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Standard deviation
By Anonymous on Thursday, July 13, 2000 - 10:38 am:

Hello everyone

What is standard devation ?
What is the method in simple form ?

Thanks a lot

By Dave Sheridan (Dms22) on Thursday, July 13, 2000 - 12:35 pm:

"Standard deviation" is a property of data. It is not a method of any kind. Here's why it's useful though.

Think about two machines which produce pencils. One machine produces five pencils whose lengths are 9.8cm, 9.9cm, 10.0cm, 10.1cm, 10.2cm respectively. This is an average of 10cm. The other machine produces five pencils whose lengths are 1cm, 5cm, 9cm, 15cm, 20cm respectively. The average length of a pencil from the second machine is also 10cm. Hopefully, though, it should be pretty obvious that the first machine was better at producing pencils of around 10cm. How do we quantify this though?

That's where standard deviation comes in. It measures the spread of data around its mean. I won't give you the mathematical definition unless you want it (it looks quite complicated but is simple to understand if you try) but will just tell you that it's more like an "average spread" of data - it takes into account whether most data points are close to the average, and gives a way of measuring how far away they are.

It is very useful in statistics since a small standard deviation means that large deviations from the mean are unlikely, whereas for a large standard deviation, we should not be surprised to see wildly fluctuating values.

Hope that's useful,

-Dave

By Dan Goodman (Dfmg2) on Thursday, July 13, 2000 - 12:37 pm:

Standard deviation is basically a number to measure how "spread out" some numbers are. For instance, the numbers 4.1,4.2,4.2,4.3 are all very close to 4.2, and so aren't very spread out. The numbers 1, 4.6, 28, 495 are very spread out.

Do you know what the "mean" of a collection of numbers is? It is a number which is "in the middle" of the numbers, the way you work it out is to add up all the numbers, and divide by how many numbers there are. For instance, the mean of 4.1, 4.2, 4.2, 4.3 is (4.1+4.2+4.2+4.3)/4 because there are 4 numbers, this comes out to be 4.2, which is what you would have probably guessed.

To work out the standard deviation, you work out the mean, then subtract the mean from all your numbers. So for the example above, the new numbers you would come up with are -0.1, 0, 0, 0.1 (because 4.1-4.2=-0.1, 4.2-4.2=0, 4.3-4.2=0.1). Then, you square each of these numbers, so we would get 0.01, 0, 0, 0.01 (because -0.1×-0.1=0.01 and 0×0=0 and 0.1×0.1=0.01). Then you add up all the numbers, we get 0.02. Then you divide by how many numbers there are (4), to get 0.005. Finally, you have to work out the square root of this number, you can do this with your calculator, for this case, the square root is about 0.0707, so the standard deviation of 4.1, 4.2, 4.2, 4.3 is 0.0707. See if you can work out the standard deviation of 1, 2, 3, 4, 5, 6, 7.