6.DS.6c Lesson 2-9-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.9 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Visual Models · Mean Absolute Deviation · Deviation · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What is the mean absolute deviation (MAD)?
1MAD = the average of how far each number is from the mean (always a positive distance).
  • 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. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me
  1. My data set: 6, 8, 10, 12. First I find the mean: 6 + 8 + 10 + 12 = 36, then 36 ÷ 4 = 9. The mean is 9.
  2. Next I find each deviation (value − mean): 6−9 = −3, 8−9 = −1, 10−9 = 1, 12−9 = 3.
  3. Then I take the absolute value of each (the distance, always positive): 3, 1, 1, 3.
  4. Finally I average those distances: 3 + 1 + 1 + 3 = 8, then 8 ÷ 4 = 2. So the MAD = 2 points.
3Mathematical Word Bank
  • Mean Absolute Deviation (Desviación media absoluta) — The average distance of data values from the mean; it describes spread.
  • Deviation (Desviación) — How far a number is from the mean.
  • Absolute Value (Valor absoluto) — How far a number is from zero. It is never negative.
  • Spread (Dispersión) — How far apart the numbers are.
  • Data distribution (Distribución de datos) — How the data looks: where it sits and how spread out it is.
  • Variability (Variabilidad) — How spread out the numbers are.
4Watch out
  • 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.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    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 A — lower MAD means more consistent times
    2. BRunner B — higher MAD means faster potential
    3. CEither — they have the same average
    4. DNeither — MAD doesn't matter for relay races
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    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
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  3. 3 MULTIPLE CHOICE

    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 A, because a smaller MAD means scores stay closer to the average
    2. BShooter B, because a bigger MAD means a bigger average
    3. CThey are equally consistent because they have the same mean
    4. DYou cannot tell consistency from MAD
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Data set:A 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 MAD:MAD = (−2 + 2 + 0) ÷ 3 = 0 ÷ 3 = 0

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Level 2 Extension — The Deviations That Vanished

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

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find the MAD Error

    1. 1Data set:5, 10, 15, 20, 25
    2. 2Find mean:Sum = 75, Count = 5, Mean = 15
    3. 3Find deviations:−10, −5, 0, 5, 10
    4. 4Find MAD:MAD = (−10 + −5 + 0 + 5 + 10) ÷ 5 = 0

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It