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 calculate standard deviation for the first time and examine the process for its calculation more closely. Through questioning and discussion, students link each step in the process to its meaning in the context of the problem and explore the many questions about the rationale behind the development of the formula.

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.

This lesson unit is intended to help teachers assess how well students are able to interpret data using frequency graphs and box plots. In particular this unit aims to identify and help students who have difficulty figuring out the data points and spread of data from frequency graphs and box plots. It is advisable to use the lesson: Representing Data 1: Frequency Graphs, before this one.

iframe embedded Scientific Calculator Web 2.0 Calc, with fill in the blank questions for practice.

In this Khan Academy activity, students will find the standard deviation of a set of numbers in a word problem.

In this graph project students will create a statistical question, gather, analyze, and graph data either by hand or using technology.

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.