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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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