This lesson addresses what measure of variability is appropriate for a skewed data distribution. Students construct a box plot of the data using the 5-number summary and describe variability using the interquartile range.

Students will explore distributions of various census data sets to determine whether it can be reasonably assumed that those data follow a normal distribution, based on students' analysis of either a histogram or a normal probability plot for each data set. They will then discuss their findings with a partner who analyzed the other type of graph for each data set.

Website with article on what outliers are and their effect on data. Interactive practice problems are also included.

In four linked activities, students will apply their knowledge of ratios, proportions, fractions, decimals, percents, scientific notation, mean, median, mode, range, and pie graphs to interpret data and statistics regarding the U.S. government’s budget for prisons and correctional services. Then students will synthesize what they have learned and communicate it using diagrams and mathematical evidence.

The lesson prepares students for a future understanding of the standard deviation of a data set, focusing on the role of the deviations from the mean. Students practice calculating deviations from the mean and generalize their calculations by relating them to the expression ?? - ??¯. Students reflect on the relationship between the sizes of the deviations from the mean and the spread (variability) of the distribution.

In this task, students will use prior knowledge to interpret data using a histogram, and then represent the same data with a box plot. Students will discuss the shape (bimodal), center, and spread (outliers) of the data, the information highlighted or hidden by each representation, and compare two data sets using different representations. Comparing data sets is the focus of the task.

Students drop and catch a yardstick to determine if there is significant evidence (via a matched pairs randomization test) that people are faster with their dominant than their non- dominant hand.