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# Standard Deviation Question

Discussion in 'Educational Resources' started by Dustin, Jun 8, 2002.

1. There are many different kinds of probability density functions, (one of which is the normal distribution, also called the Gauss density). For example, there is the Gamma density, Chi-squared density, Maxwell-Boltzmann density, etc. They have different kinds of shapes and you try to choose one that best represents your data sample. Each different function basically has an "equation" which graphs out the shape of the curve, and various parameters control the shape. The common thing among the various distributions is that the area under the curve = 1. (and is continuous and greater than or equal to zero on all points, but that is less interesting) In normal distribution, for example, it is described by two parameters, the mean and standard deviaton. The mean just shifts the whole thing left or right on the x-axis (horizontal), and the standard deviation controls the shape. The smaller the standard deviation, the steeper and narrower the "hill", and a large standard deviation will produce a wide short "hill". The main concept is that the area under each of the curves equals one. When you want to find probalities, say that it lies between A and B, you need to calculate the area under the curve between A and B.

#11     Jun 9, 2002
2. Well you can tell that a finance degree from SFSU really means nothing...I have one more question.

I have always used the regular stdev command in excel, but there is also the stdevp command if your data is the entire population. Is a set of t&s data a sample or population?

#12     Jun 10, 2002
3. It would most likely be a sample, however:

The difference between the two excel functions (stdev & stevp) should be very small if you're going to analyze data of more than 30 observations (Central limit theorem), and the more observations you have the better the representation of the sample to the real population. So if you're using the day's T&S, you should have enough observations that it really doesn't matter which funtion you're using. I usually just do the 'stdev' for everything.

#13     Jun 10, 2002
4. StdDev "it's not a component, it describes the Bell curve."
Not true
Here is an equation for a Bell curve.
f(x)=y=[1/(S*sqrt(2Pi)]*e^[-0.5*[(x-u)/S]^2]
Where
u=mean (constant, calculated), locates the center
S=StdDev (constant,calculated), determines dispersion
e=2.7183 (constant, natural number)
x= (variable)=domain=input
f(x)=y=range=output (a function of x)
.
u,S,and e are components of the Bell curve f(x).

#14     Jun 10, 2002
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