Curriculum / Math / 7th Grade / Unit 7: Statistics / Lesson 9
Math
Unit 7
7th Grade
Lesson 9 of 9
Jump To
Identify meaningful differences between populations using the mean and mean absolute deviation (MAD) of samples.
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.A.3 — Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
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
Anchor Problems #1 and #2 are designed to happen concurrently in class, with half the class working on each problem. See the notes in Anchor Problem #1 to see how the two problems differ and what conclusions students should be guided toward.
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Below are the heights of the players on the University of Maryland women's basketball team for the 2012–2013 season and the heights of the players on the women's field hockey team for the 2012 season. Note: it is typical for a women's field hockey team to have more players than a women's basketball team would.
a. Based on visual inspection of the dot plots, which group appears to have the larger average height? Which group appears to have the greater variability in the heights?
b. Find the mean and the mean absolute deviation (MAD) for each group. Here is a list of the heights in numerical form: Anchor Problem 1 Data Set
c. What is the difference between the two sample means?
d. How many MADs separate the two means? If the MADs are different, use the larger value.
e. Do you think there is meaningful difference between the two centers? Is there statistical evidence to infer that female college basketball players are typically taller than female college field hockey players? Explain your reasoning.
f. Compare your conclusions with the half of your class who looked at Anchor Problem #2.
College Athletes, accessed on Feb. 6, 2017, 5:30 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
One particular position on a football team is called "offensive lineman," and it is generally believed that the offensive linemen of Division I schools are heavier on average than the offensive linemen of Division III schools.
For the 2012 season, the University of Mount Union Purple Raiders football team won the Division III National Football Championship, while the University of Alabama Crimson Tide football team won the Division I National Championship. Below are the weights of the offensive linemen for both teams from that season.
a. Based on visual inspection of the dot plots, which group appears to have the larger average weight? Which group appears to have the greater variability in the weights, or do they look similar?
b. Find the mean and the mean absolute deviation (MAD) for each group. Here is a list of the weights in numerical form: Anchor Problem 2 Data Set
e. Do you think there is meaningful difference between the two centers? Is there statistical evidence to infer that offensive linemen of Division I schools are heavier on average than offensive linemen of Division III schools? Explain your reasoning.
f. Compare your conclusions with the half of your class who looked at Anchor Problem 1.
Offensive Linemen, accessed on March 29, 2018, 2:20 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
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
Raj was curious if animated movies tended to be shorter in length than action movies. He took a random sample of action movies released in 2015 and of animated movies released in 2015 and found the length of each movie in minutes. His results are shown in the dot plots below.
a. Which statement below is best supported by Raj’s sample data?
a. Every action movie in 2015 was longer in length than every animated movie in the same year.
b. At least one animated movie in 2015 was longer in length than an action movie in 2015.
c. There is greater variability in the sample lengths for action movies than there is for animated movies.
d. The sample mean length of time for action movies is about the same as the sample mean length of time for animated movies in 2015.
b. Raj calculates the mean and MAD for each sample. The mean length of action movies is 131 minutes and the MAD is 7.3. The mean length of animated movies is 95 minutes and the MAD is 4.7. Does there appear to be a meaningful difference between the lengths of action movies and the lengths of animated movies from 2015? 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.
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
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
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 different populations by analyzing visual data distributions.
Compare populations by analyzing numerical data.
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
Access rigorous, relevant, and adaptable math lesson plans for free