I'm going to use the example numbers 12, 3, 10, and 7.
1) Find the average of your numbers:
(12 + 3 + 10 + 7) / 4 = 32 / 4 = 8
2) Find the distance of each number from the average:
12 - 8 = 4, 3 - 8 = -5, 10 - 8 = 2, 7 - 8 = -1
3) Square each of these distances:
4 * 4 = 16, -5 * -5 = 25, 2 * 2 = 4, -1 * -1 = 1
4) Find the average of the squares:
(16 + 25 + 4 + 1) / 4 = 46 / 4 = 11.5
5) Take the square root of this number, you have your standard deviation:
sqrt(11.5) = about 3.3912
Standard Deviation
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