# Mean Absolute Deviation

Many times in life we skip or jump or even leap to a level that is where we do not belong. If you are evaluating a series of information to better understand if something is common or even average the measure that makes the most sense to calculate falls into the acronym of MAD which stands for Mean Absolute Deviation. This value indicates how far the most common data value lies from the most deviant data value. In common words, it states how far everything in a information stream is off from the center. This value gives you a clear indication of how far everything is off center. While this does not clearly explain anything, it does vividly speculate how distantly from the middle your information is from being correct.

### Aligned Standard: Grade 6 Statistics - 6.SP.B.5C

- Step-by-Step Lesson- Rover is digging up bones all over the neighborhood. Is he being lazy or unlucky on some days? (MAD will tell us)
- Mean Absolute Deviation - Practice Worksheet 1 - We set them up on a nice chart for you. That will allow you to restate the data, determine the average, distance from the mean, and the MD.
- MAD of of Data Sets Worksheet 1 - These are all quick word - based problems and data sets.

- Answer Keys - These are for all the unlocked materials above.
- MAD Worksheet 2 - Complete the charts to determine the Mean Average Deviation.
- MAD Worksheet 3 - A nice surprise to help you nail this topic.
- MAD Worksheet 4 - More practice problems for you. The more reps you get with this skill, the easier it gets.
- Data Sets MAD Worksheet 2 - Mary recorded daily temperature with these totals for degrees, {75,72,71,83,86,79}. Calculate the average.
- Data Sets MAD Worksheet 3 - Mark worked at a vet clinic. He was curious what the mean absolute deviation was for the number of visitors per day in one week. Help him calculate using these figures, {25,13,24,16,7}.
- Data Sets MAD Worksheet 4 - Wendy bought 5 packs of bubble gum. Help her determine the mean absolute deviation of the gum with prices {$.50, $.60, $.43, $.65,$.52}
- MAD- Quiz 1 - You should be familiar enough with these by now to handle the problems.
- Data Based- Quiz 2 - Tom bought 6 packs of hamburger buns. Help him determine the mean absolute deviation of the buns with prices {$.90, $.60, $.93, $.85,$.72, $.86}

### What Is Mean Absolute Deviation?

A value that gives an insight into the degree of difference between a set of data in a set is known as mean absolute deviation. It is equal to the average distance between each value of the data and the mean of the data. It is very simple to calculate. If you know the exact center of the position, this measure just indicates how far you are off course from that. The step that you would take to derive this measure would be:

**Step 1: Calculate Mean** - Mean is the average value of the data set. You sum all the values in a data set and divide by the total number of values in the data set.

**Step 2: Calculate Absolute Deviation** - The next step is to find the difference between each data point and the mean using positive distances.

**Step 3: Sum all Absolute Deviations** - The third step is to sum all absolute deviations and divide the sum of these absolute deviations with the total number of terms.

### How is This Measure Used in the Real World?

Regardless of the nature of the data you are analyze this measure can be very helpful to make sense of the data. This measure basically tells you how far the population of data is from the average. Some analysts will refer to this as the strength of your data. The closer the data population is to the mean, the more closely the mean represents the data. A good way to visualize this is to think of a basketball video game. Often video game characters, in this case players, will have a rating as to how good they are. What if you had a team of 5 players that had a mean score of 80 out of 100? That team of 5 players could be assembled with skill levels any form of combination as long as the mean was 80 in the end. The players could all have the rating of 80, that would satisfy the mean. They would all be a solid reflection of that mean. You could also have a team of players with the following ratings: 40, 60, 100, 100, 100 or 70, 80, 90, 95, 65. In those cases, the mean would not be good reflection of all the players. Some players would be superstars and others would be weaker. As you can see this measure indicates how close all the data is to the calculated average.