Math Mammoth Bivariate Data

51 pages
(includes answers)

Sample pages (PDF)
Contents
Scatter Plot Features and Patterns
Equation of the Trend Line
Relative Frequences

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Math Mammoth Bivariate Data is a worktext that covers statistical topics meant for 8th grade in the Common Core Standards (CCS) (specifically, the standards 8.SP.1, 8.SP.2, 8.SP.3, and 8.SP.4). These topics have to do with bivariate data, or data involving two variables.

The first lesson introduces scatter plots. Students analyze the data in a variety of scatter plots, and determine visually whether there is an association between the variables. Next, they learn about basic patterns we often see in scatter plots, such as positive and negative association, linear association, clusters, and outliers. They also make scatter plots from given data, describe any special features in the plot, and answer a variety of questions related to the data.

In the following lesson, students fit a line (informally) to the data points displayed in a scatter plot. Mathematicians have developed several algorithms for finding a line of best fit, such as linear regression, but we are not using those here. Students use the basic idea of trying to leave close to an equal number of points on each side of the line, and also judging the fit by the closeness of the points to the line. This resembles the thought behind the linear regression algorithm, which finds the line of best fit by minimizing the squares of the distances of the data points to the line.

The last topic relating to scatter plots is the equation of the trend line. Students use the equation of the trend line to solve problems in the context of the data, interpreting the slope and intercept of the equation.

Then we turn our attention to categorical bivariate data, that is, data involving two variables that may or may not be numerical, but is divided into categories. Students learn that bivariate categorical data can be summarized in a two-way table, and if there is a pattern of association between the variables, it can be seen in the table.

Students construct and interpret two-way tables summarizing data on two categorical variables. In the last lesson, they calculate relative frequencies for rows or columns, and use those to describe the possible association between the two variables.

The book ends with a review lesson. The answers are appended.

The PDF version of this book can be filled in on a computer, phone, or tablet, using the annotation tools found in many PDF apps. See more.