Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.3

Lesson 2.5Comparing Variability

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the range and the interquartile range of a data set and use them to describe how spread out the data is.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Range and Interquartile RangeSpanish: 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 26 covers 68 to 94; IQR 12.5 covers only 75.5 to 88
RangeSpanish: Rango The distance from the least value to the greatest value, found by subtracting: greatest − least. greatest − least
QuartileSpanish: Cuartil One of the three values that cut an ordered data set into four equal-sized groups. Q1 = 75.5, median = 83.5, Q3 = 88
Interquartile rangeSpanish: Rango intercuartílico The distance across the middle half of the data, found by subtracting the first quartile from the third: Q3 − Q1. IQR = Q3 − Q1
VariabilitySpanish: Variabilidad How much the values in a data set differ from one another — whether they sit close together or far apart. Close together or far apart
Measure of variationSpanish: 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. One number stands in for the spread of all 20 scores

How it worksWorked examplecomparing the spread of two groups

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Class A: min 52, Q1 61, median 68, Q3 74, max 89. Class B: min 57, Q1 63, median 69, Q3 71, max 83.

  1. Range: take each set's least value away from its greatest value.
  2. Class A stretches from 52 to 89. Class B stretches from 57 to 83.
  3. IQR: take quartile 1 away from quartile 3. A runs 61 to 74; B runs 63 to 71.
  4. The set with the larger range and the larger IQR is the one that varies more.

Answer: Class A varies more: its whiskers reach further and its box is wider than Class B's.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Team X: min 14, Q1 22, median 27, Q3 36, max 48. Team Y: min 19, Q1 24, median 28, Q3 31, max 44.

  1. Range of X: Range of Y: Which is larger?
  2. IQR of X: IQR of Y: Which is larger?
  3. Which team's results are more consistent?
  4. One sentence using both measures:
Answer:which team varies more, with both measures

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The range of is and the range of is .
  • The IQR of is , so its middle half is .
  • is more consistent because .
  • I trust the more here because .

Word bank rangeinterquartile rangequartilespreadvariabilityconsistentcomparemiddle halfextremewidernarrowertypical

Watch outA common mistake

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.

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.3

Lesson 2.5Comparing Variability

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the range and the interquartile range of a data set and use them to describe how spread out the data is.

  1. 1Complete each step, then write the final answer.

    A box plot shows: least 3, Q1 7, median 10, Q3 14, greatest 18. What is the range?

    Show your work

    Hint The range uses the least and greatest values.

    Final answer:
  2. 2Complete each step, then write the final answer.

    A box plot shows: least 20, Q1 24, median 29, Q3 33, greatest 41. What is the IQR?

    Show your work

    Hint The IQR uses Q1 and Q3.

    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the range of 13, 8, 22, 17, 10.

    Show your work

    Hint Find the least and greatest values first.

    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.3

Lesson 2.5Comparing Variability

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the range and the interquartile range of a data set and use them to describe how spread out the data is.

  1. 1Circle the letter of the best answer. Show how you know.

    Class D has a range of 30 and an IQR of 8. Class E has a range of 22 and an IQR of 15. Which class has its middle half of scores closer together?

    1. AClass D
    2. BClass E
    3. CThey are the same.
    Show your work
  2. 2Complete each step, then write the final answer.

    Find the IQR of 2.5, 3, 4.5, 5, 6, 7.5, 8, 9.5.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    A box plot shows: least 10, Q1 16, median 21, Q3 27, greatest 35. What is the IQR?

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.3

Lesson 2.5Comparing Variability

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the range and the interquartile range of a data set and use them to describe how spread out the data is.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    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 a higher median.
    2. BClass B has greater variability, even though the centers are the same.
    3. CClass A has more students.
    4. DThe two classes performed identically.
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Data: 10, 11, 12, 13, 14, 15. A new value, 50, is added. Which measure changes more?

    1. AThe range
    2. BThe IQR
    3. CThey change by the same amount.
    Show your work
  2. 3Complete each step, then write the final answer.

    Find the IQR of 12, 14, 15, 17, 18, 20, 21, 45.

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help