson will have students constructing two-way tables, calculating relative frequency and analyzing the bivariate data to determine a possible association between the two variable categories.

  • Can You Make Heads or Tails of It?: Students learn how to make two-way tables, frequency, and relevant frequency tables. Students make predictions, collect data, and display it in two-way tables for interpretation.

  • Two-Way Frequency Table and Relative Frequency: In this lesson, the student will learn how to set up a two-way frequency table from two categorical variables and use the two-way frequency table to calculate frequency counts and relative frequency. The vocabulary terms learned in this lesson are two-way frequency table, relative frequency, joint frequency, marginal frequency, and conditional frequency.

  • Is It a Guess or Statistics?: This lesson teaches random sampling which leads to making inferences about a larger group or population. Students will determine the best measure of center to use for a data set. Students will collect data, select a data display and then analyze the data.

  • How hot are hot dogs?: In this lesson, students will learn how to convert simple and two-way frequency tables into relative frequency tables using data collected in the classroom.

  • Legos, Lunch, and Lollipops: an introduction to two-way frequency tables: Students will learn how to read, complete, and interpret two-way frequency tables.

  • Modeling Conditional Probabilities 1: Lucky Dip: This lesson unit is intended to help you assess how well students are able to understand conditional probability, represent events as a subset of a sample space using tables and tree diagrams, and communicate their reasoning clearly.

Problem-Solving Tasks
  • Musical Preferences: This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table.

  • The Titanic 1: This task asks students to calculate probabilities using information presented in a two-way frequency table.

  • Music and Sports: This task asks the student to gather data on whether classmates play an instrument and/or participate in a sport, summarize the data in a table and decide whether there is an association between playing a sport and playing an instrument. Finally, the student is asked to create a graph to display any association between the variables.

  • What's Your Favorite Subject?: Students are asked to examine data given in table format and then calculate either row percentages or column percentages and state a conclusion about the meaning of the data. Either calculation is appropriate for the solution since there is no clear relationship between the variables. Whether the student sees a strong association or not is less important than whether his or her answer uses the data appropriately and demonstrates understanding that an association means the distribution of favorite subject is different for 7th graders and 8th graders.