Authentic Learning Task (ALT) #1: Measures of Central Tendency

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Overview

In this Authentic Learning Task (ALT), you learn about the measures of central tendency: the mean, median, and mode. You also describe the differences between these measures when analyzing data sets. While you probably already have encountered and know how to calculate or find the mean, median, and mode, in this ALT you apply these measures to data sets and demonstrate your understanding of the significance of the resulting analysis.

After completing this ALT, you should be able to demonstrate the following competencies:

• Collect, process, and display data so that usable information is represented (Comp. 1).
• Make inferences based on data analysis
  (Comp. 3).
• Apply measure of central tendency and variability (Comp. 4).
• Describe in general terms the normal curve and use its properties to make conjectures about sets of data that are normally distributed (Comp. 6).

Materials and Equipment
1 graphing calculator, such as model TI-82, TI-85, or TI-86

Safety and Disposal
No special safety and disposal procedures are required.

Pre-Activity

As you will see in your study of statistics, there are a large number of measurements that you can make on any given set. However, most of these measurements measure one of two characteristics: the variability of the data or its central tendency.

A measure of central tendency on a data set will measure the data's tendency to cluster or center about a certain numerical value. A measure of variability on a data set will measure how much the data is spread out.

In this ALT, we will consider three common measures of central tendency: the mean, median, and mode. We will learn how to calculate these measures and what they can tell us about a data set.

To prepare for the activity:

• Read Information Sheet: Measures of Central Tendency in your Basic Statistical Variation Participant Journal.
• Read more about central tendency and mean, median, and mode.
• Complete a sports statistics activity to practice what you have learned.

Activity

In your team, perform the following steps to complete the activity:

1. Complete Data Sheet: Measures of Central Tendency.

Post-Activity

Your team should now post all of its results recorded on Data Sheet: Measures of Central Tendency to the discussion board.

Assignment
To prepare for ALT #2: Measures of Variability, read Information Sheet: Measures of Variability in your Basic Statistical Variation Participant Journal.

Assessment
Your facilitator may use Assessment Sheet: Measures of Central Tendency from your Basic Statistical Variation Participant Journal to evaluate your results from the activity and your posting to the Discussion Board.

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