Curriculum  /  Math  /  7th Grade  /  Unit 7: Statistics  /  Lesson 5

Statistics

Lesson 5

Math

Unit 7

7th Grade

Lesson 5 of 9

Objective

Determine the impact of sample size on variability and prediction accuracy.

Common Core Standards

Core Standards

  • 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.A.3
  • 6.SP.B.4
  • 6.SP.B.5

Criteria for Success

  1. Understand that larger sample sizes tend to provide more accurate predictions of the population than smaller sample sizes. 
  2. Understand that larger sample sizes tend to produce less variability in the sample distribution than smaller sample sizes.
  3. Understand that the less variability in a data set, the more accurate predictions tend to be.

Tips for Teachers

  • To prepare for this activity, each group of students will need a brown paper bag filled with 20 cubes. Of the 20 cubes, 5 should be blue and the other 15 can be any other color. Provide each group with a table and number line for their dot plot. 
  • Students work in groups of two or three. Have half of the class conduct Trial A (Anchor Problem 1) and the other half of the class conduct Trial B (Anchor Problem 2). Note, Trial B may take slightly longer than Trial A due to the increased sample size.
  • The goal of these Anchor Problems is to guide students toward discovering three tendencies: 1) the larger the sample size, the more accurate a prediction based on the sample tends to be, 2) the larger the sample size, the less variability in the sample distribution, and 3) the less variability in a data set, the more accurate a prediction tends to be.  

Lesson Materials

  • Brown bag (2 per pair of students)
  • Cubes (1 set per small group) — 5 of one color and 15 of different color(s)
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Anchor Problems

25-30 minutes

Problem 1

Your group will conduct Trial A. Follow the directions listed below:

  1. Select 3 cubes from the bag and take note of how many blue cubes are in your sample.
  2. Calculate and record the percentage of cubes in your sample that are blue. Use the table below.
  3. Repeat the first two steps 10 times.
  4. Draw a dot plot to represent the percentages of blue cubes from your 10 samples.
  5. Find the mean and mean absolute deviation (MAD) of your data.
  6. Make a prediction of the percent of blue cubes in the bag based on your data.
     
Sample 1 2 3 4 5 6 7 8 9 10
% Blue                    

 

Guiding Questions

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Student Response

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Problem 2

Your group will conduct Trial B. Follow the directions listed below:

  1. Select 10 cubes from the bag and take note of how many blue cubes are in your sample.
  2. Calculate and record the percentage of cubes in your sample that are blue. Use the table below.
  3. Repeat the first two steps 10 times.
  4. Draw a dot plot to represent the percentages of blue cubes from your 10 samples.
  5. Find the mean and MAD of your data.
  6. Make a prediction of the percent of blue cubes in the bag based on your data.
     
Sample 1 2 3 4 5 6 7 8 9 10
% Blue                    

Guiding Questions

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Student Response

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Problem 3

As a class:

a.   Look at the results from each trial as a whole class.

b.   Find the actual percentage of blue cubes in the bag.

c.   How do the mean percentages of blue cubes from Trial A and Trial B compare to the population percentage? Which trial was more accurate? Why do you think this is so?

d.   What conclusions can you draw about sampling size, variability, and accuracy?

Guiding Questions

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Student Response

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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

Three data sets are shown below. 

a.   Estimate each population mean based on the data in the samples.

b.   Which estimate do you think is most accurate? Explain your reasoning.

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

Estimate population proportions using sample data.

Lesson 6
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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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