Average absolute deviation
The average absolute deviation (AAD) of a data set is the average of the absolute deviations from a central point. It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be a mean, median, mode, or the result of any other measure of central tendency or any reference value related to the given data set.
AAD includes the mean absolute deviation and the median absolute deviation.
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In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
The bean machine, a device invented by Francis Galton, can be called the first generator of normal random variables. This machine consists of a vertical board with interleaved rows of pins. Small balls are dropped from the top and then bounce randomly left or right as they hit the pins. The balls are collected into bins at the bottom and settle down into a pattern resembling the Gaussian curve.
Carl Friedrich Gauss discovered the normal distribution in 1809 as a way to rationalize the method of least squares.
Pierre-Simon Laplace proved the central limit theorem in 1810, consolidating the importance of the normal distribution in statistics.
