Mean Absolute Deviation

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

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.

Phase

Before/Engage

Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.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.

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

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.

Activity Details

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?

Variation Tips

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.

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

Background / 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.

Learning Activity (Before)

Mean Absolute Deviation

Learning Activity (During)

Calculate Standard Deviation

Learning Activity (After)

Quizizz Standard Deviation

Deviations – Mean Absolute vs. Standard

https://drive.google.com/file/d/1CBxKkyd-ChjjBALPUzyYDEdMZjYYc0YY/view?usp=shar…

Approved Date

2022-07-23

Owner (Author)

pamelawest

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