standard deviation help

[BruceZ]

Here's an everyday example of rms average. In the US we say the AC coming from your wall is 120 volts. This is a sine wave, but if we measured the amplitude we would see it actually goes up to a peak of 170 volts. The 120 volts is an rms average. It is the result of integrating [170*sin(x)]^2 over a period of 2*pi, dividing by 2*pi, and taking the square root. This is the square root of the average of the squares of all the amplitudes which turns out to be 170/sqrt(2) = 120 rms. It will produce the same power as a constant DC voltage of 120 volts. It is not the same as the average excursion from 0 ignoring sign, which turns out to be 170*2/pi = 108 volts.

[BruceZ]

<pre><font class="small">code:</font><hr>



170----*-*------------------
v * * &lt;--- rms level = 120 volts
o * *
l 0---*-------*-------*-------&gt; time
t * *
s * *
-170-----------*-*----------

</pre><hr>
120 volts is the standard deviation of the voltage (how many people realized that?) however, in this case it is not true that 68% of the voltages lie within 1 standard deviation of average because that is generally true only for normally distrubuted data (like your poker results). If your poker results look like the above, you've got a problem.

I had a slight indexing problem with the above formulas which I might as well correct here:

If x[n] are values of N measurments, and the average value is u, then:

variance = 1/N*sum[n=1 to N](x[n]-u)^2
standard deviation = sqrt(variance)

average distance from average would be:
1/N*sum[n=1 to N](|x[n]-u|)