Mean Absolute Deviation

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Objective

SWBAT: • Collect and display data in a table and line plot • Define mean absolute deviation. • Calculate the mean and mean absolute deviation of a data set. • Compare the distribution of two data sets using mean absolute deviation.

Big Idea

What is mean absolute deviation? Students apply their knowledge of mean and absolute value to understand mean absolute deviation. Students collect data about estimating 30 seconds that they will use in the next lesson.

Do Now

7 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to analyze a bar graph in order to answer questions. Each edition of Scholastic Action  typically includes a graph at the end each edition.

I ask for students to share their thinking.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

How long is 30 seconds?

7 minutes

I read over the questions.  I call on students to share out their answers.  Most students think they are a pretty good judge of passing time.  Students may bring up situations like having a job where it is important to be able to accurately judge how much time has passed.

For step 1, I ask students which question is a statistical question.  I want students to realize that the second question is interesting, it addresses a specific population, and it will allow for variability.

I explain that students will get a laptop to use the count up timer to measure the amount of time that has passed.  I ask students what procedures are important to have in place to ensure that our data is accurate.  Students participate in a Think Pair Share.  I call on students to share their ideas.  My students wanted to make sure that students didn’t look at the clock or watches.  They also wanted to make sure that the student was not able to see the count up timer of another group.  They also brought up that students shouldn’t count out loud because it might distract others.

Collecting the Data

5 minutes

Notes:

  • Students will need access to a laptop or another timer. 
  • I put students in groups of 2-3 to time each other.

Each group gets a laptop and collects their data. Once they are finished, they record their data on the “Our Class Data” sheet that I have displayed on the document camera.  I will use this data to input into the next lesson’s packet, Comparing Mean Absolute Deviation.  Students are engaging in MP5: Use appropriate tool strategically and MP6: Attend to precision.

Measures of Center vs. Measures of Variability

5 minutes

I review the vocabulary with students.  Students should recognize that the measures of center (or central tendencies) are mean, median, and mode.  Students should be familiar with the differences and similarities between range and interquartile range.

Mean absolute deviation is a new term for my students.   I acknowledge that it sounds intimidating, but I assure students that their existing knowledge will help them make connections.  I break down the different parts of MAD by review what students know about mean and absolute value.  I explain that deviation is just a fancy word for the difference between values.

Students may be overwhelmed by this definition, but I assure them that we will work together during this lesson and the next lesson to build an understanding of MAD.

Calculating MAD

16 minutes

I explain that Data Set A and B came from two groups of people measuring how long each person thought it took for 30 seconds to pass.  Students use the data in the tables to create two line plots. 

I ask students what they notice about these data sets.  I want students to notice that the values in Data Set B are more spread out.  Students may compare the ranges of the two data sets.  I want students to notice that the values in Data Set A are more clustered together. 

I ask students to make a prediction: Which data set will have the higher MAD?  Students participate in a Think Pair Share.  I call on students to share their ideas.  Some students may recognize that the MAD of Data Set B will be bigger, since the values are more spread out. 

Next we go through the steps of calculating the MAD together.  To help speed up the process, I give students the sum of each data set so they can more efficiently calculate the mean.  We label the mean on each grid.  Then we go through the data set and count the distance from each value in the set and the mean.  For example, for Data Set A the mean is 29.  For the value 26, I put a 3 in the grid above the 26, since that value is 3 seconds away from the mean.  Since there are three 26’s, my grid will have three 3’s stacked on top of the 26. I do this for each value of in the set.  I do not put positive and negative distances.  Instead, I just explained to students that we were finding the absolute distance between the value and the mean.   I found that the grid helped students to organize the distances and see their distribution. 

The last step is to add up all of the distances and divide by the number of values in the data set.  We revisit the predictions that students made at the beginning of this section.

Closure and Ticket to Go

10 minutes

I read over the questions.  Students participate in a Think Pair Share.  I want students to be able to use the line plot to explain that the values in Data Set B are further from the mean, compared to Data Set A.   I want students to be able to summarize that the MAD measures the average distance between each point in a data set and the mean.  Furthermore, if Data Set C has a MAD of 12.4 seconds it tell us that the values are more spread out from the mean than the values in Data Set A and Data Set B.  Just from the MAD we do not know the mean or values in the data set. I pass out the Ticket to go and the Homework.