15 # 16 - Statistics

The field of statistics provides tools for studying questions that can be answered with data. A seemingly endless variety of data is available for populations, health, financial and business activities, and the environment. It is virtually impossible to think of a social activity or a physical phenomenon for which we cannot collect data. Statistical concepts help to interpret these data and to recognize trends.

In this chapter, we focus on the following topics and practices within the Common Core State Standards for Mathematics (CCSSM).

Standards for Mathematical Content in the CCSSM

In the domain of Measurement and Data (Kindergarten–Grade 5), students organize categorical and numerical measurement data and they represent data in picture graphs, bar graphs, and dot plots (line plots). They use these representations as they ask and answer questions in order to interpret data.

In the domain of Statistics and Probability (Grades 6–8), students appreciate that statistical questions anticipate variability. They work with distributions displayed in dot plots or histograms, they use measures of center (median or mean) and variation (interquartile range or mean absolute deviation) to summarize distributions and to compare sets of data, and they interpret the comparison in terms of the context. Students learn that we can use random samples to draw inferences about a population. They use scatterplots and their understanding of relationships, especially linear relationships, to investigate patterns of association between two quantities.

Standards for Mathematical Practice in the CCSSM

Opportunities to engage in all eight of the Standards for Mathematical Practice described in the CCSSM occur throughout the study of statistics, although the following standards may be especially appropriate for emphasis:

• 2 Reason abstractly and quantitatively. Students engage in this practice when they reason about proportional relationships to make an informal inference about a population based on a random sample.

• 4 Model with mathematics. Students engage in this practice when they investigate questions by gathering, displaying, and summarizing data and by applying statistical reasoning to draw conclusions.

• 5 Use appropriate tools strategically. Students engage in this practice when they ask and answer questions about statistical displays such as bar graphs and dot plots as part of the process of analyzing data and interpreting data in a context. (From Common Core Standards for Mathematical Practice. Published by Common Core Standards Initiative.)