Descriptive Statistics

Lesson 9

Objective

Given summary statistics, describe the best measures of center and spread. Describe reasoning.

Common Core Standards

Core Standards

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  • HSS-ID.A.2 — Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Foundational Standards

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  • 7.SP.B.3

  • 7.SP.B.4

Criteria for Success

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  1. Use the measures of center, shape, and spread to describe a data set and/or a graph.
  2. Use the shape to determine whether mean/standard deviation or median/interquartile range is a better measure. 
  3. Describe why interquartile range and standard deviation are used to measure spread. Median is paired with interquartile range, and mean is paired with standard deviation. 
  4. Use your analysis to draw conclusions and make predictions.

Tips for Teachers

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This lesson provides students with focused practice on all of the skills they will need to complete the project in lessons 10–12. 

Anchor Problems

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Problem 1

A science museum has a “Traveling Around the World” exhibit. Using 3-D technology, participants can make a virtual tour of cities and towns around the world. Students at Waldo High School registered with the museum to participate in a virtual tour of Kenya, visiting the capital city of Nairobi and several small towns. Before they take the tour, however, their mathematics class decided to study Kenya using demographic data from 2010 provided by the US Census Bureau. They also obtained data for the United States from 2010 to compare to data for Kenya.
The following histograms represent the age distributions of the two countries.

Guiding Questions

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References

EngageNY Mathematics Algebra I > Module 2 > Topic B > Lesson 8Exploratory Challenge #1

Algebra I > Module 2 > 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..

Problem 2

A random sample of 200 people from Kenya in 2010 and a random sample of 200 people from the United States were available for study. Box plots constructed using the ages of the people in these two samples are shown below.

Describe the center, spread, and shape of each graph. 

Guiding Questions

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References

EngageNY Mathematics Algebra I > Module 2 > Topic B > Lesson 8Exploratory Challenge #2

Algebra I > Module 2 > 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..

Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Illustrative Mathematics Haircut Costs
  • Mathematics Vision Project: Secondary Mathematics One Module 9: Modeling DataLessons 9.1 and 9.2: Use the stem of these problems but alter the tasks. Have students create a graph showing the data and then describe the shape, center, and spread of the data (box plot would likely be easiest.)

Target Task

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A statistically-minded state trooper wondered if the speed distributions are similar for cars traveling northbound and for cars traveling southbound on an isolated stretch of interstate highway. He uses a radar gun to measure the speed of all northbound cars and all southbound cars passing a particular location during a 15-minute period. Here are his results:

Draw box plots of these two data sets, and then use the plots and appropriate numerical summaries of the data to write a few sentences comparing the speeds of northbound cars and southbound cars at this location during the fifteen-minute time period. 

References