Statistics

Lesson 11

Math

Unit 8

6th Grade

Lesson 11 of 14

Objective


Compare measures of center and measures of spread to describe data sets.

Common Core Standards


Core Standards

  • 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.

Criteria for Success


  1. Understand that measures of center summarize all of the values in a data set in a single number. 
  2. Understand that measures of variation describe how the values in a data set vary.
  3. Determine if a measure of center or variation better answers a question.

Tips for Teachers


Lesson Materials

  • Calculators (1 per student)
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Anchor Problems


Problem 1

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.

City Jan Feb March April May June July Aug Sept Oct Nov Dec
NYC 39 42 50 61 71 81 85 84 76 65 55 47
SF 57 60 62 63 64 67 67 68 70 69 63 58

a.   Find the average monthly temperature for each city. 

b.   Find the mean absolute deviation for each city. 

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic B > Lesson 8Example 1

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..

Modified by Fishtank Learning, Inc.

Problem 2

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.

Guiding Questions

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Problem 3

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.

  Training Plan #1 Training Plan #2 Training Plan #3
Mean # of miles 4.8 4.6 4.8
Median # of miles 5 5 7
Range, in miles 6 1 10
Interquartiles range, in miles 4.5 1 8.5

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?

Guiding Questions

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Problem 4

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?

Guiding Questions

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References

Illustrative Mathematics Is It Center or Is It Variability?Example 2

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.

Modified by Fishtank Learning, Inc.

Problem Set

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Target Task


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?

References

Illustrative Mathematics Is It Center or Is It Variability?Examples 1 and 3

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.

Modified by Fishtank Learning, Inc.

Student Response

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Additional Practice


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.

  • Examples where students make arguments to defend a decision based on either a measure of center or a measure of variability.
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Lesson 10

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Lesson 12

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Statistics & Distributions

Topic B: Measurements of Center & Variability

Topic C: Box Plots & Circle Graphs

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