Curriculum / Math / 7th Grade / Unit 7: Statistics / Lesson 6
Math
Unit 7
7th Grade
Lesson 6 of 9
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Estimate population proportions using sample data.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
6.SP.B.4 — Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.B.5 — Summarize numerical data sets in relation to their context, such as by:
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Akilah is running for seventh-grade class president. There are 100 students in the seventh grade at her school. To better understand her chances of winning, Akilah asks a random sample of 20 seventh graders if they plan to vote for her. In her sample, 12 out of the 20 students said they planned to vote for her. Akilah asks several friends to also ask a random sample of 20 students. Together, they combine their results to get a better understanding of her chances of winning. After winning the election, Akilah finds out that 55 out of the 100 seventh graders at her school voted for her.
Using the situation above, define and describe the following terms:
a. sample
b. population
c. sample proportion
d. population proportion
e. sample distribution
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All two hundred middle school students at Roosevelt Middle School responded to several survey questions, and the results were combined in a table which your teacher will share with you.
The first column represents a unique student ID number for each student. The last column represents students’ responses to the question “Which of the following superpowers would you most like to have: invisibility, super strength, telepathy, fly, or freeze time?”
The class wants to determine the proportion of Roosevelt Middle School students who choose freeze time as their superpower.
a. In your group, use the random number table to collect a random sample of 20 student responses to the superpower question. Record your data in a table.
b. Determine the sample proportion for your sample.
c. Will the other groups in your class have the same sample proportion as you? Explain your reasoning.
d. Collect the sample proportions from the class and present the distribution in a dot plot. According to the dot plot, what is a good estimation for the population proportion? What is a good estimation for the number of students who chose freeze time as their superpower?
Grade 7 Mathematics > Module 5 > Topic C > Lesson 20 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..
This diagram shows some trees in a tree farm. The circles show old trees and the triangles show young trees. Tom wants to know how many trees there are of each type, but he says it would take too long to count them all one by one. (Note, there are 50 columns and 50 rows in the diagram.)
a. What method could he use to estimate the number of trees of each type? Explain your method fully.
b. On the Counting Trees Worksheet, use your method to estimate the number of old trees and young trees.
Counting Trees from the Summative Assessment Tasks for Middle School is made available through the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed March 29, 2018, 12:40 p.m..
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15-20 minutes
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
A developer purchased an empty building on the corner of a busy intersection. She wants to open up a commercial business and is deciding between three options: coffee shop, barber shop, or deli/market.
She collects a random sample of 25 residents in the local neighborhood and asks them, “Which type of business would you prefer to have in the empty building: a coffee shop, a barber shop, or a deli/market?” Her results are shown below.
a. What is the sample proportion in favor of opening a deli/market?
b. Estimate the population proportion in favor of opening a deli/market.
c. If there are about 500 residents in the local neighborhood, about how many can be expected to be in favor of a deli/market?
d. The developer decided to repeat her random sample of 25 residents several more times to ensure she had the most accurate prediction. The dot plot below shows the distribution of sample proportions. Based on the information in the dot plot, should the developer consider opening a deli/market in the empty building? Explain your reasoning.
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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Compare different populations by analyzing visual data distributions.
Topic A: Understanding Populations and Samples
Understand and identify populations and sample populations for statistical questions.
Standards
7.SP.A.1
Describe sampling methods that result in representative samples.
Generate a random sample for a statistical question.
7.SP.A.17.SP.A.2
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Topic B: Using Sample Data to Draw Inferences About a Population
Analyze data sets using measures of center and measures of variability.
7.SP.B.37.SP.B.4
Determine the impact of sample size on variability and prediction accuracy.
7.SP.A.2
Topic C: Using Sample Data to Compare Two or More Populations
Compare populations by analyzing numerical data.
Identify meaningful differences between populations using the mean and mean absolute deviation (MAD) of samples.
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