IPBWiki/BasicStatistics

(Difference between revisions)

Revision as of 17:00, 2 February 2011

Median: The individual value from the collection such that 1/2 the observations are less and 1/2 are greater

Standard Deviation (rms/sigma): $\sigma_x = \sqrt{\frac{1}{N-1} \sum (x_i - \bar{x})^2}$

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 ; Variance: <math>\sigma_x^2 = \frac{1}{N-1} \sum (x_i - \bar{x})^2</math>
 ; Standard Deviation (rms/sigma): <math>\sigma_x = \sqrt{\frac{1}{N-1} \sum (x_i - \bar{x})^2}</math>
-The standard deviation tells us something about the expected value of a single observation.
-If the data are normally distributed
-    * 68% of the points will lie within &plusmn 1 sigma
-    * 95% of the points will lie within &plusmn 2 sigma
-    * 99.7% of the points will lie within &plusmn 3 sigma
-Usually we accept a variation as statistically significant only if it is more than 3 sigma from the mean.
-; Error bars (standard error/standard deviation of the mean):  <math>\sigma_{\bar{x}} = \sqrt{\frac{1}{N}} \sigma_x = \sqrt{\frac{1}{N(N-1)} \sum (x_i - \bar{x})^2}</math>
-* Moments of the Gaussian distribution
-   '''variance''' =  <math>\frac{1}{N-1} \sum \left[(x_i - \bar{x})\right]^2
-   '''skewness''' =  <math>\frac{1}{N} \sum \left[\frac{(x_i - \bar{x})}{\sigma}\right]^3
-   '''kurtosis''' =  <math>\frac{1}{N} \sum \left[\frac{(x_i - \bar{x})}{\sigma}\right]^4 - 3