6.DS.6d Lesson 2-10-part2 Apply Day · Set B
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2.10 · Part II

Second Practice Form · Independent Application and Spiral Review

Appropriate Measures of Center · Mean

Interactive Workbench & Models →
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■ 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.
  1. 1 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
  2. 2 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
  3. 3 MULTIPLE CHOICE

    A gymnast's scores are: 8.5, 8.8, 8.7, 8.6, 8.9. There are no outliers. Which measure best represents a typical score?

    1. AMean
    2. BMedian
    3. CNeither — the data is too small
    4. DBoth are equally bad
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    A runner's mile times are: 7:10, 7:15, 7:12, 7:20, 12:00. The 12:00 was due to a cramp. Which measure best represents a typical mile?

    1. AMedian — the outlier 12:00 pulls the mean too high
    2. BMean — it uses all the data
    3. CMode — it shows the most common time
    4. DNeither measure works
    ✏️ Workspace & Solution Steps
  5. 5 MULTIPLE CHOICE

    Data set: 5, 6, 7, 7, 8, 50. The mean is about 13.8 and the median is 7. Which better represents the typical value?

    1. AMedian (7) — the outlier 50 inflates the mean
    2. BMean (13.8) — it includes all values
    3. CBoth are equally good
    4. DNeither works for this data
    ✏️ 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