6.DS.4 Lesson 2-3-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.3 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

Describe the Data Using the Median · Median · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What are mean, median, and mode?
1The median is the middle value once the data is in order. With an even count, it is the mean of the two middle values — and it is the measure that an unusually high or low value cannot drag around — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
2Worked Example — Watch me find the median
  1. My data set: 2, 4, 4, 6, 9 — five values, already in order. Ordering first is what makes a middle exist at all.
  2. With 5 values, the middle is the 3rd one. Counting in from both ends: 2 and 9 pair off, 4 and 6 pair off, and 4 is left alone.
  3. So the median is 4. Half the values sit at or below it and half at or above it.
  4. Now an even set: 2, 4, 6, 9. There is no single middle, so I take the mean of the two middle values: (4 + 6) ÷ 2 = 5. The median is 5, even though 5 is not in the data.
3Second Model — Try it together — then prove it
  1. New data set, out of order: 13, 3, 7, 10, 7. Put it in order first.
  2. In order: 3, 7, 7, 10, 13. Five values, so the middle is the 3rd.
  3. The median is 7. Say what it means: a typical value in this set is about 7.
  4. Now change the 13 to 130. Does the median move? It does not — still 7. That resistance is exactly why the median is used.
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • Describe the Data Using the Median (Describir los datos con la mediana) — Using the middle value of the ordered data to say what is typical for the whole set.
  • Median (Mediana) — The middle number when you put them in order.
  • Mode (Moda) — The number that shows up most often.
  • Outlier (Valor atípico) — A number that is much bigger or smaller than the rest.
  • 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.
5Watch out
  • A common mistake in Mean, Median, and Mode is finding the median without ordering the data first — students pick the middle number straight from the list as given (for 9, 4, 7, 2, 6 they say the median is 7, the middle position in that original order) instead of sorting least to greatest (2, 4, 6, 7, 9) and finding the true middle value, 6. Before finalizing a median, always reorder the data smallest to largest, then count to the middle position — and if there is an even number of values, average the two middle numbers.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    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

    Data set: 4, 6, 6, 8, 10, 12. What is the median?

    1. A7
    2. B6
    3. C8
    4. D7.67
    Put the data in order
    Work
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 ERROR ANALYSIS

    Level 2 Extension — The Median Mistake

    1. 1Data set:Points per game: 9, 4, 7, 2, 6
    2. 2Goal:Find the median number of points.
    3. 3Pick the middle:The number in the middle of the list is 7, so the median = 7.
    4. 4Answer:Median = 7

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:One game was a 55-point outlier. Which measure of center best shows a TYPICAL game?
    2. 2A classmate at our table answered:The mode, because it is always the typical value

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 5 ERROR ANALYSIS

    The Even-Count Median Mistake

    1. 1Data set:Points per game, in order: 3, 8, 10, 14, 16, 20 (6 values)
    2. 2Goal:Find the MEDIAN number of points.
    3. 3Pick the middle:With 6 values the student grabs a single middle number and says median = 10.
    4. 4Answer:Median = 10

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

    ✏️ Corrected Mathematical Work & Explanation
  4. 6 ERROR ANALYSIS

    Find the Stats Error

    1. 1Data set:12, 15, 18, 15, 20
    2. 2Find mean:Sum = 80, Count = 5, Mean = 80 ÷ 5 = 16
    3. 3Find median:Ordered: 12, 15, 15, 18, 20 → Median = 15
    4. 4Find mode:Mode = 18 (the biggest number)

    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
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