Probability and Statistical Inference

Lesson 7

Math

Unit 8

11th Grade

Lesson 7 of 13

Objective


Describe the center, shape, and spread of distributions by reasoning visually about the mean, standard deviation, and shape of a histogram.

Common Core Standards


Core Standards

  • S.IC.A.1 — Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Foundational Standards

  • S.ID.A.4

Criteria for Success


  1. Describe that a sample needs to be random to be reliable. A larger data set increases reliability of data. 
  2. Describe a normal distribution as the result of perfect randomness and that we approximate “normal” by the symmetric and mound shape of a distribution. 
  3. Describe that a larger standard deviation describes data that is less centered around the mean, or more spread out, and that a smaller standard deviation is more centered around the mean, or less spread out. 
  4. Describe that a normal distribution is one in which the mean and median are approximately equal. 
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Anchor Problems


Problem 1

Part A: Predict the shape of the graph at 2,000 trials.

10 trials 100 trials 533 trials

Part B: At 1,799 trials, the graph looks like this:

The mean of the data is approximately 6, and the standard deviation is 1.7. The blue lines around the graph are what should be the "ideal" normal distribution.

Describe what the mean and the standard deviation mean in terms of this situation.

Guiding Questions

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References

PhET Resource: Plinko Probability

PhET Interactive Simulations
University of Colorado Boulder
https://phet.colorado.edu

Problem 2

Match the following distributions with the histograms. Explain your reasoning.

Distribution Shape Mean Standard Deviation
A Skewed to the right 100 10
B Approximately symmetric, mound shaped 100 10
C Approximately symmetric, mound shaped 100 40
D Skewed to the right 100 40

Guiding Questions

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References

EngageNY Mathematics Algebra II > Module 4 > Topic B > Lesson 8Exercise 7

Algebra II > Module 4 > 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.

Target Task


A local utility company wanted to gather data on the age of air conditioners that people have in their homes. The company took a random sample of 200 residents of a large city and asked if the residents had an air conditioner and, if they did, how old it was. Below is the distribution in the reported ages of the air conditioners. 

  1. Would you describe this distribution of air conditioner ages as approximately symmetric or as skewed? Explain your answer. 
  2. Is the mean of the age distribution closer to 15, 20, or 25 years? Explain your answer. 
  3. Is the standard deviation of the age distribution closer to 3, 6, or 9 years? Explain your answer.

References

EngageNY Mathematics Algebra II > Module 4 > Topic B > Lesson 8Exit Ticket

Algebra II > Module 4 > 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..

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.

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Lesson 6

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Lesson 8

Lesson Map

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

Topic A: Probability

Topic B: The Normal Distribution

Topic C: Statistical Inferences and Conclusions

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