6.DS.6d Lesson 2-10-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.10 Small Group · Group 1

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

Appropriate Measures of Center · Mean · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — Should I use the mean or the median?
1Use the mean for data with no outliers; use the median when an outlier or a skewed shape would pull the mean away from typical.
  • The mean and the median both describe the center of a data set, but one fits better depending on the shape. When the data has an outlier (a value far from the rest), the median is usually the better choice. 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, the top scorer's points: 22, 24, 20, 25, 23, 21, 58. I notice 58 is much bigger than the rest, so it is an outlier.
  2. Mean: 22 + 24 + 20 + 25 + 23 + 21 + 58 = 193, then 193 ÷ 7 ≈ 27.6.
  3. Median: in order they are 20, 21, 22, 23, 24, 25, 58. The middle (4th) value is 23.
  4. The mean (27.6) is higher than 6 of the 7 games because 58 pulled it up. So the median (23) better shows a typical game.
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 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. 2 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
  3. 3 MULTIPLE CHOICE

    The equipment manager needs to order the MOST COMMON jersey size from this list: M, L, M, S, M, L, M. Which measure answers the question?

    1. AMode, because it names the value that appears most
    2. BMean, because it averages the sizes
    3. CMedian, because it finds the middle size
    4. DRange, because it shows the size gap
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    A coach wants to know how SPREAD OUT the team's free-throw makes are: 6, 7, 6, 8, 18. Which measure of spread is most affected by the lone 18?

    1. ARange, because it is the highest minus the lowest value
    2. BMedian, because it is in the middle
    3. CMode, because it is the most common
    4. DMean absolute deviation only, never the range
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Spot the Mistake — Choosing the Mean Despite an Outlier

    1. 1Data:A receiver's catches per game: 12, 14, 13, 15, 11, 60 (the 60 was a record-setting playoff game).
    2. 2Find the mean:Sum = 125, Count = 6, Mean = 125 ÷ 6 ≈ 20.8.
    3. 3Find the median:Ordered: 11, 12, 13, 14, 15, 60 → Median = (13 + 14) ÷ 2 = 13.5.
    4. 4Choose a measure:The student reports the mean (≈ 20.8) as the typical number of catches because it uses every game.

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Level 2 Extension — The Analyst's Wrong Measure

    1. 1Data:A player's points per game: 19, 21, 20, 22, 23, 2 (the 2 was a game cut short by an early ejection).
    2. 2Find mean:Sum = 107, Count = 6, Mean = 107 ÷ 6 ≈ 17.8
    3. 3Find median:Ordered: 2, 19, 20, 21, 22, 23 → Median = (20 + 21) ÷ 2 = 20.5
    4. 4Analyst's choice:The analyst reports the mean (17.8) as the player's typical scoring because it uses all the data.

    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