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Finding standard deviation or error from normalized data. 
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#1
Sep2611, 07:04 PM

P: 142

Hello All,
I am trying to figure out how to find the standard deviation or error in sets of data. So lets say I have sets x1, x2, x3 and x4 with various values and I found the average and standard deviations for it. Now I have to take the averages, lets say a1, a2, a3, a4, and normalize a2,a3,a4 to a1. Now how do I find the standard deviation or error in the normalized sets? Forgive my ignorance, but I am suppose to do this for a project and I have never taken any stats course before.. Thanks DoubleMint 


#2
Sep2811, 03:20 AM

Sci Advisor
P: 3,313

What do you mean by "normalize"? For example, do you mean that multiply each datum in the data set x2 by the factor (a2/a1) ?
Let the data be the [itex] d_i [/itex]. Let the sample mean be [itex] m[/itex] . Let the scaling factor be [itex] k [/itex] The mean of the scaled data [itex] k d_i [/itex] is [itex] m k [/itex] The variance of the scaled data is: [itex] \sum \frac { ( k d_i  m k )^2}{n} = \sum \frac{k^2 (d_i  k)^2 }{n} = k^2 \sum \frac{(d_i  m)^2}{n} [/itex] This is [itex] k^2 [/itex] times the variance of the original sample. So the sample standard deviation of the scaled data is [itex] k [/itex] times the standard deviation of the original data. 


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