Curriculum / Math / 7th Grade / Unit 7: Statistics / Lesson 7
Math
Unit 7
7th Grade
Lesson 7 of 9
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Compare different populations by analyzing visual data distributions.
The core standards covered in this lesson
7.SP.B.3 — Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
7.SP.B.4 — Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
The foundational standards covered in this lesson
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
In Lessons 7 through 9, students bring together the concepts they’ve learned in the unit thus far to compare more than one population using samples.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
The diagram below shows a sample distribution of female life expectancies for Africa and for Europe.
Which statements best describe the data in the diagram above? Select all that apply and explain your reasoning for each one.
a. The mean life expectancy for females in Europe is greater than the mean life expectancy for females in Africa.
b. The mean absolute deviation (MAD) for Europe is similar to the MAD for Africa.
c. There are some females in Africa who are expected to live longer than some females in Europe.
d. There is significant overlap in the sample distributions of the two countries.
e. The sample distribution for life expectancies for females in Africa is skewed right.
f. The range of life expectancies for females in Europe is less than the range of life expectancies for females in Africa.
Progressions for the Common Core State Standards in Mathematics (6-8 Statistics and Probability), by the Common Core Standards Writing Team is made available by Institute for Mathematics and Education, University of Arizona. © 2007 The Arizona Board of Regents. All contents copyrighted. All rights reserved. Accessed March 29, 2018, 6:51 p.m.. For updates and more information about the Progressions, see http://ime.math.arizona.edu/progressions.
The box plots below show the average amount of time a sample of seventh graders and eleventh graders spend on homework each night.
a. Is there a lot of overlap in the number of hours seventh graders and eleventh graders spend on homework each night?
b. Do any seventh graders in the sample spend more time on homework than an eleventh grader in the sample?
c. Does it appear that most of the eleventh graders spend more time on homework than seventh graders? Explain your reasoning.
d. Anup is a seventh grader and he believes the variability in the seventh grade data and in the eleventh grade data is about the same. Do you agree with Anup? Explain your reasoning.
A set of suggested resources or problem types that teachers can turn into a problem set
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
The box plots below show the heights of a sample of NBA basketball players and the heights of a sample of high school basketball players.
Which statements best describe the data? Select all that apply and explain your reasoning for each one.
An example response to the Target Task at the level of detail expected of the students.
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.
Lesson 6
Lesson 8
Topic A: Understanding Populations and Samples
Understand and identify populations and sample populations for statistical questions.
7.SP.A.1
Describe sampling methods that result in representative samples.
Generate a random sample for a statistical question.
7.SP.A.1 7.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.3 7.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 populations by analyzing numerical data.
Identify meaningful differences between populations using the mean and mean absolute deviation (MAD) of samples.
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