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.
My explanation might be rudimentary but the eli5 answer is:
Mean of (0,1, 99,100) is 50
Mean of (50,50,50,50) is also 50
But you can probably see that for the first data, the mean of 50 would not be of as importance, unless we also add some information about how much do the actual data points ‘deviate’ from the mean.
Standard deviation is intuitively the measure of how ‘scattered’ the actual data is about the mean value.
So the first dataset would have a large SD (cuz all values are very far from 50) and the second dataset literally has 0 SD
When you add and subtract a standard deviation to the mean, 68% of your data (age of participants) is within the interval.
That’s from 12.93 -. 76 all the way to 12.93+.76
If you add and subtract two standard deviations, 95% are within the interval.
That’s from 12.93 -2 * 0. 76 all the way to 12.93+2 * 0.76
If you tested another group and you got stdev >. 76 it would mean that the new group is more diverse, the ages are more spread out.
Conversely, if you tested a group with stdev<. 76 it would mean that their ages are more close to the mean value, less spread out.
Latest Answers