Mean Absolute Deviation

Definition The average distance each data point is from the mean of all the data points. HUH?!?!? I know this is confusing but lets try going through an example and see if that helps you understand exactly what this all means!

To Find the M.A.D. Example: The chart below represents money raised at a school fair. Bake Sale$50 Lemonade Stand$35 Dunk Tank$75 Pie in the Face$15 Crafts$40 Pizza Stand$25 STEP 1: Find the mean of the set of numbers by adding each data point and dividing by the number of data points. 240 / 6 = 40

STEP 2: Find the difference between each data point and the mean. Find the absolute value of the difference and record that number in the chart below. To Find the M.A.D. FundraiserAmount Raised Difference from Mean Absolute Value of the Difference Bake Sale$50 Lemonade Stand$35 Dunk Tank$75 Pie in the Face$15 Crafts$40 Pizza Stand$25 STEP 3: Find the mean of the “absolute value of the differences.” FundraiserAmount Raised Difference from Mean Absolute Value of the Difference

To Find the M.A.D =90 Step 4: Find the mean of the sum of the absolute values of the differences: 90/6=15 M ean A bsolute D eviation Each fundraiser is $15 dollars away from each total “on average”. This is either $15 more or $15 less.

What Does the Mean Absolute Deviation Indicate to the Reader? It indicates how far each data point is from the mean, “on average.” A “large” MAD indicates that the information is spread far out from the mean. A “small” MAD means that the information is more clustered and therefore more predictable. “LARGE” and “SMALL” are relative terms… it depends on what the unit of measure you are discussing is and other factors.

Mr. Frommann compared the mean absolute deviation for his 4 math classes with his sister who is teacher in Florida. Mr. Frommann had a mean absolute deviation of 3 students. His sister had a mean absolute deviation of 10 students. What can you conclude about the class sizes for Mr. Frommann and his sister? All of Mr. Fro’s classes are close in size while his sister has class sizes that are very different. They may be bigger or smaller, we just can’t tell which. MAD does not tell us the size of the classes!!!

Can you think of a time where mean absolute deviations of 3 and 10 are actually close in value? They would be close in value if you were discussing the number of students on an entire team or in a whole school. Another example would be if you were examining the total number of points scored by a football team over the course of many seasons.

Write “large impact” or “small impact” on the line next to each of the following scenarios. 1) A mean absolute deviation of $150 in the bank account of several professional athletes. _____________ 2)A mean absolute deviation of $150 dollars in the bank account of several 10 year-olds. ______________ How can one of these situations be a large impact and the other a small? $150 is a small amount if you are talking about an athlete who makes millions of dollars. But if you are talking about a 10 year-old, $150 is a lot of money small impact large impact

Write “large impact” or “small impact” on the line next to each of the following scenarios. 1) A mean absolute deviation of 1000 citizens when conducting a census population count for an entire state. _____________ 2)A mean absolute deviation of 40 miles when surveying how far people drive to reach work each morning. ______________ 3)A mean absolute deviation of 3 points on a test that is worth 100 points. ______________ 20 points. ______________ small impact large impact small impact

The mean absolute deviation of a set of numbers is 8. Describe a situation where this would be a large mean absolute deviation. The mean absolute deviation of a set of numbers is 97. Describe a situation where this would be a small mean absolute deviation.