First of all, an example; mean age of the children in a test is 12.93, with a standard deviation of .76.
Now, maybe I am just over thinking this, but everything I Google gives me this big convoluted explanation of what standard deviation is without addressing the kiddy pool I’m standing in.
Edit: you guys have been fantastic! This has all helped tremendously, if I could hug you all I would.
In: Mathematics
So far the answers you’re getting seem to only apply to the normal distribution (bell-curve) which is kind of misleading, since not all data is normally distributed and we use standard deviation in any case.
At its core, standard deviation is a way of telling you how spread out your data is. Of course there are other ways of doing this (range, average distance from mean etc.) but standard deviation has some nice properties that we like.
The best way of thinking about it I’ve found is geometrically. If you take a sample of n values from a distribution (such as the age of children in your example) and plot this as a point in n dimensions (so the first value is the first co-ordinate etc.) and also plot the point that has the mean in every co-ordinate, then the expected distance between those points is the standard deviation. In the case of a single dataset, you are computing exactly the distance between your data as a point and this mean-point.
We like this because this is exactly the value that the mean minimises – if you took any other value as the mean then this distance would be bigger.
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