What is a standard deviation?

One standard deviation away from the mean in either direction on the horizontal axis (the two shaded areas closest to the center axis on the above graph) accounts for somewhere around 68 percent of the people in this group. Two standard deviations away from the mean (the four areas closest to the center areas) account for roughly 95 percent of the people. And three standard deviations (all the shaded areas) account for about 99 percent of the people. If this curve were flatter and more spread out, the standard deviation would have to be larger in order to account for those 68 percent or so of the people. So that’s why the standard deviation can tell you how spread out the examples in a set are from the mean. Why is this useful? Here’s an example: If you are comparing test scores for different schools, the standard deviation will tell you how diverse the test scores are for each school. Let’s say Springfield Elementary has a higher mean test score than Shelbyville Elementary. Your first reaction might be to say that the kids at Springfield are smarter. But a bigger standard deviation for one school tells you that there are relatively more kids at that school scoring toward one extreme or the other. By asking a few follow-up questions you might find that, say, Springfield’s mean was skewed up because the school district sends all of the gifted education kids to Springfield. Or that Shelbyville’s scores were dragged down because students who recently have been “mainstreamed“ from special education classes have all been sent to Shelbyville. In this way, looking at the standard deviation can help point you in the right direction when asking why information is the way it is. Of course, you’ll want to seek the advice of a trained statistician whenever you try to evaluate the worth of any scientific research. But if you know at least a little about standard deviation going in, that will make your talk with him or her much more productive. #StandardDeviation #StatisticsFieldOfStudy #MathematicsFieldOfStudy #mean #statistics