6.DS.3 Lesson 2-5-group1 🟡 Group 1 · Set B
MASTERY CHECK
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2.5 Small Group · Group 1

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

Range and Interquartile Range · Range · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How spread out is the data?
1Range = greatest − least, and it covers every value. Interquartile range = Q3 − Q1, and it covers only the middle half, so one faraway value cannot stretch it.
  • A measure of center like the median tells you where the data sits. It does not tell you how far apart the values are. Two classes can share the same median and still look nothing alike. Range and interquartile range are the two numbers that describe that spread. 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 measure the spread of the test scores
  1. Here are 20 history test scores in order: 68, 70, 73, 74, 75, 76, 77, 80, 82, 83, 84, 85, 86, 86, 88, 88, 90, 90, 93, 94. Ordering them first is what makes every step after this possible.
  2. Range: I subtract the least value from the greatest. 94 − 68 = 26. The scores span 26 points from end to end.
  3. Now the quartiles. The median splits the 20 scores into two halves of 10. The median is halfway between the 10th and 11th values: (83 + 84) ÷ 2 = 83.5.
  4. Q1 is the median of the lower 10 values: halfway between 75 and 76, so Q1 = 75.5. Q3 is the median of the upper 10: halfway between 88 and 88, so Q3 = 88.
  5. Interquartile range: IQR = Q3 − Q1 = 88 − 75.5 = 12.5. The middle half of the students' scores differed by only 12.5 points, even though the full range was 26.
3Mathematical Word Bank
  • Range and Interquartile Range (Rango y rango intercuartílico) — Two numbers that describe spread: the range covers all the data, and the interquartile range covers only the middle half.
  • Range (Rango) — The distance from the least value to the greatest value, found by subtracting: greatest − least.
  • Quartile (Cuartil) — One of the three values that cut an ordered data set into four equal-sized groups.
  • Interquartile range (Rango intercuartílico) — The distance across the middle half of the data, found by subtracting the first quartile from the third: Q3 − Q1.
  • Variability (Variabilidad) — How much the values in a data set differ from one another — whether they sit close together or far apart.
  • Measure of variation (Medida de variación) — A single number that describes the spread of a whole data set. The range and the IQR are both measures of variation.
4Watch out
  • A common mistake with Range and Interquartile Range is adding the two quartiles instead of subtracting them — writing IQR = Q3 + Q1. With Q1 = 42 and Q3 = 58 that gives 100, which is larger than the data set's entire range of 20. Every measure of variation is a DIFFERENCE, and the IQR can never exceed the range, because the middle half is part of the whole span. If your IQR comes out bigger than your range, you added when you should have subtracted.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    Team A's salaries have a range of $14M and an IQR of $7M. Team B's have a range of $7M and an IQR of $2.5M. Both teams have the same median salary. What does this tell a player?

    1. ATeam B's salaries cluster much more tightly around the median
    2. BTeam B pays more overall
    3. CTeam A has more players
    4. DTeam B's highest salary is greater
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    A box plot shows: least 68, Q1 75.5, median 83.5, Q3 88, greatest 94. What are the range and the IQR?

    1. ARange 26, IQR 12.5
    2. BRange 12.5, IQR 26
    3. CRange 26, IQR 83.5
    4. DRange 20, IQR 12.5
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    What is the range of 7, 9, 12, 15, 20?

    1. A13
    2. B20
    3. C7
    4. D9
    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  3. 4 MULTIPLE CHOICE

    A box plot has Q1 = 30 and Q3 = 45. What is the IQR?

    1. A15
    2. B75
    3. C37.5
    4. D45
    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  4. 5 MULTIPLE CHOICE

    Which data set has the greater range: A (12, 14, 15, 18) or B (5, 9, 14, 25)?

    1. AB, because 25 − 5 = 20
    2. BA, because it has larger values
    3. CThey are equal
    4. DYou cannot tell without the median
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Find the error

    1. 1Setup:Data: 40, 42, 45, 50, 55, 58, 60. Q1 = 42, median = 50, Q3 = 58.
    2. 2Step 1:Range = 60 − 40 = 20
    3. 3Step 2:IQR = 58 + 42 = 100
    4. 4Step 3:The middle half of the data spans 100 units.

    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