6.DS.3 Lesson 2-5-part2 Apply Day · Set B
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2.5 · Part II

Second Practice Form · Independent Application and Spiral Review

Range and Interquartile Range · Range

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■ 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

    (Lesson 2.2) In a histogram, what does the height of each bar represent?

    1. AThe average of the data in that interval
    2. BThe range of the interval
    3. CThe median of the data
    4. DThe frequency (count) of data in that interval
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Class A and Class B both have a range of 40 on a test. Class A's IQR is 8; Class B's is 30. What does that tell you?

    1. AClass A's scores cluster tightly with a few far-out scores; Class B's are spread through the whole range
    2. BClass A did better than Class B
    3. CNothing — equal ranges mean the classes performed the same
    4. DClass B has more students than Class A
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    (Lesson 2.2) A histogram shows these frequencies: 0–4: 3 players, 5–9: 8 players, 10–14: 12 players, 15–19: 5 players. How many players are represented in total?

    1. A20
    2. B15
    3. C28
    4. D12
    per 1
  2. 4 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
  3. 5 MULTIPLE CHOICE

    A data set runs from a least value of 12 to a greatest value of 30. What is the range?

    1. A18
    2. B30
    3. C12
    4. D21
    Put the data in order
    Work
  4. 6 MULTIPLE CHOICE

    On a box plot, Q1 = 20 and Q3 = 36. What is the interquartile range?

    1. A16
    2. B56
    3. C28
    4. D36
    Put the data in order
    Work
  5. 7 MULTIPLE CHOICE

    Which measure of spread uses ONLY the middle half of the data?

    1. AThe interquartile range
    2. BThe range
    3. CThe median
    4. DThe mode
    ✏️ 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