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
Here’s my way of thinking about it. Imagine you have a row of cans marked 1 through 10. You give a guy a BB gun, stand him 30 feet from the target, and tell him to shoot can 5 near the middle. Most of the time he hits can 5, but sometimes he hits can 6 or can 4, and there’s a few times he will hit cans further away from the targe. Maybe he hits a single 7. You tally up each time he hits a can.
What you’ll see is that there is a distribution of shots around the target, with the most number shots hitting can 5, and then quickly going down as you get further away from the center. The curve of this distribution looks like a bell, and it has a special name: the normal distribution. It appears a lot in nature where something is normally a certain value, but due to random chance it varies up or down from that value.
Now, the distribution of shots isn’t the same for each situation. What if you move the shooter to 100 feet away from the cans? Well, his accuracy is going to go down, so there’s a lot more shots that hit cans further from the center. If you tally up the new distribution, you notice the “bell” is wider than before. Fewer shots hit can 5, and more hit cans 9 or 10. But he is trying hard so still more shots hit the target than other cans.
The *width* of the distribution indicates the accuracy of the shooter. This width is measured using a mathematical formula called *stardard deviation*, also called “Sigma”. So the value of sigma tells you how accurate the shooter is – bigger sigma is less accurate, smaller sigma is more accurate.
It is important in science to be able to calculate this number because it gives you a numerical score for how accurate the shooter is, and it allows you to actually predict the chance of hitting any single can on the next shot. So if a shooter had a sigma score of 1, then most his shots (68%) are going to hit within one can of the mean – can 4, 5, or 6. We can also predict that this shooter is supposed to hit can 9 only once every three hundred shots. So if suddenly he starts hitting can 9 every ten shots, we know something changed with the situation – his sigma must be different now. At this point maybe he’s getting tired and needs a rest.
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