What Is A Standard Deviation?
Anyone who follows education policy debates might hear the term “standard deviation” fairly often. Most people have at least some idea of what it means, but I thought it might be useful to lay out a quick, (hopefully) clear explanation, since it’s useful for the proper interpretation of education data and research (as well as that in other fields).
Many outcomes or measures, such as height or blood pressure, assume what’s called a “normal distribution.” Simply put, this means that such measures tend to cluster around the mean (or average), and taper off in both directions the further one moves away from the mean (due to its shape, this is often called a “bell curve”). In practice, and especially when samples are small, distributions are imperfect — e.g., the bell is messy or a bit skewed to one side — but in general, with many measures, there is clustering around the average.
Let’s use test scores as our example. Suppose we have a group of 1,000 students who take a test (scored 0-20). A simulated score distribution is presented in the figure below (called a “histogram”).
The numbers on the horizontal axis are test scores, from 0-20. The bars for each individual score tell you how many students received that score (frequencies are on the vertical axis). The bars for the scores around 10 (the average) are the highest, and they get shorter the further you move to the left of the right, since fewer and fewer students receive scores that are far away from the average.
Now look at the second graph, which is, let’s say, the same test and number of students but a very different distribution.
In this case, the average score is still 10, but the distribution is much “tighter,” with far fewer students scoring much higher or lower.
As you can see, the average score can be a useful summary statistic, but it can’t tell you about how students’ scores are actually distributed around that average. In the second graph, the scores are clustered fairly compactly, Shanker Blog » What Is A Standard Deviation?: