I love the potential oxymoron in this phrase. I imagine two gossips talking about another’s peccadillo, and being interrupted by a third declaring ‘oh, that’s rather a dull, standard, deviation’.
Statistically it’s a concept which it is easy to explain, but I find hard to understand. It’s a formula which attempts to describe how spread out the data is in a set of data, in other words, on average how distant is each data point from the average of the whole data set.
Or, in other words it attempts to answer the question “how spread out is the data?”
In the video above I can follow this fairly well until he does the difference between x and ‘x bar’. What he’s referring to here is a calculation which gives you the difference between each data point and the mean of the whole data point. You square these, I think, so that you end up with a positive number. This seems to be the case because the final step is to find the square root, so you’re sort of taking the square out again (sort of).
What does the number tell you? I think that it tells you very little on its own – the SD means little unless you know the mean of the data set, beyond the general rule that the closer the number is to zero the narrower the spread of results. If the mean is 50 and the SD is 10 this would suggest a wider spread than if the mean is 100 and the SD is 10.