Description of Data
Statistical Mean
The statistical mean, also know as the average, is the sum of a series divided by the number of data points in that series. As the number data points increases the accuracy of that mean is said to be increased. The mean can be calculated with the following formula.
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Standard Deviation
The standard deviation is the sum of the difference between the statistical mean and each point in the series, squared, divided by the number of data points minus one, square-rooted. The standard deviation is a measurement of the variability from the mean. A low standard deviation indicates a very low variability and high precision. The formula for calculating and unbiased standard deviation is as follows.
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Gaussian Distribution
Gaussian distribution, also known as normal distribution, is a symmetrical approximation of the frequency distribution for a series of data. The symmetry creates a bell shaped graph which is centered about the mean. The formula for a Gaussian curve is as follows. a= the average, σ= the standard deviation.
When looking at a set of data for the purpose of statistical analysis, it is important to adjust your data such that all important outliers are removed and all data is of the same type and same units. Prior to any statistical analysis it is essential that all data exist in a Gaussian distribution. Gaussian distributions are necessary to perform statistical tests. If the data does not take the shape of a Gaussian distribution, then the potential exists such that one of the statistical tests performed might return a result that is falsely positive or negative. One must look at the graphical form of the data prior to use. If the data is skewed or otherwise in a non-Gaussian distribution then the data must be adjusted such that it is in a Gaussian distribution. One method of making a data set normally distributed is to take the difference between each value and the mean and divide it by the standard deviation to obtain a new value.
Sources:
Güler, C.; Thyne, G.D.; McCray, J.E.; A.K. Turner. Hydrogeology Journal [Online] 2002, 10, 455-474. https://carmen.osu.edu/d2l/lms/content/viewer/main_frame.d2l?ou=9772362&tId=4196452 (accessed Nov 22, 2011).
http://www.mathmotivation.com/symbolic/standard-deviation.html
http://www.answers.com/topic/normal-distribution#ixzz1eOR5eNAy
http://hyperphysics.phy-astr.gsu.edu/hbase/Math/gaufcn.html
Content on this web page authored by Cody Holland, Muhammad Abdi, Alex Brawn, Zack Nellom & Robby Blizzard