This lesson is a good opportunity for students to use the information they have learned in the unit and apply it to different situations, but may be shortened to fit time constraints.
In this lesson, students compare the center and spread of different distributions. They determine what these different measures (mean and MAD or median and IQR) represent in context. They select an appropriate representation for the distribution based on the structure of the data, an appropriate set of measures of center and spread, and interpret their meaning in the context (MP4).
For students who are curious why we are asking them to compute measures of center and variation by hand when computers would be more efficient and accurate, tell them that understanding the meaning of the values and knowing what questions to ask are skills computers have not yet mastered. By practicing with calculations on small data sets, students are becoming familiar with these measures as well as questioning skills so they can correctly interpret results from computers in the future. If students do not raise the question themselves, this point may be left until the topics are revisited in later grades.
- Recognize that different graphical displays offer different insights into a distribution. Choose an appropriate graphical display to represent a data set, and justify the choice (orally and in writing).
- Recognize that different measures of center and variability offer different insights into a data set. Choose an appropriate measure of center and variability to describe a data set, and justify the choice (orally and in writing).
Let's compare data sets using visual displays.
Provide access to straightedges for students to use when drawing box plots. Preview the background information about the yellow perch fish for the main activity. Prepare tools for creating a visual display, one set for every 3–4 students.
- I can decide whether mean and MAD or median and IQR would be more appropriate for describing the center and spread of a data set.
- I can draw an appropriate graphical representation for a set of data.
- I can explain what the mean and MAD or the median and IQR tell us in the context of a situation and use them to answer questions.