The mathematical purpose of this lesson is for students to compare measures of center and the standard deviation and the IQR for different data sets. This lesson provides opportunities for students to collaborate, share mathematical ideas and reflect on their mathematical thinking about measures of center and measures of variability. This lesson also gives students another opportunity to compare measures of center and variability, but now using standard deviation and outliers too in the comparisons. The work of this lesson connects to upcoming work because students will collect and analyze data to answer a statistical question using measures of center and measures of variability. When students are describing measures of center and measures of variability in the context of marathon time they are reasoning abstractly and quantitatively (MP2) because they are interpreting the meaning of their answer in context.
- Compare and contrast (orally and in writing) situations using measures of center and measures of variability.
- Let’s compare statistics for data sets.
- I can compare and contrast situations using measures of center and measures of variability.
A data value that is unusual in that it differs quite a bit from the other values in the data set. In the box plot shown, the minimum, 0, and the maximum, 44, are both outliers.
A measure of the variability, or spread, of a distribution, calculated by a method similar to the method for calculating the MAD (mean absolute deviation). The exact method is studied in more advanced courses.
A quantity that is calculated from sample data, such as mean, median, or MAD (mean absolute deviation).