ALEX Learning Activity

  

Mean Absolute Deviation

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  This learning activity provided by:  
Author: Pamela West
System:Montgomery County
School:Montgomery County Board Of Education
  General Activity Information  
Activity ID: 2918
Title:
Mean Absolute Deviation
Digital Tool/Resource:
Deviations – Mean Absolute vs. Standard
Web Address – URL:
Overview:

In this learning activity, students will make a comparison of Deviations – Mean Absolute vs. Standard – 

This learning activity allows a brief review of the Mean Absolute Deviation compared to the Standard Deviation. The expectation is for the students to understand they are related.
  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Geometry with Data Analysis
10. Use statistics appropriate to the shape of the data distribution to compare and contrast two or more data sets, utilizing the mean and median for center and the interquartile range and standard deviation for variability.

a. Explain how standard deviation develops from mean absolute deviation.

b. Calculate the standard deviation for a data set, using technology where appropriate.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given two or more different data sets,
  • Compare the center (median, mean) and the spread (interquartile range, standard deviation) of the data sets to describe differences and similarities of the data sets.
  • Explain how standard deviation develops from mean absolute deviation.
  • Calculate the standard deviation for a data set, and use technology where it is appropriate.
Teacher Vocabulary:
  • Center
  • Median
  • Mean
  • Spread
  • Interquartile range
  • Standard deviation
  • Absolute mean deviation
Knowledge:
Students know:
  • Techniques to calculate the center and spread of data sets.
  • Techniques to calculate the mean absolute deviation and standard deviation.
  • Methods to compare data sets based on measures of center (median, mean) and spread (interquartile range and standard deviation) of the data sets.
Skills:
Students are able to:
  • Accurately find the center (median and mean) and spread (interquartile range and standard deviation) of data sets.
  • -Present viable arguments and critique arguments of others from the comparison of the center and spread of multiple data sets.
  • Explain their reasoning on how standard deviation develops from the mean absolute deviation.
Understanding:
Students understand that:
  • Multiple data sets can be compared by making observations about the center and spread of the data.
  • The center and spread of multiple data sets are used to justify comparisons of the data.
  • Both the mean and the median are used to calculate the mean absolute and standard deviations
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
GEO.10.1: Accurately find the center (median and mean) and spread (interquartile range and standard deviation) of data sets.
GEO.10.2: Present viable arguments and critique arguments of others from the comparison of the center and spread of multiple data sets.
GEO.10.3: Reason how standard deviation develops from the mean absolute deviation.

Prior Knowledge Skills:
  • Define measure of variability, distribution, and measure of center.
  • Compare the measure of center and measure of variability of two distributions.
  • Relate the measure of variation with the concept of range.
  • Relate the measure of the center with the concept of mean.
  • Recall how to calculate measure of center and measure of variability.
Alabama Alternate Achievement Standards
AAS Standard:
M.G.AAS.9.9 10 After collecting data or with given data, construct a simple graph (line, pie, bar, picture, etc.) or table and interpret the data in terms of range and mode.

Learning Objectives:

The students will be able to:

  • Explain the difference between mean absolute deviation and standard deviation

  • Compare the center, shape, spread, and unusual features of multiple data sets.

  • Calculate and learn to interpret the standard deviation of a data set using students’ conceptual understanding of mean absolute deviation.

  • Use technology to determine the standard deviation.
  Strategies, Preparations and Variations  
Phase:
Before/Engage
Activity:

Deviations: Mean Absolute vs. Standard

  • The teacher will have students work in pairs or small groups for this activity.

  • The teacher will pass out copies of the Deviations: Mean Absolute vs. Standard worksheet.

  • The lesson begins by having the students look at the page's top and calculate the data set's mean. The teacher will review the answer once everyone has calculated the mean.

  • Next, the teacher will have the students look at the left side of the page and he/she will teach the students how to find the requested data using the first row of the chart on the left side.

  • Once the teacher has taught how to find the data on the left side, he/she will set a timer for 6-8 minutes (based on the level of the students) to keep students on track. The teacher will instruct the students to work with their partners to fill in the remaining left side. The teacher will monitor the students' work to make notes for reviewing the lesson whole group.

  • After everyone has completed filling in the left side, the teacher will as the students to move to the right side of the page. The teacher will complete the first row as a whole group drawing students’ attention to the first 3 columns. They are the same for both types of deviations.

  • Next, the teacher will instruct the students to complete the right side of the page. The teacher will allow the students to work for about 5-6 minutes to complete the chart.

  • The teacher will review the answers to the page with a whole class discussion using the notes he/she collected from observing the students. The teacher will point out errors that could be made during calculations.
Assessment Strategies:

  • The student responses during class discussion and group work will be used as a formative assessment.

  • The teacher will make notes while the students are working to help with whole group discussion at the end of the lesson.

  • If time permits, close the class with an exit ticket, “What are the differences and similarities of mean absolute deviation and standard deviation?
Advanced Preparation:

  • Students should be familiar with quantitative measures of mean absolute deviation, interquartile range, and range to a new quantitative measure of spread called standard deviation.

  • The teacher should note students are not required to calculate standard deviation by hand, but the standard does require students to connect the idea of standard deviation to spread. 

  • The teacher needs to choose the piece of technology that best fits their classroom situations to display the Deviations: Mean Absolute vs. Standard worksheet.

  • The teacher will make copies of the Deviations: Mean Absolute vs. Standard worksheet.

 
Variation Tips (optional):

As the teacher monitors the pairs or groups and the teacher notices the class is struggling, he/she may want to model more problems whole group and then break into smaller groups.

 
Notes or Recommendations (optional):

The teacher should note the worksheets can stand alone if needed due to time constraints.

 

This activity corresponds to the "During" activity Calculate Standard Deviation and the "After" activity Quizizz Standard Deviation.
  Keywords and Search Tags  
Keywords and Search Tags: Mean, Mean Absolute Deviation, Range, Spreads, Standard Deviation