IPBWiki/BasicStatistics

From MediaWiki

Gaussian distribution

Mean

Median

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

Mode

The most frequently occurring value.

Variance

Standard Deviation (rms/sigma)

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)

• Moments of the Gaussian distribution

  variance =  Failed to parse (PNG conversion failed;

check for correct installation of latex, dvips, gs, and convert): \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