6.DS.5 Lesson 2-4-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.4 Small Group · Group 1

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

Display Data with Box Plots · Box Plot · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What is a box plot?
1The box always holds the middle 50% of the data, and the line inside the box is the median.
  • A box plot is a simple picture that shows how a set of data is spread out, using just five key numbers: the lowest value, the first quartile (Q1), the median (middle), the third quartile (Q3), and the highest value. 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 build one
  1. My data, in order: 4, 6, 8, 10, 12, 14, 15, 18, 22, 24, 28. There are 11 numbers.
  2. The middle number is the 6th one, 14, so the median = 14.
  3. The lower half is 4, 6, 8, 10, 12. Its middle is 8, so Q1 = 8.
  4. The upper half is 15, 18, 22, 24, 28. Its middle is 22, so Q3 = 22.
  5. The lowest is 4 and the highest is 28. I draw a box from 8 to 22, a line at 14, and whiskers out to 4 and 28.
3Mathematical Word Bank
  • Display Data with Box Plots (Representar datos con diagramas de caja) — Show a data set's five-number summary in a box-and-whisker display.
  • Box Plot (Diagrama de caja) — A graph that shows how data is spread using five key numbers.
  • Median (Mediana) — The middle number when you put them in order.
  • Quartile (Cuartil) — Numbers that split the data into four equal parts.
  • Interquartile Range (Rango intercuartílico) — The spread of the middle half of the data (Q3 − Q1).
  • Data distribution (Distribución de datos) — How the data looks: where it sits and how spread out it is.
4Watch out
  • A common mistake in Display Data: Box Plots is treating a quartile as just one data point instead of the median of a half — for the lower half 4, 8, 10, 14, some students pick 10 (the last value) as Q1 instead of finding the median of that half: Q1 = (8 + 10) ÷ 2 = 9. A second common slip is finding IQR by adding the quartiles instead of subtracting, writing IQR = Q3 + Q1 (like 30 + 18 = 48) instead of IQR = Q3 − Q1 (30 − 18 = 12) — always order the data first, then subtract Q1 from Q3 to find the spread of the middle 50%.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    Two box plots show: Team A has IQR = 8, Team B has IQR = 22. What does this tell you?

    1. ATeam A's middle 50% is more consistent; Team B's is more spread out
    2. BTeam B is a better team
    3. CTeam A has a higher median
    4. DThe IQRs don't tell you about consistency
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    The Hawks' points per quarter are 2, 4, 5, 7, 8, 10, 12. Resting on the scoreboard, what are the minimum, median, and maximum?

    1. AMinimum 2, median 7, maximum 12
    2. BMinimum 2, median 5, maximum 12
    3. CMinimum 0, median 7, maximum 12
    4. DMinimum 2, median 8, maximum 10
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    The Comets scored 6, 10, 14, 18, 22, 26, 30, 34 across 8 games. After ordering, what are Q1 and Q3?

    1. AQ1 = 12, Q3 = 28
    2. BQ1 = 10, Q3 = 30
    3. CQ1 = 14, Q3 = 26
    4. DQ1 = 20, Q3 = 34
    ✏️ Workspace & Solution Steps
  3. 4 MULTIPLE CHOICE

    A box plot for the Rockets shows Min = 8, Q1 = 15, Median = 22, Q3 = 30, Max = 38. The middle 50% of their scores falls between which two values?

    1. ABetween 15 and 30
    2. BBetween 8 and 38
    3. CBetween 8 and 22
    4. DBetween 22 and 38
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    The Added-Quartiles IQR Mistake

    1. 1Box plot values:Bobcats' box plot: Min = 10, Q1 = 18, Median = 24, Q3 = 30, Max = 40
    2. 2Goal:Find the interquartile range (IQR).
    3. 3Student's work:IQR = Q3 + Q1 = 30 + 18 = 48

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    The Quartile-Is-One-Value Mistake

    1. 1Data (ordered):Eagles' game scores: 4, 8, 10, 14, 18, 22, 26, 30 (8 values)
    2. 2Median:With 8 values, Median = (14 + 18) ÷ 2 = 16 ✓
    3. 3Q1:Lower half = 4, 8, 10, 14 → Q1 = 10
    4. 4Q3:Upper half = 18, 22, 26, 30 → Q3 = (22 + 26) ÷ 2 = 24

    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