Previously, students learned about decomposing a data set into two halves and using the halfway point, the median, as a measure of center of the distribution. In this lesson, they learn that they could further decompose a data set—into quarters—and use the quartiles to describe a distribution. They learn that the three quartiles—marking the 25th, 50th, and 75th percentiles—plus the maximum and minimum values of the data set make up a fivenumber summary.
Students also explore the range and interquartile range (IQR) of a distribution as two ways to measure its spread. Students reason abstractly and quantitatively (MP2) as they find and interpret the IQR as describing the distribution of the middle half of the data. This lesson prepares students to construct box plots in a future lesson.
Lesson overview
 15.1 Warmup: Notice and Wonder: Two Parties (5 minutes)

15.2 Activity: The FiveNumber Summary (15 minutes)
 Includes "Are you Ready for More?" extension problem
 15.3 Activity: Range and Interquartile Range (15 minutes)
 Lesson Synthesis
 15.4 Cooldown: How Far Can You Throw? (5 minutes)
Learning goals:
 Calculate the range and interquartile range (IQR) of a data set and interpret (orally and in writing) what they tell us about the situation.
 Comprehend that “interquartile range (IQR)” is another measure of variability that describes the span of the middle half of the data.
 Identify and interpret (in writing) the numbers in the fivenumber summary for a data set, i.e., the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
Learning goals (student facing):

Let's look at other measures for describing distributions.
Learning targets (student facing):
 I know what quartiles and interquartile range (IQR) measure and what they tell us about the data.
 When given a list of data values or a dot plot, I can find the quartiles and interquartile range (IQR) for data.
 I can use IQR to describe the spread of data.
Glossary:
 interquartile range (IQR)  The interquartile range is one way to measure how spread out a data set is. We sometimes call this the IQR. To find the interquartile range we subtract the first quartile from the third quartile. For example, the IQR of this data set is 20 because \(5030=20\).
 quartile  Quartiles are the numbers that divide a data set into four sections that each have the same number of values. For example, in this data set the first quartile is 30. The second quartile is the same thing as the median, which is 43. The third quartile is 50.
 range  The range is the distance between the smallest and largest values in a data set. For example, for the data set 3, 5, 6, 8, 11, 12, the range is 9, because \(123=9\).
 Access the complete Grade 6 glossary.
Standards:
 This lesson builds towards the standard: CCSS.6.SP.B.4MS.6.SP.4
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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