6.DS.6c Lesson 2-9-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.9 · Part II

Supported Application · Guided Entry to Today's Problem

Mean Absolute Deviation · Deviation

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 2.9 · Part II
1Mean Absolute Deviation (MAD)
2Strategy Model — step by step
  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
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.
  1. 1 MULTIPLE CHOICE

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

    1. ATeam A — lower MAD means scores are closer to the mean
    2. BTeam B — higher MAD means better performance
    3. CBoth are equally consistent
    4. DCannot tell from MAD alone
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    (Lesson 2.1) Which of the following is a statistical question?

    1. AHow many points did each player score this season?
    2. BHow many points are scored for a free throw?
    3. CWhat sport does this team play?
    4. DHow many halves are in a soccer game?
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    (Lesson 2.1) Which question is NOT a statistical question?

    1. AHow many innings are in a baseball game?
    2. BHow many home runs did each player hit this year?
    3. CHow many miles does each runner train per week?
    4. DHow tall is each player on the basketball team?
    ✏️ Workspace & Solution Steps
📐 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
6.DS.6c Lesson 2-9-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.9 · Part II

On-Level Application · Standard Rigor

Mean Absolute Deviation · Deviation

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 2.9 · Part II
1Mean Absolute Deviation (MAD)
2The Structural Procedure
  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
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.
  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
  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
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

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

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It
6.DS.6c Lesson 2-9-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.9 · Part II

Extension & Non-Routine Application

Mean Absolute Deviation · Deviation

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 2.9 · Part II
1Mean Absolute Deviation (MAD)
2The Structural Procedure
  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
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.
  1. 1 MULTIPLE CHOICE

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

    1. A3
    2. B7
    3. C28
    4. D2
    Put the data in order
    Work
  2. 2 MULTIPLE CHOICE

    Claim: “A data set's MAD can equal 0.” Always, sometimes, or never true — and when?

    1. ASometimes — exactly when every value in the set is identical
    2. BNever — absolute values are always positive, so their average is too
    3. CAlways — every data set has SOME value equal to its mean
    4. DSometimes — whenever the mean happens to be 0
    ✏️ Workspace & Solution Steps
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

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

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It