6 - Bivariate Statistics

In this unit students will create and analyze data displays for both categorical and quantitative data. In eighth grade students constructed and interpreted two-way tables summarizing data on two categorical variables collected from the same subjects. They used relative frequencies calculated for rows or columns to describe possible association between the two variables. In this unit, students will deepen their knowledge of relative frequencies to find and use conditional, marginal and joint relative frequencies. In Algebra 2, students will use their understanding of two-way tables to analyze a sample space, decide if events are independent, and to approximate conditional probabilities.

In sixth, seventh and eighth grade students represented and analyzed both univariate and bivariate quantitative data. In eighth grade students constructed and interpreted scatter plots focusing on estimating lines of best fit and informally analyzing the closeness of the fit. They also described patterns including clustering, outliers, positive or negative association and linear or nonlinear association. In this unit students formalize their analysis of the line of best fit by using residuals to analyze the variance in a bivariate data set. This is an extension of 6th and 7th grade standards where students find the average distance from the mean to analyze the variance in an univariate data set. In addition, students will analyze the relation between the two variables in a linear model by using technology to compute and interpret the correlation coefficient. However, a cause and effect relationship is not necessarily related to the strength of the correlation, and students should recognize instances where causation is unrelated to this strength. Students will also use what they know about exponential and quadratic functions from previous units to fit a function to the data to solve problems in the context of the data. Solving problem might include describing patterns, like they did in eighth grade, or making predictions inside and outside of the data set.

There are standards listed in this section for two reasons.

1. The standards have been modified to be appropriate for this unit. Text in gray font is part of the Michigan K-12 standard but does not apply to this unit. Text in brackets denotes a modification that has been made to the standard.
2. The standards contain content that is developed and/or utilized across multiple units.

Modified For this Unit

n/a

Developed and/or Utilized Across Multiple Units

Quantities

HSN-Q.A. Reason quantitatively and use units to solve problems.

HSN-Q.A.2. Define appropriate quantities for the purpose of descriptive modeling.

HSN-Q.A.3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

1. When looking at both categorical and quantitative data how can the strength of the association between two variables be analyzed?
2. What impact can an outlier have on the correlation coefficient for a scatter plot?
3. What is the difference between correlation and causation?
4. How are the parameters from different functions modeling data interpreted in real- world contexts?
5. How are joint, marginal, and conditional relative frequencies similar? Different?