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
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.
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
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.
The mean is the average of all the values.
The standard deviation is-in effect- a measure of the average distance of each value from the mean.
It takes the sum of the distances from each value to the mean squared, divides by the number of values, and takes a square root.
In basic terms, a small standard deviation means most of the values are close to the mean, while larger standard deviation means the values are more spread out away from the mean.
Almost all the other answers here are explaining SD in terms of normal distributions (“the bell curve”). No five year old needs to learn about normal distributions to understand SDs.
1) you have a mean, the average of all the data points in your set.
2) each one of those data points will have a variance between themselves and the mean.
3) you’d like to know what is the average amount of variance of those data points from the mean.
That’s it. That’s the standard deviation. The stuff about what it means for a normal distribution can come later.
Mean (or average) gives you a measure of a ‘center’ (in one definition) of a number of measurements.
Standard deviation (SD) gives you a measure of how much those measurements are spread out around that mean, i.e., how much the measurements “deviate” from that average. If you calculate two more values — mean plus SD and mean minus SD — it tells you that 2/3 of your measurements are within that range.
So, the smaller the standard deviation, the closer 2/3 of the measurements are to the mean.
In your example above, rounding off to make things simpler, 2/3 of the measurements are well within the age range of 12-14.
I’ll give my shot at it:
Let’s say you are 5 years old and your father is 30. The average between you two is 35/2 =17.5.
Now let’s say your two cousins are 17 and 18. The average between them is also 17.5.
As you can see, the average alone doesn’t tell you much about the actual numbers. Enter standard deviation. Your cousins have a 0.5 standard deviation while you and your father have 12.5.
The standard deviation tells you how close are the values to the average. The lower the standard deviation, the less spread around are the values.
In your data set you have an average age of 13. The standard deviating is close to one.
This means that, in the group, you’ll have some 12 and 14yo kids, too.
If the standard deviation were like 5, you could have an average of 13 still, but also have a bunch of 8 and 18yo kids.
ELI5: It’s literally just tells you how “spread out” the data is.
Low SD = most children are close to the mean age
High SD = most children’s age is away from the mean age
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ELI10: it’s useful to know how spread out your data is.
The simple way of doing this is to ask “on average, how far away is each datapoint from the mean?” This gives you MAD ([Mean Absolute Deviation](https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/other-measures-of-spread/a/mean-absolute-deviation-mad-review))
“Standard deviation” and “Variance” are more sophisticated versions of this with some advantages.
Edit: I would list those advantages but there are too many to fit in this textbox.
At one restaurant they cook their steaks perfectly every time. At another restaurant it’s a crapshoot whether your steak is served raw or burnt to a crisp. At both restaurants the average steak is cooked perfectly. The first restaurant has less variance/less standard deviation and the second restaurant has greater variance/standard deviation.
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