6.DS.6d Lesson 2-10-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.10 · Part II

Supported Application · Guided Entry to Today's Problem

Appropriate Measures of Center · Mean

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 2.10 · Part II
1Choosing Appropriate Measures of Center & Spread
2Strategy Model — step by step
  1. Symmetric Data (No Outliers): Use Mean and MAD
  2. Skewed Data (Has Outliers): Use Median and IQR (outliers distort the mean)
  3. Compare distributions using both center (typical value) and spread (variability)
3Mathematical Word Bank
  • Appropriate Measures of Center (Medidas de centro apropiadas) — A mean, median, or mode chosen because it describes a data set fairly.
  • Mean (Media) — The average. Add all the numbers, then divide by how many there are.
  • Median (Mediana) — The middle number when you put them in order.
  • Outlier (Valor atípico) — A number that is much bigger or smaller than the rest.
  • Skewed (Sesgado) — When most data sits on one side with a tail on the other.
  • Data distribution (Distribución de datos) — How the data looks: where it sits and how spread out it is.
4Watch out
  • A common mistake in Appropriate Measures is defaulting to the mean just because "it uses all the data," without first checking whether an outlier or skewed shape is present. For example, given a player's points per game 14, 16, 15, 17, 16, 58, a student calculates the mean (136 ÷ 6 ≈ 22.7) and reports that as the typical game — but 58 is far from the cluster of 14–17, so it pulls the mean above 5 of the 6 games. The median (16) actually represents a typical game here. Before choosing a measure, always scan the data for an outlier or a long tail first: only use the mean once you've confirmed the data has neither.
  1. 1 MATCHING

    Match each data description with the best measure of center.

    1. Test scores: 88, 90, 85, 92, 87 (no outliers)
    2. Salaries: $30K, $32K, $35K, $31K, $250K
    3. Race times: 12.1s, 12.3s, 12.0s, 12.2s, 12.1s
    4. Goals scored: 1, 2, 1, 0, 2, 1, 15
    • AMean
    • BMedian
    • CMean
    • DMedian
📐 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.6d Lesson 2-10-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.10 · Part II

On-Level Application · Standard Rigor

Appropriate Measures of Center · Mean

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 2.10 · Part II
1Choosing Appropriate Measures of Center & Spread
2The Structural Procedure
  1. Symmetric Data (No Outliers): Use Mean and MAD
  2. Skewed Data (Has Outliers): Use Median and IQR (outliers distort the mean)
  3. Compare distributions using both center (typical value) and spread (variability)
3Mathematical Word Bank
  • Appropriate Measures of Center (Medidas de centro apropiadas) — A mean, median, or mode chosen because it describes a data set fairly.
  • Mean (Media) — The average. Add all the numbers, then divide by how many there are.
  • Median (Mediana) — The middle number when you put them in order.
  • Outlier (Valor atípico) — A number that is much bigger or smaller than the rest.
  • Skewed (Sesgado) — When most data sits on one side with a tail on the other.
  • Data distribution (Distribución de datos) — How the data looks: where it sits and how spread out it is.
4Watch out
  • A common mistake in Appropriate Measures is defaulting to the mean just because "it uses all the data," without first checking whether an outlier or skewed shape is present. For example, given a player's points per game 14, 16, 15, 17, 16, 58, a student calculates the mean (136 ÷ 6 ≈ 22.7) and reports that as the typical game — but 58 is far from the cluster of 14–17, so it pulls the mean above 5 of the 6 games. The median (16) actually represents a typical game here. Before choosing a measure, always scan the data for an outlier or a long tail first: only use the mean once you've confirmed the data has neither.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MATCHING

    Match the reason with whether to use mean or median.

    1. Data is symmetric and has no extreme values
    2. Data has one or more outliers
    3. Data is skewed to one side
    4. All values are clustered close together
    • AUse Mean
    • BUse Median
    • CUse Median
    • DUse Mean
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    A baseball player's batting averages over 6 seasons are: .280, .295, .290, .285, .300, .110. The .110 was an injury-shortened season. Which measure better represents the player's typical batting average?

    1. AMedian, because the .110 outlier pulls the mean down
    2. BMean, because it uses all the data
    3. CMean, because .110 is a real season
    4. DNeither measure works
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    A scout records points per game: 14, 16, 15, 17, 16, 58. To report a TYPICAL game, which measure of center is best?

    1. AMedian, because 58 is an outlier that pulls the mean up
    2. BMean, because it uses every game
    3. CRange, because it shows the highest game
    4. DMode, because 16 appears twice
    ✏️ 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.6d Lesson 2-10-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.10 · Part II

Extension & Non-Routine Application

Appropriate Measures of Center · Mean

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 2.10 · Part II
1Choosing Appropriate Measures of Center & Spread
2The Structural Procedure
  1. Symmetric Data (No Outliers): Use Mean and MAD
  2. Skewed Data (Has Outliers): Use Median and IQR (outliers distort the mean)
  3. Compare distributions using both center (typical value) and spread (variability)
3Mathematical Word Bank
  • Appropriate Measures of Center (Medidas de centro apropiadas) — A mean, median, or mode chosen because it describes a data set fairly.
  • Mean (Media) — The average. Add all the numbers, then divide by how many there are.
  • Median (Mediana) — The middle number when you put them in order.
  • Outlier (Valor atípico) — A number that is much bigger or smaller than the rest.
  • Skewed (Sesgado) — When most data sits on one side with a tail on the other.
  • Data distribution (Distribución de datos) — How the data looks: where it sits and how spread out it is.
4Watch out
  • A common mistake in Appropriate Measures is defaulting to the mean just because "it uses all the data," without first checking whether an outlier or skewed shape is present. For example, given a player's points per game 14, 16, 15, 17, 16, 58, a student calculates the mean (136 ÷ 6 ≈ 22.7) and reports that as the typical game — but 58 is far from the cluster of 14–17, so it pulls the mean above 5 of the 6 games. The median (16) actually represents a typical game here. Before choosing a measure, always scan the data for an outlier or a long tail first: only use the mean once you've confirmed the data has neither.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A data set of house prices contains one mansion worth far more than every other home. Which pair of measures best describes this data?

    1. AMedian and IQR
    2. BMean and MAD
    3. CMean and range
    4. DMode and range
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    A local newspaper reports that the average home price in a neighborhood is $450,000. The actual prices are: $180K, $200K, $190K, $210K, $195K, $1,725K. Is the reporter's claim misleading? Calculate the mean and median and explain which better represents a 'typical' home price.

    ✏️ 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