# Chapter 5: Measures of Central Tendency

## Introduction

Here's an activity that will involve all the students in your class and will also serve as a learning tool to enhance your understanding of mean, median and mode. Prior to the beginning of class, fill a pail with single, plastic interlocking blocks similar to those shown below. You and your classmates will each use only 1 hand to gather a handful of blocks from the pail.

Before you and your classmates begin to pick your handfuls of blocks, have a brain-storming discussion to reveal your knowledge of the measures of central tendency. Record the various responses and refer to these as the lessons progress.

You and your classmates can now each proceed to the pail to collect a handful of blocks. Once you have had some time to compare your handful with those of your classmates, record each of your numbers of blocks on post-it notes. The post-it notes for you and your classmates can now be placed in order on a large sheet of grid paper. The grid paper allows for repeated numbers to be posted in the same column.

What do you think you would be finding if you were to determine the mean number of blocks that had been picked from the pail? Now share your blocks with your classmates, and have your classmates do the same. so that you each have a similar number of blocks. From this sharing process, it is very likely that 2 groups of students will be created. One group will have stacks of one number of blocks, and another group will have stacks of another number of blocks. You and your classmates may come to realize that further sharing will not create stacks of the same size for each of you. Is it clearer to you now what we are talking about when we use the term mean?

Place your stacks of blocks in a safe place, for they will be used again in the discovery of the mode and the median. The numbers that were placed on the grid paper can also be used for mathematical calculations of the mean, median, and mode of your data.

## Chapter Outline

- 5.1. Mean
- 5.2. Ungrouped Data to Find the Mean
- 5.3. Grouped Data to Find the Mean
- 5.4. Median
- 5.5. Median of Large Sets of Data
- 5.6. Mode

### Chapter Summary

## Summary

This chapter covers three different measures of central tendencies, meaning where the center of a distribution is. The three measures covered - the mean, the median, and the mode - may each define a different point as the center. The **mean** is determined by dividing the sum of all values in a data set by the number of values. Three lessons cover calculating from raw values, frequency distribution tables (grouped), and frequency distribution tables (ungrouped). The **median** is the value of the middle term in a set of organized data (i.e. the raw values sorted into ordered list). The **mode** of a data set is the value or values that occur with the greatest frequency in the data set.