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Glencoe Math Course: Online Textbook Help12 chapters | 94 lessons

Instructor:
*Lynne Hampson*

Lynne Hampson has a Masters in Instr. Design & Bach. in Elem./Spec. Educ. She taught 8 years in Elem. Core, Science, Coding, Microsoft, Internet Safety, and Life Skills.

In this lesson, we will first learn how to use the mean absolute deviation to find not only the average of a set of numbers but the average distance each number is from the average number. Then, we will show a step-by-step, real-world problem, to practice your skills.

**Mean absolute deviation** is the average distance between the mean of a set of numbers.

We must first understand **mean** before adding absolute deviation. Finding the mean is essentially finding the average of a set of numbers.

Once the mean is found, the next step is the **absolute deviation**. This part of the process is to determine the distance between each of the original numbers from the mean you found in step one.

Finally, find the mean of the second set of numbers.

Many professionals use the mean in their everyday lives. Teachers give tests to students and then average them to see if the average score was high, in between, or too low. Each average tells a story. Absolute deviation could further help to see the distance between each of the scores and the beginning average scores. Analyzing information in this way helps the teacher to see if the test was too hard, too easy, or just right, based upon the mathematical outcomes.

Biologists can use this concept to compare the differences in animal weight to decide what a healthy weight might be.

First, find the mean (average) of a number group. Let's say the number group is the rounded-up weight of infants at birth at a specific hospital in the month of January. Five births were recorded, so there should be five numbers representing their weights:

5 lbs., 9 lbs., 6 lbs., 7 lb., 8 lbs.

To find the mean, first add up the numbers: 5+9+6+7+8. The total should come to 35. Now, divide the number of birth weights by the total weight. 35/5= the mean (average) of 7.

Now, refer to your original 5 baby weights. Use addition or subtraction to find the difference in distance between each of those numbers and the average. If the difference is negative, ignore that it is negative. You are only looking for the distance apart, not the value regarding negative or positive. Keep record of your findings:

5 and 2 are 7

9 and 2 are 7

6 and 1 are 7

7 and 0 are 7

8 and 1 are 7

Add up the numbers again: 2 +2 +1 +0 + 1 = 6

Then, divide 4 by the number of weights again: 6/5= 1.2

So, the mean of the baby weights is 7, and the mean absolute deviation between the numbers is 1.2 lbs.

**Mean absolute deviation** is used to analyze statistics in many fields. Not only do you find the mean (average), but the distance between each number to the mean. There are several steps in completing the process. First, find the mean, then find the difference between the first set of data and the mean. Find the mean of those numbers in order to determine the average distance between each data number and the mean.

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Lesson
4 in chapter 11 of the course:

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Glencoe Math Course: Online Textbook Help12 chapters | 94 lessons

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