Statistics

Lesson 10

Math

Unit 8

6th Grade

Lesson 10 of 14

Objective


Understand and determine mean absolute deviation (MAD) as a measure of variability of a data set.

Common Core Standards


Core Standards

  • 6.SP.B.5.C — Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Criteria for Success


  1. Understand the mean absolute deviation (MAD) as a measure of variability of a data set. 
  2. Determine the MAD of a data set by finding the mean and the average distance of each data point from the mean.
  3. Understand that the higher the MAD of a data set, the greater the variation or spread of the data, and the lower the MAD, the less variation or spread of a data set.

Tips for Teachers


  • This GeoGebra applet One-Variable Data Analysis is a helpful tool to analyze data sets and determine mean, median, MAD, etc. It works best with small data sets that fit within the window.
  • If you are teaching in Massachusetts, you may consider skipping this lesson, as the concept of mean absolute deviation is introduced in 7th Grade in the MA Curriculum Frameworks.

Lesson Materials

  • Standard deck of playing cards (1 per small group)
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Anchor Problems


Problem 1

In groups of two or three, play the Game of 22.

Your teacher will give your group a deck of cards. Shuffle the cards, and put the deck face down on the playing surface.

  • To play: Draw three cards and add up the values. An ace is worth 1. A jack, queen, and king are each worth 10. Cards 2–10 are each worth their face value. If your sum is anything other than 22 (either above or below 22), say: “My sum deviated from 22 by ____ ” or “My sum was off from 22 by ____ .”
  • To keep score: Record each sum and each distance from 22 in the table. After five rounds, calculate the average of the distances. The player with the lowest average distance from 22 wins the game.

Sample Table:

Player Name Round 1 Round 2 Round 3 Round 4 Round 5
Sum of cards          
Distance from 22          

Average distance from 22: _________

If a player had a high average distance from 22 at the end, what do you notice about their sums in each round? How is this different from a player who had a low average distance from 22 at the end?

Guiding Questions

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References

Open Up Resources Grade 6 Unit 8 Lesson 11Lesson 11.4: Game of 22

Grade 6 Unit 8 Lesson 11 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 29, 2018, 1:18 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Shot put is an event in track and field that involves throwing a heavy ball, or shot, as far as possible.

In a high school competition, Michelle and Christina compete in the shot put event. Their distances, in feet, for their first five throws are shown below.

Michelle 32 22 35 23 38
Christina 28 29 34 29 30

a.   Complete a table, like the one below, for Michelle and for Christina to determine the MAD for each competitor. 

Throw 1 2 3 4 5  
Distance (ft.)                               Mean:
Distance from mean (ft.)           MAD:

b.   What does the mean tell you about each competitor’s data set?

c.   What does the MAD tell you about each competitor’s data set? 

Guiding Questions

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Problem Set

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Target Task


Over a two-week period, Jenna had the following number of math homework problems given each day:

20,   0,   7,   10,   1,   11,   0,   25,   15,   1

a.   What is the mean number of homework problems Jenna had?

b.   What is the MAD of the number of homework problems?

c.   What do the mean and MAD tell you about the number of homework problems Jenna had over these two weeks?

Student Response

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References

Illustrative Mathematics Math Homework Problems

Math Homework Problems, accessed on March 29, 2018, 1:28 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.

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 9

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Lesson 11

Lesson Map

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

Topic A: Understanding Statistics & Distributions

Topic B: Measurements of Center & Variability

Topic C: Box Plots & Circle Graphs

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