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
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Thanks, from reading the sum of all these comments and averaging the answer I actually understand 🙂
It’s a measure of how tightly clumped your date is around the mean. If your data has low standard deviation then all your datapoints are tightly clumped around your mean. If your data has high standard deviation then your datapoints are very spread out, with the mean somewhere in the middle.
Standard deviation is simply a commonly accepted way of measuring this spread. You calculate it as follows
– take every datapoint and work out how far from the mean it is, the simplest way to do that is simply minus the mean from it which will give you the distance if the datapoint is bigger than the mean and minus the distance if the datapoint is smaller than the mean
– square them all to make them all positive so they’re easier to compare (don’t worry we’ll undo this later)
– work out the average (ie the mean) of those answers
– take the square root of that average (to undo the fact that you squared them all earlier)
and that’s your standard deviation
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.
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.
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.
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.
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.
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.
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.
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