6.DS.6c Lesson 2-9-part2 Apply Day · Set B
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2.9 · Part II

Second Practice Form · Independent Application and Spiral Review

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.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    (Lesson 2.3) Find the mean of: 10, 14, 8, 12, 16

    1. A12
    2. B14
    3. C10
    4. D60
    Put the data in order
    Work
  2. 2 MULTIPLE CHOICE

    (Lesson 2.3) Find the median of: 3, 7, 2, 9, 5

    1. A5
    2. B3
    3. C7
    4. D5.2
    Put the data in order
    Work
  3. 3 MULTIPLE CHOICE

    (Lesson 2.1) A coach asks: "How many hours does each athlete on the track team sleep the night before a meet?" Why is this a statistical question?

    1. ABecause the answers will vary from athlete to athlete
    2. BBecause it is about sports
    3. CBecause it has a numerical answer
    4. DBecause the coach asked it
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    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. C26
    4. D11
    ✏️ Workspace & Solution Steps
  5. 5 MULTIPLE CHOICE

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

    1. A3
    2. B5
    3. C15
    4. D1
    ✏️ Workspace & Solution Steps
  6. 6 MULTIPLE CHOICE

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

    1. A6
    2. B−6
    3. C46
    4. D26
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 7 OPEN RESPONSE

    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.

    ✏️ Mathematical Justification & Response
📐 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