Lesson 13: The Median of a Data Set
About this lesson
In this lesson, students consider another measure of center, the median, which divides the data into two groups with half of the data greater and half of the data less than the median. To find the median, they learn that the data are to be arranged in order, from least to greatest. They make use of the structure of the data set (MP7) to see that the median partitions the data into two halves: one half of the values in the data set has that value or smaller values, and the other half has that value or larger. Students learn how to find the median for data sets with both even and odd number of values.
Students engage in MP2 as they find the median of a numerical data set and interpret it in context. They begin to see that, just like the mean, the median can be used to describe what is typical in a distribution, but that it is interpreted differently than is the mean.
Lesson overview
 13.1 Warmup: The Plot of the Story (5 minutes)

13.2 Activity: Siblings in the House (15 minutes)
 Includes "Are you Ready for More?" extension problem
 13.3 Activity: Finding the Middle (15 minutes)
 Lesson Synthesis
 13.4 Cooldown: Practicing the Piano (5 minutes)
Learning goals:
 Comprehend that the “median” is another measure of center, which uses the middle of all the values in an ordered list to summarize the data.
 Identify and interpret the median of a data set given in a table or on a dot plot.
 Informally estimate the center of a data set and then compare (orally and in writing) the mean and median with this estimate.
Learning goals (student facing):

Let's explore the median of a data set and what it tells us.
Learning targets (student facing):
 I can say what the median represents and what it tells us in a given context.
 I can find the median for a set of data.
Required materials:
 index cards
Required preparation:
 For the Finding the Middle activity, each student will need an index card.
Glossary:
 median  The median is one way to measure the center of a data set. It is the middle number when the data set is listed in order. For the data set 7, 9, 12, 13, 14, the median is 12. For the data set 3, 5, 6, 8, 11, 12, there are two numbers in the middle. The median is the average of these two numbers. \(6+8=14\) and \(14 \div 2 = 7\).
 Access the complete Grade 6 glossary.
Standards:
 This lesson builds towards the standard: CCSS.6.SP.B.5.dMS.6.SP.5d
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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