Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.6c

Lesson 2.92.9 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the mean absolute deviation (MAD) to describe how spread out data is, explain how I can tell, and judge a case I have not seen before.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Mean Absolute DeviationSpanish: Desviación media absoluta The average distance of data values from the mean; it describes spread. Written as MAD
DeviationSpanish: Desviación How far a number is from the mean. Mean 19, value 23 → 4
Absolute ValueSpanish: Valor absoluto How far a number is from zero. It is never negative. Distance is never below zero
SpreadSpanish: Dispersión How far apart the numbers are. Small MAD = tight set
Data distributionSpanish: Distribución de datos How the data looks: where it sits and how spread out it is. A set clustered tightly around the mean has low MAD; a set spread far from the mean has high MAD
VariabilitySpanish: Variabilidad How spread out the numbers are. Low variability (MAD = 1): very consistent. High variability (MAD = 8): very spread out

How it worksWorked examplefinding the mean absolute deviation

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Five snack prices in cents are 80, 90, 100, 110, 120. Find the mean absolute deviation.

  1. Find the mean: the five prices total 500, and sharing that evenly gives 100.
  2. Measure each price's distance from 100: 20, 10, 0, 10, 20.
  3. Add the distances. They come to 60.
  4. Share that total distance among the five prices.

Answer: The MAD is 12 cents — a typical price sits about 12 cents away from the mean.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Five backpack weights in ounces are 33, 36, 37, 38, 41. Find the MAD.

  1. Add the five weights: Mean:
  2. Distance of each weight from the mean: , , , ,
  3. Total of the distances:
  4. Share that total among the number of values. MAD: ounces
Answer:mean absolute deviation in ounces

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The mean of this set is .
  • The distance from to the mean is .
  • The distances total , and there are values.
  • The MAD is , which means .

Word bank mean absolute deviationdeviationdistanceabsolute valuemeanspreadaveragetotaldividetypicalconsistentvariation

Watch outA common mistake

A common mistake in Mean Absolute Deviation is adding the signed deviations (value − mean) instead of their absolute values, so the positives and negatives cancel out to 0. For 6, 8, 10, 12 (mean = 9), the deviations are −3, −1, 1, 3 — they sum to 0, but that is NOT the MAD. Before averaging, take the absolute value of every deviation so each becomes a positive distance: |−3| = 3, |−1| = 1, |1| = 1, |3| = 3. Sum = 8, so MAD = 8 ÷ 4 = 2. A MAD of exactly 0 is a warning sign — it only happens if every value in the data set equals the mean.

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.6c

Lesson 2.92.9 Small Group · Group 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the mean absolute deviation (MAD) to describe how spread out data is, explain how I can tell, and judge a case I have not seen before.

  1. 1Complete each step, then write the final answer.
    Team ADistance from 10Team BDistance from 10
    4691
    91111
    100100
    13382
    144122
    Team A's scores are farther from the mean.

    Team A scored 4, 9, 10, 13 and 14 goals. Team B scored 9, 11, 10, 8 and 12 goals. Both means are 10. Which team is more consistent?

    1. 1Find each distance from 10 for Team A.
    2. 2What is Team A's MAD?
    3. 3What is Team B's MAD?
    4. 4Which team is more consistent?
    Final answer:
  2. 2Complete each step, then write the final answer.
    2345678910111213
    One value is far from the others.

    Find the MAD of 3, 4, 5, 6, 12. The MAD of 3, 4, 5, 6 alone is 1. Why does 12 change it so much?

    1. 1The values add to 30. What is the mean?
    2. 2Find each distance from 6. Then find the MAD.
    3. 3Why does the value 12 make the MAD larger?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the MAD of this data set: 1.5, 2.5, 3.5, 4.5.

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Five snacks cost $2, $5, $3, $6 and $4. Find the MAD of the prices.

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    Slide heights at a water park are 60, 75, 80, 85 and 100 feet. Find the MAD of the heights.

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Kai finds the deviations of 2, 6, 7, 9 from their mean, 6. He gets −4, 0, 1 and 3. He adds them and says the MAD is 0. What is the MAD?

    Show your work
    Final answer:

Explain your thinkingTwo classes have the same mean test score. One class has a MAD of 3. The other has a MAD of 12. Which class has scores more alike? Defend it.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help