The topic Describing distributions with center and spread appears under the 6th grade (U.S.) Math Mission. (this exercise became "Comparing the center and spread of data distributions" so was unnecessary) This exercise has several opportunities to use and better understand statistical terms that measure spread and center of distributions.
Types of Problems
There are three types of problems in this exercise:
- Compare the center and spread based on numerical summaries: This problem provides numerical summaries of the center and spread of two data sets. The student is asked to use this to determine whether one of the sets of data has more or less value and more or less variability.
- Compare the center and spread based on graphs: This problem provides graphical displays. The student is asked to use the displays to describe how the center and the spread of the two distribution would compare.
Statistical vocabulary is necessary for this exercise, while statistical calculation is not. However, knowing how to calculate various statistical measures will assist in answering questions.
- The typical measures of center are mean and median (mode does not appear).
- The typical measures of spread are mean deviation and inter-quartile range (standard deviation does not appear.
- The graphical displays can be boxplots, bar charts or dot plots.
- The spreads of graphical displays are approximately the same if there displays have a certain amount of symmetry with each other.
- The median is the center line in the boxplot and the IQR is the third line minus the first line if finding actual value is desired.