6.DS.3 Lesson 2-5-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.5 · Part II

Supported Application · Guided Entry to Today's Problem

Range and Interquartile Range · Range

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 2.5 · Part II
1Measures of Variability: Range & IQR
2Strategy Model — step by step
  1. Range measures the total spread across the entire data set
  2. IQR (Interquartile Range) measures the spread of the middle 50% of data
  3. Both are non-negative distance measures of variability
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.
  1. 1 MULTIPLE CHOICE

    Two classes both have a median score of 81. Class A's IQR is 13 and Class B's IQR is 8. Which statement is true?

    1. AThe middle half of Class B's scores is less spread out
    2. BClass B has a higher median
    3. CClass A has more students
    4. DClass B's highest score is greater
    ✏️ Workspace & Solution Steps
  2. 2 DRAG SORT

    Sort each fact under the measure of variation it describes.

    Target Categories: Range Interquartile range
    • Greatest value − least value
    • Q3 − Q1
    • The width of the box on a box plot
    • The distance from whisker tip to whisker tip
    • Changes a lot when one value is unusually high
    • Describes the middle 50% of the data
  3. 3 DRAG SORT

    A value far above the rest is added to a data set. Sort what happens.

    Target Categories: The range grows a lot The IQR barely changes
    • Because it uses the greatest value
    • Because it uses only Q1 and Q3
    • It measures the whole span of the data
    • It measures only the middle half
📐 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
6.DS.3 Lesson 2-5-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.5 · Part II

On-Level Application · Standard Rigor

Range and Interquartile Range · Range

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 2.5 · Part II
1Measures of Variability: Range & IQR
2The Structural Procedure
  1. Range measures the total spread across the entire data set
  2. IQR (Interquartile Range) measures the spread of the middle 50% of data
  3. Both are non-negative distance measures of variability
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 MATCHING

    Match each value from the history test data (68, 70, 73, 74, 75, 76, 77, 80, 82, 83, 84, 85, 86, 86, 88, 88, 90, 90, 93, 94) with what it is.

    1. 26
    2. 12.5
    3. 83.5
    4. 75.5
    5. 88
    • ARange
    • BInterquartile range
    • CMedian
    • DFirst quartile
    • EThird quartile
  2. 2 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. 3 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
📐 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
6.DS.3 Lesson 2-5-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.5 · Part II

Extension & Non-Routine Application

Range and Interquartile Range · Range

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 2.5 · Part II
1Measures of Variability: Range & IQR
2The Structural Procedure
  1. Range measures the total spread across the entire data set
  2. IQR (Interquartile Range) measures the spread of the middle 50% of data
  3. Both are non-negative distance measures of variability
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

    Two classes have the same median score of 81. Class A scores range from 78 to 84; Class B scores range from 60 to 99. What does this tell you?

    1. AClass B has greater variability, even though the centers are the same.
    2. BClass B has a higher median.
    3. CClass A has more students.
    4. DThe two classes performed identically.
    ✏️ Workspace & Solution Steps
  2. 2 DRAG SORT

    A coach wants ONE number for each question. Sort each question under the measure that answers it.

    Target Categories: Range Interquartile range
    • How far apart are our best and worst games?
    • How consistent is a typical night for this team?
    • How much did the middle half of our scores vary?
    • What is the full span from lowest to highest?
    • Which measure survives one record-breaking game?
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 OPEN RESPONSE

    Two students both scored 80 on a make-up test — one joins Class A (range 28, IQR 13) and one joins Class B (range 20, IQR 8). Both classes have a median of 81. Predict how each class's IQR changes, and explain your reasoning.

    ✏️ Mathematical Justification & Response
📐 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