Standard Deviation Explained

One of the best things about statistics is that it's not really that old as a science. The language that is used is fairly recent, kind of an old english stodginess to it. Most terms just have to be taken back to their strict dictionary definition to be understood. So standard deviation simply means, The Standard... Deviation.



You know both of these words, we just don't tend to use them a lot in every day language. At least not together, or in this way. The American Oxford Dictionary defines standard, as

Standard: used or accepted as normal or average : the standard rate of income tax | it is standard practice in museums to register objects as they are acquired. 

Something that you expect to have happen, or what you would expect to see on Average. Let's go with that, the average.

Now, we often hear deviation in one of its variants; deviate or deviant.  "You deviated from what you were told," meaning not quite correct. Or, "they're a social deviant", meaning unacceptable. So deviation means something has changed from what was expected. Together they give us,

The Average Change from the Expected.

If you take the whole data set, and take the average difference between each point and what is expected you get the standard deviation. In statistics this is often reported as a single value and will have the same units as the expected value. For instance, men in Canada are 1.736 m on average with a standard deviation of 16cm (Made this up, I still can't find it). That means that the average Canadian male height is on average 16cm from 1.736 m. Yes this tells you nothing about the individual person, or what you might expect to see in a small group, but it does tell you information about all Canadians in general.