How to Compute the Mean Deviation

The "mean deviation" is a measure of how spread out or how concentrated a series of values is. You can think of it as finding the mean of the mean. Suppose you run a restaurant and have a 12-oz. New York strip steak on the menu. You cut your own steaks in-house and want them all to be close to 12 oz. Too light, and you are cheating the customer. Too heavy, and you are losing profit. The mean deviation will tell you if your steaks are consistently near 12 oz.

Instructions

1. Collect your data and find the mean.

   Using the steak example, you would cut a number of steaks, weigh them, add their weights together and divide this sum by the number of steaks you weighed. If you cut five steaks weighing 9.2 oz., 15.6 oz., 11.6 oz., 12.3 oz. and 14.1 oz., the sum would be 62.8 oz. Divided by 5, you would find their mean weight to be 12.56 oz. That's the kind of mean you want. It is close to 12 oz. and is above it rather than below it. You will look like a generous restaurateur without sacrificing too much profit.

   Although this is just an example--in reality--a sample size of five is not enough. It is important to use a large, random sample. In fact, the larger the sample is, the better--within practicality.

2. Subtract the mean from each value individually, and convert these differences to their absolute value.

   In the steak example:

   | 9.2 -- 12.56 | = 3.36
   | 15.6 -- 12.56 | = 3.04
   | 11.6 -- 12.56 | = 0.96
   | 12.3 -- 12.56 | = 0.26
   | 14.1 -- 12.56 | = 1.54

3. Add these values, and divide by the sample size. This is the mean deviation.

   In the steak example:

   3.36+3.04+0.96+0.26+1.54 = 9.16
   9.16 / 5 = 1.83

   Thus, in the example, the mean deviation in the five steaks is 1.83 oz. What this means is that, on average, each steak is 1.83 oz. away from the mean of 12.56 oz. If you divide those numbers, that works out to roughly a 15 percent average variation. As you can see, that is not what you want. It means many of your steaks are too light or too heavy. The mean itself is good--at 12.56 oz.--but some individual steaks are way off the mark. The steak weighing 9.2 oz. would cheat the customer by a big margin. The steaks weighing 14.1 oz. and 15.6 oz. would be way too generous and would cut into your profits.

   You can see how the mean deviation is useful information here. If you really were running a restaurant, you could look at this number and realize that you would have to tell the person cutting the steaks to do a better job, because the individual steak weights are spread out too far and need to be more consistent.

References

• Wolfram MathWorld
• College of the Sequoias