Teaching Statistics Investigations > Chapter 3
Teaching Statistics Investigations Chapter 3-Developing Conceptual Understanding of Measures of Variability
Variability is at the heart of statistics, and understanding and measuring it is an important aspect of analyzing data. This chapter is not a statistical investigation. Instead, teachers use two free online apps to explore the mathematical structures of common measures of variability. Specifically, for measuring variability in univariate data, a dynamic geometric diagram is used, created with Web Sketchpad, to understand the structure of the mean absolute deviation, variance, and standard deviation. For bivariate data, a free online app is used to understand variation through correlation, the coefficient of determination, and deviations from linear models. The chapter materials include 2 sections, with separate PDFs, and suggested readings (PDF).
Class Materials
Deviations From the Mean: Teachers engage with an interactive applet developed using WebSketchpad that uses a geometric representation of 5 data values, the mean of these values, and how each point deviates, or varies, from the mean. They explore the meaning, geometrically and symbolically, for three common measures of variation: mean absolute deviation (MAD), variance, and standard deviation. |  Section 1 |
| A dynamic diagram used in Section 1 to explore deviations from a set of random data points, designed by Hollylynne Lee with Web Sketchpad. | Deviations Interactive Diagram |
| Measuring and Modeling Covariation in Bivariate Data: Teachers use a free online app to explore the meaning of covariation in bivariate data. They can develop a better understanding of measures such as correlation and the coefficient of determination. The dynamic dragging feature of the app allows users to explore the effect of outliers on these measures and to consider how they can be used along with a linear regression model. NOTE: The app used in this section is no longer functioning. | Section 2 |
| Suggested homework tasks and supplemental readings | Assignments & Readings |