I have heard of this before but I cannot remember what it means—what is meant by the term standard deviation?

Response:

This is a good question.  Many of us learned this in our statistics course in college, but we tend to forget such things if they go unused.

The standard deviation (SD) is a measure of spread in your data.  The larger the SD, the more spread there is in your data.  Think in terms of dispersion.  The larger the SD, the more dispersion there is in your data.  The smaller the SD, the less dispersion exists in your data.  The standard deviation is a measure of variability around a mean score.  In statistical terms, the standard deviation is the square root of a measure called the variance, which is the average of the squares of the deviation scores for the sample for a particular item. 

To illustrate the standard deviation and the type of insight it provides, the following table presents scores for two students, Bill and Tom, over their last ten college exams.

Both students ended up with an average exam score of 80, as indicated by a mean of 80.0 for each student.  Note that the standard deviation around Bill’s mean of 80.0 is 10.1, while the standard deviation around Tom’s mean of 80.0 is only 2.6.  Obviously, by looking at the scores for the two students, we can see that Tom is much more consistent than Bill.  Tom’s scores range from a low of 76 to a high of 84 (a range of only 8 points), whereas Bill’s scores range from a low of 66 to a high of 96 (a range of 30 points).

If there is no spread or dispersion in your data, then the SD is zero.  While a zero SD would be unlikely in a large sample, this is something that could happen in a small sample of physicians when rating administrator communication, for example.  If each physician gave the same rating on an item, then that would mean there is no spread or dispersion in the data at all.  Thus, the SD would be zero.  On the other hand, if the physician responses were dispersed evenly across the rating scale, the SD would be larger. 

Here is something else to remember.  If the data are normally distributed or shaped in a “bell curve,” approximately 68% of the scores will fall between one SD above the mean and one SD below the mean.  Furthermore, 95% of all scores will fall between 2 SDs above and below the mean.  Finally, 99.7% of scores will fall between 3 SDs above and below the mean. 

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