Statistics

Lesson 8

Math

Unit 7

7th Grade

Lesson 8 of 9

Objective


Compare populations by analyzing numerical data.

Common Core Standards


Core Standards

  • 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.

Foundational Standards

  • 6.SP.B.5

Criteria for Success


  1. Find measures of center and variation of numerical data sets and use them to better understand data sets.
  2. Compare populations by looking at numerical data sets simultaneously, and draw inferences about the populations using statistical measures.

Tips for Teachers


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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Anchor Problems


Problem 1

James wants to get to work as quickly and reliably as possible in the mornings. He tries three different transport methods:

  • cycle all the way
  • drive all the way
  • walk to the railway station, take the train, and walk from the station

He tries each method several times and records how many minutes the entire journey takes:

Bicycle 28 24 25 29 25 26 26 23 29 25
Car 19 21 32 57 31 27 21 24    
Walk-train-walk 21 24 31 26 24 30        

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. 

Guiding Questions

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References

MARS Formative Assessment Lessons for Grade 7 Comparing Data Using Statistical Measures

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..

MARS Formative Assessment Lessons for Grade 7 Assessment Task "Getting James to Work"

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..

Problem 2

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.

Infant (birth-3 months) 110 145 130 150 145
Toddler (1-3 years) 85 95 80 75 100
Big kid (12+ years) 70 65 70 75 80

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.

Guiding Questions

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Target Task


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. 

  Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
# of goals in fall season 3 8 6 2 3 5
# of goals in spring season 6 6 4 5 4 5

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.

Student Response

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Additional Practice


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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Lesson 7

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Lesson 9

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Populations and Samples

Topic B: Using Sample Data to Draw Inferences About a Population

Topic C: Using Sample Data to Compare Two or More Populations

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