In this unit, students collect, display, and analyze data using statistics, such as mean, median, interquartile range, and standard deviation.
In grades 6–8, students used histograms, dot plots, and box plots as a way to summarize data and worked with basic measures of center (mean and median) as well as measures of variability (mean absolute deviation and interquartile range). These concepts are revisited in the first two sections of this unit, but with a focus on interpretation and what they reveal about the data in addition to the mechanics of constructing the data displays.
The optional third section is available to familiarize students with spreadsheets and technology that will be used to calculate statistics, such as mean, median, quartiles, and standard deviation, as well as create data displays.
The fourth section introduces additional ways to interpret data using standard deviation and outliers. Students finish the unit by using these tools to compare related data sets using measures of center and measures of variability.
The last lesson gives students a chance to practice their skills by posing a statistical question, designing an experiment, collecting data, and analyzing their data.
Because the first half of the unit mostly revisits material from middle school, a Mid-Unit Assessment is not included in this unit. The Cool-downs and Checkpoints can be used to monitor student understanding.
In this unit, only the population standard deviation is used. Sample standard deviation is introduced in a later course.
GeoGebra’s spreadsheets are chosen for their versatility for the on-level mathematics in this course. While other spreadsheet programs have additional functionality and uses, they are limited in other ways. That said, please adapt the materials to the needs of your students.
Create and interpret data displays such as dot plots, histograms, and box plots.
Section Narrative
In this section, students continue to build community by collecting data from their classmates, classifying the different kinds of data they might collect, and creating displays of the information that they collected.
The optional second lesson gives students a chance to practice creating dot plots, histograms, and box plots using given data before attempting to do the same with the data that they collected. This lesson would be an opportunity to introduce any technological tools the class will use for creating these displays.
Describe the shape of a distribution, including a measure of center and a measure of variability.
Section Narrative
Students work to describe distributions of data using terms such as “symmetric,” “skewed,” “uniform,” “bimodal,” and “bell-shaped.”
An optional lesson is included to remind students of prior learning about measures of center and measures of variation so that those terms can be included in distribution descriptions. Even if the optional lesson is skipped, consider creating a display about the measures of center and variability, like the one mentioned in a Synthesis of this lesson.
Use a spreadsheet as a tool for calculating values quickly.
Section Narrative
In this optional section students are introduced to using spreadsheets to create basic formulas and interpret results. It is assumed that students know nothing about spreadsheets. If students are proficient at using spreadsheets as computation tools, this sequence of lessons can be safely skipped. This technology is useful for interpreting data in this unit and is also used to examine functions in a subsequent unit.
Because this entire section is optional, no checkpoint questions are included.
Describe the effect of outliers on a distribution of data.
Recognize standard deviation as a measure of variability.
Section Narrative
In this section, students are introduced to additional tools to analyze data such as standard deviation and outliers. They finish the section by using all of these tools to compare similar data sets.
Note that in this unit, all standard deviations refer to the population standard deviation () calculation rather than the sample standard deviation ().
If students are using GeoGebra or the Spreadsheet tool in Math Tools to create a histogram, there is an issue when the maximum value is on the boundary of the greatest interval. In this case, GeoGebra includes the maximum value with the previous interval rather than following the convention of creating a new bar for the next interval. Address this issue with students if they are using either of those tools.
mean: 44.8 feet, standard deviation: 4.72 feet
Dot plot from 30 to 75 by 1's. Tree height in forest A in feet. Beginning at 30, number of dots above each increment is 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 4, 3, 4, 3, 3, 3, 2, 2, 2, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.
The final section of this unit is a lesson where students have the opportunity to apply their thinking from throughout the unit. As this is a short section followed by an End-of-Unit Assessment, there are no section goals or checkpoint questions.