How to Calculate a Standard Deviation
We can calculate the standard deviation in just
Hi, I'm Ben Owens. I'm a math educator at the University of North Texas, here for About.com, to help you calculate standard deviation.So, say I've just given my students a math exam, and these are the results. The mean, or average, of this class is 72. The standard deviation would tell us how far all the results are from the average. I know the formula for calculating the standard deviation seems pretty overwhelming, but basically, we can calculate the standard deviation in just 5 steps.First, we subtract the average from each data point. In our case, from each exam result. So, we subtract 72 from 85, then from 83, and so on. After that, we square each data point. So we square all the exam results. Let's start again with 85, square is 9.2. You do this for all your data points. When you're done with that, we just add all of these up. We divide the sum of all this by n, and square root of that. And there you go. We've calculated the standard deviation.A small standard deviation, close to zero, means that the data are very tightly packed around the mean. And a large standard deviation indicates that the data are more spread out. For more on math, visit education.about.com. Thanks for watching!
- Appraisal: French Bru Doll, ca. 1895
- Appraisal: 1919 Rockwell "The Little Model" Oil Painting
- Appraisal: Jessie Willcox Smith Oil Painting with...
- September 4, 2013 - "Impressionism, Fashion, and Modernity"
- ANTIQUES ROADSHOW - Appraisal: 1909 Charles R. Knight Oil
- Appraisal: Chinese Enameled Porcelain Bowl, ca. 1920