Curriculum / Math / 7th Grade / Unit 7: Statistics / Lesson 8
Math
Unit 7
7th Grade
Lesson 8 of 9
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Lesson Notes
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Compare populations by analyzing numerical data.
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 Lesson 7, students compared two populations, leaning in on visual representations of data such as dot plots. In this lesson, students continue to compare populations, this time using statistical measures such as mean and mean absolute deviation. In the next lesson, students will use these measures to assess if there is a statistically significant difference between the populations’ data.
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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
James wants to get to work as quickly and reliably as possible in the mornings. He tries three different transport methods:
He tries each method several times and records how many minutes the entire journey takes:
a. Use the data to make a case for why he should travel to work by bicycle.
b. Use the data to make a case for why he should travel to work by car.
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Comparing Data Using Statistical Measures from the Classroom Challenges by the MARS Shell Center team at the University of Nottingham is made available by the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed July 20, 2016, 1:05 p.m..
Assessment Task "Getting James to Work" from the Classroom Challenges by the MARS Shell Center team at the University of Nottingham is made available by the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed Nov. 21, 2022, 6:23 p.m..
As children grow up, their resting heart rate in beats per minute changes. The table below shows a sample of resting heart rates in beats per minute (bpm) for children at different ages.
a. Find the mean and mean absolute deviation for each data set by age.
b. Use your statistical measures from part A to compare the resting heart rates for children at different ages. Explain your reasoning.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
The Yellow co-ed soccer team has a season in the fall and another season in the spring. During each season they play six games. The number of goals that the Yellow team scored in each season last year is shown below.
a. Find the mean and MAD for the data set for each season.
b. Use your statistical measures you found in part A to write two observations that compare the two seasons.
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
Identify meaningful differences between populations using the mean and mean absolute deviation (MAD) of samples.
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
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.
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