# Ch 3: Common Core HS Statistics & Probability: Bivariate Data

Use our high school statistics and probability video lessons to augment classroom instruction. Prepare your students to meet the common core standards for using bivariate data.

Standard: 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. (CCSS.Math.Content.HSS-ID.B.5)

Standard: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. (CCSS.Math.Content.HSS-ID.B.6a)

Standard: Informally assess the fit of a function by plotting and analyzing residuals. (CCSS.Math.Content.HSS-ID.B.6b)

Standard: Fit a linear function for a scatter plot that suggests a linear association. (CCSS.Math.Content.HSS-ID.B.6c)

Standard: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. (CCSS.Math.Content.HSS-ID.C.7)

Standard: Compute (using technology) and interpret the correlation coefficient of a linear fit. (CCSS.Math.Content.HSS-ID.C.8)

Standard: Distinguish between correlation and causation. (CCSS.Math.Content.HSS-ID.C.9)

Students who exhibit mastery of these standards are able to perform statistical analyses using bivariate data. While completing those analyses, students will make use of two-way tables, scatter plots and linear regression models.

Lessons in these standards address concepts such as:

• Two-way tables
• Joint, marginal and conditional frequencies
• Scatter plots
• Linear regression
• Residuals
• Slope and intercept
• Correlation coefficient
• Correlation vs. causation

Students who have mastered these standards are able to create two-way tables and scatter plots with bivariate data, in addition to performing simple linear regressions to solve various types of problems. They will also demonstrate an understanding of correlation vs. causation, enabling them to interpret correlations in research being completed in their major areas of college study.

### How to Use These Lessons in Your Classroom

The following are some tips on how you can incorporate these lessons on bivariate data into your curriculum to help meet the common core standards:

#### Pre- and Post-Quiz Lessons

Have students complete the quizzes for the What is a Two-Way Table? and How to Interpret Correlations in Research Results lessons to introduce the concepts and make them aware of what to look for during the videos. After watching the video lessons, have students re-take the quizzes to assess understanding.

#### Scatter Plots Lesson

After viewing the scatter plots video lesson, supply your class with data concerning the major species of dogs' maximum longevity and typical adult weight. As a class, construct a scatter plot to find a possible correlation between longevity and adult weight in dogs.

#### Scatter Plots, Linear Regressions, Slope/Intercept, Residuals and Correlations Lessons

Share the video lessons on the topics listed above. Assign each student one or two states in the U.S. to research the number of area codes and the population in a given year. As a group, plot a scatter plot to predict the number of area codes from the population. Incorporate regression equations, computation of residuals and estimation of correlation.

11 Lessons in Chapter 3: Common Core HS Statistics & Probability: Bivariate Data
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Chapter Practice Exam
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