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Methods for Selecting a Random Sample

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Common Core For Grade 7

Examples, videos, and solutions to help Grade 7 students learn how to select a random sample from a given population.

New York State Common Core Math Grade 7, Module 5, Lesson 16

Download worksheets for Grade 7, Module 5, Lesson 16

Lesson 16 Student Outcomes

• Students select a random sample from a population.
• Given a description of a population, students design a plan for selecting a random sample from that population.

Lesson 16 Summary

In this lesson, you collected data on total number of words by selecting a random sample of children’s books. You also observed that several different samples of the same size had some characteristics in common with each other and with the population. In the second activity, you designed a statistical study. First, you considered a statistical question. Then, you went through the statistical process beginning with the question, and then thinking about how to choose a random sample, how students would take part, what data you would collect to answer the question, and how you would display and analyze the data.

Lesson 16 Classwork

In this lesson, you will obtain random numbers to select a random sample. You will also design a plan for selecting a random sample to answer a statistical question about a population.

Example 1: Sampling Children’s Books
What is the longest book you have ever read? The Hobbit has 95,022 words and The Cat in the Hat has 830 words. Popular books vary in the number of words they have—not just the number of different words, but the total number of words. The table below shows the total number of words in some of those books. The histogram displays the total number of words in 150 best-selling children’s books with fewer than 100,000 words.

Exercises 1–2
1. From the table, choose two books with which you are familiar and describe their locations in the data distribution shown in the histogram.
2. Put dots on the number line below that you think would represent a random sample of size from the number of words distribution above.

Example 2: Using Random Numbers to Select a Sample
The histogram indicates the differences in the number of words in the collection of 150 books. How many words are typical for a best-selling children’s book? Answering this question would involve collecting data, and there would be variability in that data. This makes the question a statistical question. Think about the 150 books used to create the histogram above as a population. How would you go about collecting data to determine the typical number of words for the books in this population?
How would you choose a random sample from the collection of 150 books discussed in this lesson? The data for the number of words in the 150 best-selling children’s books are listed below. Select a random sample of the number of words for 10 books.

Exercises 3–6
3. Follow your teacher’s instructions to generate a set of 10 random numbers. Find the total number of words corresponding to each book identified by your random numbers.
4. Choose two more different random samples of size 10 from the data and make a dot plot of each of the three samples.
5. If your teacher randomly chooses 10 books from your summer vacation reading list, would you be likely to get many books with a lot of words? Explain your thinking using statistical terms.
6. If you were to compare your samples with your classmates' samples, do you think your answer to Exercise 5 would change? Why or why not?

Exercises 7–9: A Statistical Study of Balance and Grade
7. Is the following question a statistical question, “Do sixth graders or seventh graders tend to have better balance?” Why or why not?
8. Berthio’s class decided to measure balance by finding out how long people can stand on one foot.
a. How would you rephrase the question above to create a statistical question using this definition of balance? Explain your reasoning.
b. What should the class think about to be consistent in how they collect the data if they actually have people stand on one foot and measure the time?

9. Work with your class to devise a plan to select a random sample of sixth graders and a random sample of seventh graders to measure their balance using Berthio’s method. Then, write a paragraph describing how you will collect data to determine whether there is a difference in how long sixth graders and seventh graders can stand on one leg. Your plan should answer the following questions:
• What is the population? How will samples be selected from the population? And, why is it important that they be random samples?
• How would you conduct the activity?
• What sample statistics will you calculate, and how you would display and analyze the data?
• What you would accept as evidence that there actually is a difference in how long sixth graders can stand on one leg compared to seventh graders.

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