Standard Deviation

This is a great document on standard deviation. All information comes from 2 websites which are noted on the top of the document. Really helpful step by step explanation and example.

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Compiled by Tilly
The information is all from 2 websites (asides from the summary). I have
copied it into this document so that you can obtain the method more simply.
This isn't actually my own work, but I found the following information very
Information from:
Standard Deviation is a measure of spread around a mean. The smaller the
Standard Deviation the closer the observations are clustered around the
First, you need to determine the mean. The mean of a list of numbers is the
sum of those numbers divided by the quantity of items in the list (add all the
numbers up and divide by how many there are).
Then, subtract the mean from every number to get the list of deviations.
Create a list of these numbers. It's OK to get negative numbers here. Next,
square the resulting list of numbers (read: multiply them with themselves).
Add up all of the resulting squares to get their total sum. Divide your result by
one less than the number of items in the list.
To get the standard deviation, just take the square root of the resulting
I know this sounds confusing, but just check out this example:
your list of numbers: 1, 3, 4, 6, 9, 19
mean: (1+3+4+6+9+19) / 6 = 42 / 6 = 7
list of deviations: 6, 4, 3, 1, 2, 12
squares of deviations: 36, 16, 9, 1, 4, 144
sum of deviations: 36+16+9+1+4+144 = 210
divided by one less than the number of items in the list: 210 / 5 = 42
square root of this number: square root (42) = about 6.48
Step by Step guide (summary)
1. Add all of the values together and divide by how many they are (mean).

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Compiled by Tilly
2. Substract the mean from every number in the list, to get deviations. This
calculates how far they are from the mean.
3. Square the deviations.
4. Add the deviations together.
5. Divide the total value for all the deviations by one less than the number
of numbers in the list. So if you had an original list of 5 numbers divide by
6. Square root this answer and get the standard deviation.…read more


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