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So I have a data set $(x_{1},y_{1}), (x_{2},y_{2}),\dots,(x_{n},y_{n})$ and from it I have the values of $\sum x$, $\sum x^{2}$, $\sum y$, $\sum y^{2}$, $\sum xy$.

My question is, how do I find a normal distribution that best fits this data set and how do I use these values to calculate the standard deviation for the normal distribution?

Basically, given a data set, how do I find the values of the mean and standard deviation for the normal distribution of best fit? Are they the same as the mean of the data set?

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    It seems that you have bivariate data (i.e. data for a scatterplot). Do you want to approximate the xi or the yi or do you want a bivariate normal distribution?2012-12-22
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    @Hans Engler: Yes, this is exactly what I want, a normal distribution for which (n,f(n))= $(x_{n},y_{n})$. How is this accomplished?2012-12-23
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    I asked an "either or" question and you responded "yes", so I am confused now. Which data are in your opinion approximately normally distributed?2012-12-23
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    As @Hans said. Also, your equation $(n,f(n))=(x_n,y_n)$ is confusing -- does that mean that $x_n=n$? In that case, why did you introduce the $x_n$ in the first place? Also, this equation appears to imply that you're considering a one-dimensional function. In that case, I wonder whether you're actually simply trying to fit a normalized Gaussian to a set of data points and the whole distribution aspect is just a distraction. In any case, what do you mean by "the mean of the data set"?2012-12-23
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    @Hans Engler: Oops, sorry. I did mean a bivariate normal distribution. Unfortunately, I am not sure how to use this to produce the desired result.2012-12-23
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    @joriki: Yes, I am just trying to "fit a normalized Gaussian to a set of data points" and I thought that a distribution was the way to do this. I guess I was wrong. But, just to clarify, my question remains: "Given a data set, how do I find the values of the parameters (such as mean and standard deviation) in the equation for a normal distribution?"2012-12-23
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    @Hans Engler: I did some searching and found this, which might answer the question ([http://www.math.uri.edu/~pakula/452webs8/regress.pdf](http://www.math.uri.edu/~pakula/452webs8/regress.pdf)) I am not sure exactly how to apply it though.2012-12-26

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