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

Lesson 2.52.5 Small Group · Group 2

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, explain how I can tell, and judge a case I have not seen before.

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 2.52.5 Small Group · Group 2

Group 2Challenge 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, explain how I can tell, and judge a case I have not seen before.

  1. 1Complete each step, then write the final answer.
    03691215182124Points scored
    Seven values are close. 25 is far away.

    Eight players scored 4, 5, 5, 6, 7, 8, 9 and 25 points. Find the range and the IQR. Which one better describes most of the data?

    1. 1Find the range.
    2. 2Find Q1 from 4, 5, 5, 6 and Q3 from 7, 8, 9, 25.
    3. 3Find the IQR.
    4. 4Which measure better describes most of the data?
    Final answer:
  2. 2Complete each step, then write the final answer.
    101520253035404550leastQ1
    Count up from the least value and from Q1.

    A data set has an IQR of 15 and a range of 40. Q1 is 22 and the least value is 10. Find Q3 and the greatest value.

    1. 1Add the IQR to Q1. What is Q3?
    2. 2Add the range to the least value. What is the greatest value?
    3. 3Why do you add the IQR to Q1, and not to the least value?
    Final answer:
  3. 3Complete 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:
  4. 4Complete each step, then write the final answer.

    A box plot has Q3 = 48 and an IQR of 17. What is Q1?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    Two classes took a quiz. Class A: least 60, Q1 70, Q3 84, greatest 98. Class B: least 66, Q1 74, Q3 83, greatest 95. How much greater is Class A's IQR than Class B's?

    Show your work
    Final answer:
  6. 6Circle 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

Explain your thinkingA coach says the range shows how close together most players' scores are. Do you agree? Use the player who scored 25 to explain.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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