What is a standard deviation?

We often face a situation where we know how to compute but we do not know what is it for or what is the reason or history of it. One of examples is standard deviation. We can use excel to compute it easily given a set of data. But what does it mean? In what cases it is meaningful to compute standard deviation.

A good elaboration including reason behind computation such as using square instead of absolute differences can be found here.

So we just need to remind ourselves one step bigger, that is standard deviation is only one of several ways to measure dispersion or how the individual data spreads. In the case of normal distribution, it is meaningful to use standard deviation. In other cases, we need to be careful. For example, if we have non-normal distribution, what does the standard deviation signify? When there are only two data points, what does standard deviation mean?

There are other ways of measuring dispersion such as range (difference between maximum and minimum data) or interquartile range (difference between 75th percentile and 25th percentile which shows the range of 50% of the data).

Back to the main point, we need to remember the objective of having something. There is no point of showing standard deviation just because it is a standard procedure. Something is meaningful when we know why we are doing it. Of course we cannot know the reasons of all things we do in this world. But if there is a way to find out such as in the case of standard deviation, let’s find it out.