MEAN ABSOLUTE DEVIATION

Situation #1

Two different groups of people were surveyed about their height. The

results are on the following slides

6’ 3”7’ 9”

2’ 9”

4’

5’ 2”

4’6”

GROUP 1

Step 1: convert everyone’s height to inches (12 inches = 1 foot)

Step 2: Find the MEAN of everyone’s height (the average)

Step 3: Write a sentence about the average height. (sentence starter…the average height in group one is…..this means…..)

For Group 1:

4’ 8”5’ 8”5’ 3”4’ 10”5’ 5” 4’ 7”

GROUP 2

Step 1: convert everyone’s height to inches (12 inches = 1 foot)

Step 2: Find the MEAN of everyone’s height (the average)

Step 3: Write a sentence about the average height. (sentence starter…the average height in group one is…..this means…..)

For Group 2:

What did you notice about the average height in group 1 compared to the average height in group 2?

Now calculate the Mean Absolute Deviation for each group

Mean group 1 Each person height in

inches

Deviation from Mean

Mean of group 2

Each person height in

inches

Deviation from Mean

1. If the mean height for each group was the same, why was the MAD different for each group?

2. Which group would you prefer if you were forming a basketball team? Why?

3. Which group’s heights vary more from the mean?

Situation #2

You are the teacher for an 8th grade math class. It is time to enter your students final grades for the 6 weeks report card. Your principal has told you it is ok to round a students grade up or down depending on how much you feel that student understanding the material being taught.

Look the following 2 students and decide if you should adjust their grade or leave it the same

Student 1

30%50%50%70%90%100%90%

Student 2

75%75%75%75%75%70%35%

MEAN GRADE =

Mean Grade student 1

Each Grade of student 1

Deviation from Mean

Mean Grade student 2

Each Grade of student 2

Deviation from Mean

MAD student 1 = MAD student 2 =

1. What did you notice about the average grade for each student?

2. Why did the average come out the same, even though they earned different scores?

3. Did the MAD come out the same?

4. Which students has scores closer to the mean?

5. Do you think each student has earned this grade?

6. Would you round either students grade up to a 70?

Situation #3

Bowler #1 Scores

Bowler #1 Mean

Deviation from Mean

Bowler #2 Scores

Bowler #2 Mean

Deviation from Mean

150 200

50 200

250 200

75 200

300 75

MAD bowler #1 = MAD bowler #2=

1. What did you notice about the mean for each bowler?

2. Which bowler had better scores?

3. Which bowler had more consistent good scores?

4. Which bowler would you choose to be on your bowling team?

5. How could the mean be the same if the scores were so different?