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The National Council of Teachers of Mathematics (NCTM, 2000) identifies data analysis and probability as a strand in its Principles and Standards for School Mathematics. In grades pre-K through 12, instructional programs should enable all students to do the following:
• | Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them |
• | Select and use appropriate statistical methods to analyze data |
• | Develop and evaluate inferences and predictions that are based on data |
• | Understand and apply basic concepts of probability |
In the grades 6-8 classroom for data analysis and statistics, students are expected to do the following:
• | Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population |
• | Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatter plots |
• | Find, use, and interpret measures of center and spread, including mean and interquartile range |
• | Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem and leaf plots, box plots, and scatter plots |
In grades 6-8, students examine relationships among populations or samples, and they examine two variables within one population, such as comparing arm spans and heights. They learn to use new representations, such as box plots and scatter plots, to help them examine these relationships. Students also use measures of center to summarize and compare data sets. Building on informal understandings of what is typical, what is usual, what is the most, and what is the middle, students develop understanding about the mode, median, and mean. However, students need to learn more than simply how to identify the mode or median in a data set and how to find the mean: They need to develop an understanding of what these measures of center tell us about the data, and what each indicates about the data set. The mean receives increased emphasis in these grade levels, but students also continue to use the median, especially in creating Five-Number Summaries for making box plots.
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Consider topics of interest to students in grades 6-8 that involve collecting data about a characteristic shared by two populations. Formulate five questions that involve collecting qualitative (categorical) data and five questions that involve collecting quantitative (numerical) data. For each question, identify the type of data that will be collected and an appropriate way to display the data (e.g., line plot, bar graph, histogram, circle graph, stem and leaf plot, box plot). Note 3
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