Curriculum / Math / 6th Grade / Unit 8: Statistics / Lesson 11
Math
Unit 8
6th Grade
Lesson 11 of 14
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Compare measures of center and measures of spread to describe data sets.
The core standards covered in this lesson
6.SP.A.3 — Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Robert is interested in moving to either New York City (NYC) or San Francisco (SF). Robert has a cousin in San Francisco, and he asked her about the weather. She told him that it doesn’t get very warm in San Francisco. Robert was surprised to hear that. He was planning on using the temperature of each location as one of the criteria to help him decide where to move. Robert investigates the temperature distributions (in degrees Fahrenheit) for NYC and SF and records his results in the table below.
a. Find the average monthly temperature for each city.
b. Find the mean absolute deviation for each city.
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Grade 6 Mathematics > Module 6 > Topic B > Lesson 8 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Robert is trying to make sense of what his temperature calculations tell him about the two cities. He knows he wants to live somewhere where the typical climate is on the warmer side.
a. Use your calculations from Anchor Problem #1 to make an argument for why Robert could decide to live in either city.
b. Use your calculations from Anchor Problem #1 to make an argument for why Robert should decide to live in San Francisco over New York City.
Rakela is training for a road race. She wants to make a five-week plan for how many miles she should run each week in order to be ready for the race. She comes up with three different options. In order to better understand each training plan and decide which one she should follow, she finds the mean, median, range, and interquartile range for each plan and records them in the table.
a. If Rakela wants to follow a training plan that is the most consistent across the five weeks, which one should she use? Why? Which information from the table helps her decide?
b. If Rakela wants to follow a training plan that allows her to gradually increases the number of miles to run each week over time, which one should she use? Why? Which information from the table helps her decide?
c. Based on the statistics, why might Rakela want to choose Training Plan #3?
For each question, decide if you would answer the question by considering center or considering variability in the data distribution.
Situation: Suppose that seventh graders at your school took both a math test and a literacy test. Scores on both tests could be any number between 0 and 100.
Question 1: On average, did the students score better on the math test or the literacy test?
Question 2: Were the students’ scores more consistent (more similar to one another) on the math test or on the literacy test?
Is It Center or Is It Variability?, accessed on April 3, 2018, 10:53 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
For each question, decide if you would answer the question by considering center or considering variability in the data distribution. Explain your choice.
Situation A: The records office at an elementary school keeps daily attendance records.
Question 1: For students at this school, what is a typical number of school days missed in the month of April?
Situation B: Bags of M&M’s don’t all have exactly the same number of candies in each bag. Suppose you count the number of candies in each of 25 bags of plain M&M’s and in each of 25 bags of peanut M&M’s and make two dot plots—one for the number of candies in the plain M&M’s bags and one for the number of candies in the peanut M&M’s bags.
Question 2: If you wanted to give each student in your class a bag of M&M’s and you wanted to try to make sure that each student got the same number of candies, should you give them bags of plain M&M’s or bags of peanut M&M’s?
Question 3: If you wanted to give each student in your class a bag of M&M’s and you wanted to try to give students bags with the greatest number of candies, should you give them bags of plain M&M’s or bags of peanut M&M’s?
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Represent data using box plots.
Topic A: Understanding Statistics & Distributions
Define and identify statistical questions.
Standards
6.SP.A.16.SP.B.5.A
Describe data that is represented in a dot plot. Represent data using dot plots and frequency tables.
6.SP.B.46.SP.B.5.A
Represent data using histograms.
6.SP.B.4
Describe and analyze the overall shape of dot plots and histograms, including symmetry, skewness, outliers, and clusters.
6.SP.A.2
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Topic B: Measurements of Center & Variability
Define and determine the mean of a data set.
6.SP.A.26.SP.B.5.C
Define and determine the median of a data set.
Define and determine the mode of a data set.
Determine which measure of center best represents a data set. Determine how measures of center change when data is added or removed.
6.SP.A.26.SP.B.5.D
Use the range and interquartile range to understand the spread and variability of a data set.
Understand and determine mean absolute deviation (MAD) as a measure of variability of a data set.
6.SP.B.5.C
6.SP.A.3
Topic C: Box Plots & Circle Graphs
6.SP.B.46.SP.B.5
Analyze box plots and other representations, and summarize numerical data in context.
Analyze circle graphs in context.
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