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

Lesson 2.9Describe Data by Mean Absolute Deviation

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.

Why This Matters The forecast shows the expected high temperatures for a week. The mean high temperature for the week is 79°F. How can you describe the variation in high temperatures over the week?

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 example

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

Four plants grew 3, 7, 8 and 10 cm. Find the MAD.

  1. Mean: 28 ÷ 4 = 7.
  2. Distances from 7: 4, 0, 1, 3.
  3. Sum = 8, and 8 ÷ 4 = 2.

Answer: MAD = 2 cm

Now you trySame steps, your turn

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

New data set: 9, 10, 11. First, what is the mean? Add the three numbers and divide by 3.

Answer:

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 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 2.9Describe Data by Mean Absolute Deviation

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.

Why This Matters The forecast shows the expected high temperatures for a week. The mean high temperature for the week is 79°F. How can you describe the variation in high temperatures over the week?

Part 1Understand the ideamodels and meaning
  1. 1Mark and label each value on the number line.

    The mean is 10. Place each data value on the number line, then find how far each is from the mean: Data: 7, 10, 13.

    56789101112131415

    Hint 7 is 3 units below the mean. 10 is exactly at the mean. 13 is 3 units above the mean.

    Show your thinking
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    The mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?

    1. A4
    2. B−4
    3. C11
    4. D26

    Hint Absolute deviation asks: how FAR is the value 11 from the mean of 15? A distance is never negative; zero is allowed.

    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    A data set has absolute deviations of 3, 1, 5, 2, 4. What is the MAD?

    1. A1
    2. B3
    3. C5
    4. D15

    Hint You're given the five absolute deviations already — no subtracting needed. MAD is their average.

    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    The mean of a data set is 20. A value is 26. What is the absolute deviation?

    1. A6
    2. B−6
    3. C26
    4. D46

    Hint Same skill as before: absolute deviation is the distance between the value 26 and the mean 20.

    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    Team A has MAD = 2.1 points. Team B has MAD = 6.8 points. Which team is more consistent?

    1. ATeam B — higher MAD means better performance
    2. BBoth are equally consistent
    3. CCannot tell from MAD alone
    4. DTeam A — lower MAD means scores are closer to the mean

    Hint Consistent means scores stay close to the team's average game after game. MAD measures exactly that closeness.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Data setA player's points: 6, 10, 8. Mean = (6 + 10 + 8) ÷ 3 = 8.
    2. 2Find each deviation (value − mean)6 − 8 = −2, 10 − 8 = 2, 8 − 8 = 0
    3. 3Find the MADMAD = (−2 + 2 + 0) ÷ 3 = 0 ÷ 3 = 0

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint The deviations −2 and 2 cancel to 0 — that's the warning sign. MAD is never 0 unless every value equals the mean.

    Correct work
    Correct answer:

Explain your thinkingPlayer A's MAD is 2.4 points. If Player B's MAD is 7.2 points, what does that tell you about their consistency?

Sentence starter Player A has a ___ MAD, which means their scores are ___ to the mean. Player B has a ___ MAD, which means their scores are ___ from the mean. The more consistent player is ___ because ___.

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 2.9Describe Data by Mean Absolute Deviation

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.

Why This Matters The forecast shows the expected high temperatures for a week. The mean high temperature for the week is 79°F. How can you describe the variation in high temperatures over the week?

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Deviation Detective: the quiz scores are 12, 8, 10, 14, 6 and the mean is 10. Complete each deviation and absolute deviation, then compute the MAD.

    ScoreDeviation (Score − Mean)Absolute Deviation
    12
    8
    10
    14
    6
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match each MAD value to what it tells you about the data.

    1. MAD = 1.5
    2. MAD = 8.0
    3. MAD = 0
    4. MAD = 4.2
    • AVery consistent data
    • BVery spread out data
    • CAll values are identical
    • DModerate spread
  3. 3Write the name of the correct group on each line.

    Rank from least to most spread out.

    Groups: Least to most spread out
    • Set A: 9, 10, 10, 11 (MAD ≈ 0.5)
    • Set B: 5, 10, 10, 15 (MAD = 2.5)
    • Set C: 1, 10, 10, 19 (MAD = 4.5)
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    Two runners have the same average time of 60 seconds. Runner A's MAD is 1.2 seconds. Runner B's MAD is 5.8 seconds. Which runner is the coach more likely to pick for a relay race that needs a reliable time?

    1. ARunner B — higher MAD means faster potential
    2. BEither — they have the same average
    3. CRunner A — lower MAD means more consistent times
    4. DNeither — MAD doesn't matter for relay races
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Data setA swimmer's lap times: 2, 5, 8, 9. Mean = (2 + 5 + 8 + 9) ÷ 4 = 24 ÷ 4 = 6.
    2. 2Find each absolute deviation|2 − 6| = 4, |5 − 6| = 1, |8 − 6| = 2, |9 − 6| = 3
    3. 3Find the MADSum of absolute deviations = 4 + 1 + 2 + 3 = 10. MAD = 10 ÷ 3 ≈ 3.33

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingPlayer A's MAD is 2.4 points. If Player B's MAD is 7.2 points, what does that tell you about their consistency?

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 2.9Describe Data by Mean Absolute Deviation

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.

Why This Matters The forecast shows the expected high temperatures for a week. The mean high temperature for the week is 79°F. How can you describe the variation in high temperatures over the week?

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Sort each scenario by whether low or high variability is desirable.

    Groups: Want LOW MAD (consistent) Want HIGH MAD (lots of spread)
    • A factory making bolts that must be exactly 5 cm long
    • A bus schedule where arrival times should be reliable
    • A game show where contestants try to score as many different point values as possible
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the MAD Error

    1. 1Data set5, 10, 15, 20, 25
    2. 2Find meanSum = 75, Count = 5, Mean = 15
    3. 3Find deviations−10, −5, 0, 5, 10
    4. 4Find MADMAD = (−10 + −5 + 0 + 5 + 10) ÷ 5 = 0

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    Two basketball teams both average 75 points per game. Team A's last 5 scores: 73, 76, 74, 77, 75. Team B's last 5 scores: 60, 90, 65, 85, 75. Calculate the MAD for each team and explain which team a coach would prefer if they need predictable scoring.

    Write your answer

Explain your thinkingPlayer A's MAD is 2.4 points. If Player B's MAD is 7.2 points, what does that tell you about their consistency?

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