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

Lesson 2.52.5 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can find the range and the interquartile range of a data set and use them to describe how spread out the data is — one step at a time, with support.

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 1

Group 1Supported practice

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

Learning target With my small group, I can find the range and the interquartile range of a data set and use them to describe how spread out the data is — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    5458626670747882869094
    Class C test scores

    Class C's box plot shows: least 55, Q1 66, median 74, Q3 80, greatest 92. Find the range and the IQR.

    1. 1Find the range: greatest − least.
    2. 2Find the IQR: Q3 − Q1.
    3. 3What does each number tell you?
    Final answer:
  2. 2Complete each step, then write the final answer.
    6063666972757881848790Scores
    This time you start from the data.

    Find the range and the IQR of these 8 scores: 61, 64, 70, 72, 75, 78, 83, 90.

    1. 1Find the range.
    2. 2Find Q1 from 61, 64, 70, 72 and Q3 from 75, 78, 83, 90.
    3. 3Find the IQR: Q3 − Q1.
    Final answer:
  3. 3Complete each step, then write the final answer.

    A box plot shows: least 2, Q1 4, median 6, Q3 9, greatest 12. What is the IQR?

    Show your work

    Hint The IQR uses Q1 and Q3 only.

    Final answer:
  4. 4Complete each step, then write the final answer.

    Find the range of these test scores: 72, 88, 61, 93, 78, 81, 69.

    Show your work

    Hint Find the least and the greatest score first. They are not at the ends of the list.

    Final answer:
  5. 5Complete each step, then write the final answer.
    5254565860626466Height (inches)

    Seven friends are 54, 56, 57, 59, 60, 62 and 65 inches tall. What is the IQR of their heights?

    Show your work

    Hint The median is 59. Find the middle of each half.

    Final answer:
  6. 6Circle 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.

    Hint Which measure tells about the middle half of the data?

    Show your work

Explain your thinkingClass C has a range of 37 and an IQR of 14. What does each number tell you about the scores?

Sentence starter The range is ___, so all the scores ___. · The IQR is ___, so the middle half of the scores ___.

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