An Introduction To Mean Absolute Deviation (MAD)

An Introduction To Mean Absolute Deviation (MAD)

Which Class Did Best on the Quiz?

Opening

Which Class Did Best on the Quiz?

Look at the three line plots.

  • Working with a partner, mark the middle 50 percent of the values on each line plot.
  • Then turn to your partner and discuss the question: Which class do you think did best on the quiz?

Math Mission

Opening

Use the mean absolute deviation (MAD) to decide whether the mean of a set of data is a good representation of the data.

Which Class?

Work Time

Which Class?

To better understand whether the mean is a good representation of a data set, you can calculate a measure called the mean absolute deviation (MAD).

The MAD is a measure of how spread out the values in a data set are from the mean. The greater the MAD is, the farther away the data are, on average, from the mean.

  • Which class do you think will have the highest MAD?
  • Which class do you think will have the lowest MAD?
  • Explain your answers.

Hint:

  • Will most of the data with a low MAD be close to the mean or far away?
  • Will most of the data with a high MAD be close to the mean or far away?

Calculate the Mean Absolute Deviation

Work Time

Calculate the Mean Absolute Deviation

Follow these steps to find the MAD for each class’s line plot:

  • List the data for the class vertically.
  • Next to each score, write the distance of that score from the mean.
  • Find the mean of these distances by adding them together and dividing by the number of values.

Hint:

Remember that distances are always positive numbers.

Compare Your Prediction

Work Time

Compare Your Prediction

  • Compare your prediction of which line plots would have the highest and lowest MAD values with your actual calculations.

Prepare a Presentation

Work Time

Prepare a Presentation

Prepare a presentation that explains how to use a mean absolute deviation to analyze a set of data.

 

Challenge Problem

  • What would the line plot look like for a similar class quiz data set (12 scores with a range of 6, from 0 to 6), but with the smallest possible MAD?
  • What would the MAD be?

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about students’ reasoning about the MAD values they found.

Hint:

As your classmates present, ask questions such as:

  • How did you find the MAD for each set of data?
  • What does the MAD tell you about each set of data?
  • How did your MAD compare with your prediction?

Mean Absolute Deviation

Formative Assessment

Summary of the Math: Mean Absolute Deviation

Write a summary of what you learned about the mean absolute deviation.

Hint:

Check your summary.

  • Do you describe what the mean absolute deviation tells us about a set of data?
  • Do you explain how to calculate the MAD?

Reflect on Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use this sentence starter if you find it to be helpful.

I think the MAD is related to the mean because …