Statistics

Lesson 3

Math

Unit 7

7th Grade

Lesson 3 of 9

Objective


Generate a random sample for a statistical question.

Common Core Standards


Core Standards

  • 7.SP.A.1 — Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
  • 7.SP.A.2 — Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Foundational Standards

  • 6.SP.B.4
  • 6.SP.B.5

Criteria for Success


  1. Use a random sampling technique to generate a random sample of data. 
  2. Understand that a random sample, in which every entry in the population has an equal chance of being part of the sample, tends to be representative of the population.

Tips for Teachers


  • This lesson requires some preparation. See the Notes section for Anchor Problem #2.
  • In this lesson, students engage in MP.4. They model the selection of a random set of words by selecting numbers from bags. They use dot plots or other visual diagrams to summarize data from non-random samples and from random samples. They compare the data from these graphs and draw conclusions around the accuracy of non-random and random samples. 

Lesson Materials

  • Papers with numbers 1-29 and 1-20 (1 per pair of students)
  • Brown bag (2 per pair of students)
  • Casey at the Bat (1 per student)
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Anchor Problems

25-30 minutes


Problem 1

You are answering this statistical question: 

On average, how long is a word in the poem “Casey at the Bat”?

a.   Looking at the poem, select eight words you think are representative of words in the poem. Record the words and the number of letters in each word.

b.   Find the mean number of letters in the words you chose.

c.   Do you think your set of words is a random sample? Why or why not?

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 7 Mathematics > Module 5 > Topic C > Lesson 14Teacher Version: Exercises 3-5

Grade 7 Mathematics > Module 5 > Topic C > Lesson 14 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

(See the Notes below for preparation for this problem.)

You are answering this statistical question: 

On average, how long is a word in the poem “Casey at the Bat”?

a.   Using the bags of numbers, randomly select eight words. Record the words and the number of letters in each word.

b.   Find the mean number of letters in the words you chose. How does this mean compare to the mean you found in Anchor Problem #1?

c.   As a class, compare the mean number of letters from Anchor Problems #1 and #2, either in a chart or a dot plot.

d.   Which mean length, from Anchor Problem #1 or Anchor Problem #2, do you think is more representative of the mean length of all the words in the poem? Why?

e.   The actual mean length of the words in the poem is 4.2 letters. Based on this information, which samples, the ones selected in Anchor Problem #1 or the ones randomly selected in Anchor Problem #2, are a better representation of the population? Why do you think this is so?

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 7 Mathematics > Module 5 > Topic C > Lesson 14Teacher Version: Exercises 6-9 (See handout of poem)

Grade 7 Mathematics > Module 5 > Topic C > Lesson 14 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 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.

Target Task

5-10 minutes


As a member of the student council at your school, you want to determine if the seventh-grade students prefer to have an after-school soccer program or an after-school movie club. There are 110 seventh-grade students at your school, and you decide to take a sample of 20 students. 

Describe in detail how you can randomly select 20 seventh-grade students for your sample.

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.

Next

Analyze data sets using measures of center and measures of variability.

Lesson 4
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Lesson Map

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

Topic A: Understanding Populations and Samples

Topic B: Using Sample Data to Draw Inferences About a Population

Topic C: Using Sample Data to Compare Two or More Populations

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