Curriculum / Math / 7th Grade / Unit 7: Statistics / Lesson 3
Math
Unit 7
7th Grade
Lesson 3 of 9
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Generate a random sample for a statistical question.
The core standards covered in this lesson
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.
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
Suggestions for teachers to help them teach this lesson
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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
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?
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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..
(See the Notes below for preparation for this problem.)
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?
A set of suggested resources or problem types that teachers can turn into a 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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
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.
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.
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.
7.SP.A.17.SP.A.2
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Topic B: Using Sample Data to Draw Inferences About a Population
7.SP.B.37.SP.B.4
Determine the impact of sample size on variability and prediction accuracy.
7.SP.A.2
Estimate population proportions using sample data.
Topic C: Using Sample Data to Compare Two or More Populations
Compare different populations by analyzing visual data distributions.
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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