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

Lesson 2.9Describe Data by Mean Absolute Deviation

Set B · Version ASecond form · supported 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?

RememberDescribe Data by Mean Absolute Deviation

Mean Absolute Deviation (MAD). Formula: MAD = (Sum of distances from mean) ÷ (Total count) The mean absolute deviation, or MAD, is the average distance of each value from the mean. It tells you how spread out the data is: a small MAD means the data is close together, and a large MAD means it is spread out.

  1. Calculate the mean of the data set.
  2. Find the distance (absolute difference |value − mean|) for each data point.
  3. Average the distances: Add all distances and divide by the count

Words: Mean Absolute Deviation (Desviación media absoluta)Deviation (Desviación)Absolute Value (Valor absoluto)Spread (Dispersión)Data distribution (Distribución de datos)

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    Two soccer goalkeepers track goals allowed per game over 6 games. Keeper A: 1, 2, 1, 3, 2, 1 (mean = 1.67, MAD ≈ 0.67). Keeper B: 0, 4, 1, 3, 0, 2 (mean = 1.67, MAD ≈ 1.33). The coach needs to pick a starter for the championship game. What does a smaller MAD tell you?

    1. AThe values stay closer to the mean — the keeper is more consistent
    2. BThe keeper allowed fewer goals overall
    3. CThe keeper played fewer games
    4. DThe values are all close to zero
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Find the mean of 10, 14, 8, 12 and 16.

    1. A10
    2. B12
    3. C14
    4. D60
    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  2. 3Circle the letter of the best answer. Show how you know.

    Four friends have 6, 9, 4 and 5 stickers. If they share them equally, how many does each get?

    1. A4
    2. B5
    3. C6
    4. D24
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    A student's first three quiz scores are 82, 90 and 86. What score on a fourth quiz gives a mean of 87?

    1. A86
    2. B88
    3. C90
    4. D92
    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  4. 5Circle the letter of the best answer. Show how you know.

    The mean is called the balance point because…

    1. Ait is always the middle value in order
    2. Bthe amounts above it and below it balance out
    3. Cit is the most common value
    4. Dit is always the largest value
    Show your work
  5. 6Circle the letter of the best answer. Show how you know.

    Two soccer goalkeepers track goals allowed per game over 6 games. Keeper A: 1, 2, 1, 3, 2, 1 (mean = 1.67, MAD ≈ 0.67). Keeper B: 0, 4, 1, 3, 0, 2 (mean = 1.67, MAD ≈ 1.33). The coach needs to pick a starter for the championship game. What is each keeper's mean goals allowed per game?

    1. Aabout 1.67
    2. B2
    3. C6
    4. D10
    Show your work

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

Set B · Version BSecond form · core 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. 1Write the letter of the matching item on each line.

    Each player's points are listed. Match each player's data set to its correct MAD. (Hint: find the mean first, then average the distances.)

    1. Bench: 8, 10, 12, 14
    2. Rookie: 4, 4, 4, 4
    3. Starter: 5, 15, 5, 15
    • AMAD = 2 points
    • BMAD = 0 points
    • CMAD = 5 points
  2. 2Write the name of the correct group on each line.

    Coach is sorting players by consistency. Drag each player's MAD into the bucket that describes their scoring.

    Groups: More consistent (small MAD) Less consistent (large MAD)
    • Player with MAD = 1 point
    • Player with MAD = 0 points
    • Player with MAD = 9 points
    • Player with MAD = 12 points
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    Two soccer goalkeepers track goals allowed per game over 6 games. Keeper A: 1, 2, 1, 3, 2, 1 (mean = 1.67, MAD ≈ 0.67). Keeper B: 0, 4, 1, 3, 0, 2 (mean = 1.67, MAD ≈ 1.33). The coach needs to pick a starter for the championship game. Which keeper should the coach start, and why?

    1. AKeeper B, because two shutouts is best
    2. BEither one, because the means are equal
    3. CKeeper A, because the smaller MAD (0.67) means more consistent performance
    4. DKeeper B, because a larger MAD means more skill
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    A guard scored 2, 4, 6, 8 points in four scrimmages, so the mean is 5 points. The distances from the mean are 3, 1, 1, 3. What is the mean absolute deviation (MAD)?

    1. A1
    2. B2
    3. C5
    4. D8
    Put the data in order
    Work
  3. 5Circle the letter of the best answer. Show how you know.

    Two shooters average 11 points a game. Shooter A's MAD is 2 points and Shooter B's MAD is 6 points. Which shooter is MORE consistent?

    1. AShooter B, because a bigger MAD means a bigger average
    2. BThey are equally consistent because they have the same mean
    3. CShooter A, because a smaller MAD means scores stay closer to the average
    4. DYou cannot tell consistency from MAD
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Level 2 Extension — The Deviations That Vanished

    1. 1Data setA center's rebounds: 3, 7, 11, 15, 19
    2. 2Find the meanSum = 55, Count = 5, Mean = 55 ÷ 5 = 11
    3. 3Find each deviation (value − mean)−8, −4, 0, 4, 8
    4. 4Find the MADMAD = (−8 + −4 + 0 + 4 + 8) ÷ 5 = 0 ÷ 5 = 0

    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