How To Calculate The Standard Deviation

Which of these sets of values would you expect to have the larger standard deviation?

"A": 6 24 37 49 64 (Mean: 36)
"B" : 111 114 117 118 120 (Mean: 116)

Values in the "A" set are more dispersed (they deviate more from the mean) than those in the "B" set, so the standard deviation will be larger in the "A" set. Let's see how this works out:
Value Deviation Value Deviation
6 -30 111 -5
24 -20 114 -2
37 +1 117 +1
49 +13 118 +2
64 +28 120 +4

We can't simply take an average of the deviations because they will always add up to zero (the negative deviations cancel out the positive). To overcome this difficulty, we square each deviation. (This gets rid of negative values, since a negative multiplied by a negative yields a positive.) So for the "B" values, we have: 25 (-5 x -5), 4 (-2 x -2), 1 (l x l),4 (2x2), and 16 (4x4). The mean (average) of these squared deviations is called the Variance.

Variance =
24 + 4 + 1 + 4 +16
=
50
= 10
5
5

The variance is a measure with uses of its own. But it does have one disadvantage for everyday use: If original values are in dollars - as when you're calculating hourly winnings or losses from a poker games - then the variance is in dollars squared. To get back into the same units as the observed values, we take the square root of the variance. This result is what we call the standard deviation.

The standard deviation for the distribution shown above = 3.16 (the square root of 10). The same calculations for the "A" set yield a variance of 399.6, and a standard deviation of 19.99. Now that you've walked through the process of calculating a standard deviation and understand the process, here's how you can simplify things:

Just use a spreadsheet program or specialized poker software like Stat King to enter computer records of your results. Then you're off the hook: The spreadsheet's statistical capabilities will compute your average hourly results (mean) and standard deviation for you. Moreover, the software will track them on a cumulative basis. Alternatively, you can get yourself a pocket calculator that performs statistical functions. It'll cost under $20, and will also spare you the hassle of tedious arithmetic operations.

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