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

Lesson 2.9Comparing Sets with MAD

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.

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 72, value 78 → 6
Absolute ValueSpanish: Valor absoluto How far a number is from zero. It is never negative. |−3| = 3 and |3| = 3 — both are 3 units from zero
SpreadSpanish: Dispersión How far apart the numbers are. Low spread: 8, 9, 10, 11 (close together). High spread: 2, 9, 10, 25 (far apart)
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 example

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

Baker A made 8, 9, 11, 12 cookies per tray. Baker B made 4, 8, 12, 16. Both means are 10. Who is steadier?

  1. A’s distances: 2, 1, 1, 2. MAD = 6 ÷ 4 = 1.5.
  2. B’s distances: 6, 2, 2, 6. MAD = 16 ÷ 4 = 4.
  3. 1.5 < 4, so Baker A is steadier.

Answer: Baker A

Say it and write itSentence starters

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

  • Both sets have a mean of .
  • The MAD of is and the MAD of is .
  • is more consistent because .
  • A larger MAD means the values .

Word bank mean absolute deviationdeviationdistancemeanspreadvariationconsistentcomparelargersmallertypicalcenter

Watch out!A 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

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

Lesson 2.9Comparing Sets with MAD

Apply Day · Version ASupported 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.

  1. 1Complete each step, then write the final answer.

    Find the MAD of this data set: 1, 4, 7.

    Show your work

    Hint The mean is 4. Find how far 1, 4 and 7 are from 4.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Find the MAD of this data set: 5, 6, 10, 11.

    Show your work

    Hint The values add to 32. Find the mean, then each distance from it.

    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the MAD of this data set: 2, 4, 4, 6.

    Show your work

    Hint The mean is 4. Two values are 0 away from it.

    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.6c

Lesson 2.9Comparing Sets with MAD

Apply Day · Version BCore 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.

  1. 1Circle the letter of the best answer. Show how you know.

    Set A is 5, 6, 7. Set B is 1, 6, 11. Both sets have a mean of 6. Which set has the greater MAD?

    1. ASet A
    2. BSet B
    3. CThey have the same MAD
    Show your work
  2. 2Complete 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:
  3. 3Complete each step, then write the final answer.

    Find the MAD of this data set: 3, 7, 8, 10.

    Show your work
    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.6c

Lesson 2.9Comparing Sets with MAD

Apply Day · ChallengeExtension

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.

  1. 1Circle the letter of the best answer. Show how you know.

    A data set is 3, 5, 9, 11 with a mean of 7. What is the mean absolute deviation?

    1. A2
    2. B3
    3. C7
    4. D28
    Put the data in order
    Work
  2. 2Complete 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:
  3. 3Complete each step, then write the final answer.

    Find the MAD of this data set: 5, 7, 8, 10, 15.

    Show your work
    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help