Explain Measures of Center

Getting Started

The student is unable to identify key measures of center.

The student:

• Does not identify both mean and median.
  
  
  
  
• Includes measures that do not describe central tendency (e.g., range).
  
  

Are there any more measures of center you may have left out?

Do all of these describe the center of a distribution?

Review the vocabulary used to describe measures of center and variability. Clearly distinguish the two types of measures. Explain that both are used to summarize a distribution of values, but they do so in different ways.

Explain that measures of center provide an indication of a typical, representative, or summary value from a set of data. Review how each of the mean, median, and mode are calculated and explain how each describes or represents a typical value. Explain that each measure describes the center of a distribution in a different way, and the choice of one over the other is often based on the shape or context of the distribution. Indicate that the usefulness of a measure of center is enhanced by pairing it with a measure of variation that can describe how spread out the data are. Indicate that although data will vary around the measure of center, these measures are an integral part of a summary of a set of data.

Provide data sets with different centers (e.g., a set of math pretest scores that range from 0% to 73% and a set of math posttest scores that range from 78% to 100%). Have the student compare the data sets by calculating a measure of center. Assist the student in interpreting each measure of center in relationship to its data set.

Provide opportunities to describe and summarize distributions of data by calculating measures of center and spread. Assist the student in identifying and describing the limitations of using measures of center alone to understand a single data set or to compare two data sets.

Making Progress

The student is unable to explain what measures of center tell you about a set of data.

The student:

• Describes calculation procedures for measures of center or provides an example calculation.
• Provides a superficial or circular response (e.g., median is the middle and mean is the average).
  
  

In general, what does a measure of center tell you about a set of data?

You did a good job explaining how to calculate the mean and median, but what do these values indicate about a set of data? How do they give you information about a set of data?

Explain that measures of center provide an indication of a typical, representative, or summary value from a set of data. Review how each of the mean, median, and mode are calculated and explain how each describes or represents a typical value. Explain that each measure describes the center of a distribution in a different way, and the choice of one over the other is often based on the shape or context of the distribution. Indicate that the usefulness of a measure of center is enhanced by pairing it with a measure of variation that can describe how spread out the data are. Indicate that although data will vary around the measure of center, these measures are an integral part of a summary of a set of data.

Provide opportunities to describe and summarize distributions of data by calculating measures of center and spread. Assist the student in identifying and describing the limitations of using measures of center alone to understand a single data set or to compare two data sets.

Got It

The student provides complete and correct responses to all components of the task.

The student identifies the mean and median (and possibly the mode) without listing measures that do not describe central tendency.

The student:

• Is able to explain that measures of center provide an indication of a typical or representative value from a set of data.
  
  
  
  
• Demonstrates a general understanding of measures of center by describing the significance of both mean and median individually.
  
  

What is the difference between mean and median?

Do measures of center give you a good overall picture of a distribution? Is there any other information that would give you a better understanding of the data set?

Challenge the student to create small data sets with the same mean but different medians. Ask the student to describe differences in the data sets in terms of the shapes of their distributions.

Review considerations in choosing a measure of center. Provide the student with sample distributions, and ask him or her to describe the differences between mean and median for each distribution. Challenge the student to choose the best measure of center to represent each distribution and provide an explanation for the choice.

Consider implementing MFAS task Compare Measures of Center and Variability.