Measures of Central Tendency

Big Ideas / Questions
  • Do students understand that a measure of center is a single value used to describe an entire population?
  • When is it better to report the mean, median, mode or midrange to represent the average or typical value in a data set?

What is Typical for this Group of Cats? - Key Curriculum Press: Center Clumps
This activity is used to shift the focus from thinking about individual cases (cats) to thinking about the entire group. Students look at a distribution to find a typical body length for a group of 100 cats. Try the student activity in TinkerPlots and then read the teacher notes.

Tall Buildings
The activity was written by Todd Lunsford while he was a junior at Ball State University. Todd uses dividers and measurement tools to answer questions about the Tall Building data set. For example, How many buildings are higher/lower than the mean height? And How many buildings are higher/lower than the median height? The original activity was revised and moved to CODAP. Questions and solutions are on this wiki.

Scooters - Key Curriculum Press: How do Outliers Affect the Mean and Median?
In this activity, students learn that the median is a good choice for describing what is typical for data sets with extreme values. Try the activity in TinkerPlots and then read the teacher notes.

Midrange Exploration
The midrange is the average of the highest and lowest values in a data set. The mean, median and midrange are represented in a dot plot by vertical lines. Try to identify the lines by dragging dots in the dot plot. Then, try to position the measures of center in a specific order (mean, median, midrange), if possible. The dot plot was created in Desmos and then embedded into this wiki.

Behaviors of the mean and median - CODAP
This brief activity found on the CODAP site involves dragging points in a dot plot to explore the effect on the mean and median. The small data set includes 10 points and the large data set includes 100 points.

Mystery Mixer Activity - (Key Curriculum Press) TinkerPlots files and CODAP
This activity provides an introduction to distributions created by random sampling from a population of 500 integers. Mystery Mixers introduces the idea of the center "clump" as students estimate the mean of a sample. The sample size is generated by the student and the hat plot is encouraged as a tool to describe the center clump.

Each of the activities in this module address parts of the CCSS Grade 6 >> Statistics and Probability Standards.