In module 6, students begin to think and reason statistically. They identify statistical questions and represent data distributions by using dot plots, histograms, relative frequency histograms, and box plots. Students describe the center, spread, and shape of a data distribution. They calculate and interpret measures of center and spread including mean, mean absolute deviation, median, and interquartile range, and they use these measures to describe the typical value and variability of a data distribution. At the end of the module, students complete a project where they develop a statistical question, implement a plan to collect data, analyze and interpret the data they collect, and present their findings to their peers.
In topic A, students begin to think and reason statistically. They recognize a statistical question as one that can be answered by collecting data values that can vary. They also learn that they can describe a data distribution by describing the center, spread, and shape. In this topic and throughout the module, students visualize and represent data distributions by using dot plots, histograms, and relative frequency histograms.
In topic B, students study the mean as a measure of center. They explore the mean as the value of one equal share and then as the balance point of a data distribution. This allows students to calculate the mean from a data set or to estimate the location of the mean in a data display. Students later discover that the mean alone is not sufficient to describe a data distribution. Building upon their experiences finding the balance point of a distribution, students find the mean absolute deviation as a measure of variability.
In topic C, students continue to find numerical summaries of data distributions. After seeing that the mean does not seem to represent a typical value in a distribution that is skewed, students find that they need other measures of center and spread. They calculate the median as a measure of center and the interquartile range as a measure of variability. Students also find the five-number summaries of data distributions and use these values to create box plots. Students interpret these values in context and use the interpretations to help them compare data distributions represented in box plots.
In topic D, students synthesize what they have learned and revisit measures of center and variability more deeply. This includes selecting measures of center and variability based on the context and shape of a data distribution. Then, through a project, students implement the four-step investigative process. They develop a statistical question and then create and use a plan to collect data. The topic culminates with students analyzing the data by creating data displays and calculating numerical summaries. They interpret their results to answer a statistical question and present their findings to their peers.