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

Lesson 2.5Describe Data by Range and Interquartile Range

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, median, Q3
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. Range and IQR are both

How it worksWorked examplefinding the range and the iqr

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

Seven history test scores are 74, 90, 83, 68, 86, 77, 94. Find the range and the IQR.

  1. Order the values: 68, 74, 77, 83, 86, 90, 94.
  2. Range: take the least value away from the greatest value. That gives 26 points.
  3. The median is 83, so quartile 1 is 74 and quartile 3 is 90.
  4. IQR: take quartile 1 away from quartile 3. That gives 16 points.

Answer: The range is 26 points and the interquartile range is 16 points.

Now you trySame steps, your turn

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

Seven delivery times in minutes are 31, 45, 28, 52, 37, 41, 34. Find the range and the IQR.

  1. Order the values:
  2. Greatest: Least: Range: minutes
  3. Quartile 1: Quartile 3:
  4. Subtract quartile 1 from quartile 3. IQR: minutes
Answer:range and IQR in minutes

Say it and write itSentence starters

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

  • The greatest value is and the least value is .
  • The range is , which describes .
  • Quartile 1 is and quartile 3 is , so the IQR is .
  • The IQR describes only of the data.

Word bank rangeinterquartile rangequartilespreadvariabilitygreatestleastsubtractmiddle halfextremeorderconsistent

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 2.5Describe Data by Range and Interquartile Range

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.

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

    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. AClass B has a higher median
    2. BClass A has more students
    3. CThe middle half of Class B's scores is less spread out
    4. DClass B's highest score is greater

    Hint A smaller IQR means a narrower box.

    Show your work
  2. 2Write the name of the correct group on each line.

    Sort each fact under the measure of variation it describes.

    Groups: 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

    Hint Ask which values each measure subtracts.

Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

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

    1. A12
    2. B18
    3. C21
    4. D30

    Hint Range asks how far it is from one end of the data to the other.

    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.
  2. 4Circle the letter of the best answer. Show how you know.

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

    1. A16
    2. B28
    3. C36
    4. D56

    Hint The IQR is the width of the box on a box plot.

    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. 5Circle the letter of the best answer. Show how you know.

    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

    Hint One is measured across the box on a box plot; the other whisker to whisker.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Find the error

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

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Compare the IQR in Step 2 to the range in Step 1.

    Correct work
    Correct answer:

Explain your thinkingBoth numbers describe spread. Why might a coach trust the IQR more than the range when one player had a record-breaking night?

Sentence starter I would use the ___ because it only uses the ___, so one unusual value cannot ___.

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 2.5Describe Data by Range and Interquartile Range

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.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    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. 2Circle the letter of the best answer. Show how you know.

    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 pays more overall
    2. BTeam B's salaries cluster much more tightly around the median
    3. CTeam A has more players
    4. DTeam B's highest salary is greater
    Show your work
  3. 3Write the name of the correct group on each line.

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

    Groups: 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
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    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 12.5, IQR 26
    2. BRange 20, IQR 12.5
    3. CRange 26, IQR 12.5
    4. DRange 26, IQR 83.5
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1SetupData: 15, 18, 20, 22, 25, 60.
    2. 2Step 1The range is 60 − 15 = 45.
    3. 3Step 2The range of 45 shows that a typical value differs from the others by about 45.
    4. 4Step 3So this data set has high variability everywhere.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingBoth numbers describe spread. Why might a coach trust the IQR more than the range when one player had a record-breaking night?

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 2.5Describe Data by Range and Interquartile Range

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. 1Write the name of the correct group on each line.

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

    Groups: 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?
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1SetupClass A: least 62, Q1 74, median 81, Q3 87, greatest 90.
    2. 2SetupClass B: least 70, Q1 76, median 81, Q3 84, greatest 90.
    3. 3Step 1Both classes have a median of 81.
    4. 4Step 2Both classes reached the same greatest score, 90.
    5. 5Step 3So the two classes performed the same overall.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    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.

    Write your answer

Explain your thinkingBoth numbers describe spread. Why might a coach trust the IQR more than the range when one player had a record-breaking night?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help