Descriptive statistics, as follows from its name, describes a distribution by means of figures which characterize distribution parameters. These parameters can be divided into three main groups: central tendency measures, dispersion measures and shape measures.
Central tendency measures characterize the central value around which random variable values are distributed. These measures are the mean (first moment of distribution) and the median. The mean is used for the description of close to normal distributions. If the distribution essentially differs from normal (for example, if it has long and wide tails), the mean will converge to "true" mean too slowly. In that case, it is reasonable to use the median to estimate central value.
Dispersion measures characterize scattering whose random value is distributed around its central value. These measures are dispersion (and related with it standard deviation) and average deviation. As for central tendency measures, one of these measures (dispersion) is good for close to normal distributions while the second one (average deviation) is better for long-tailed distributions.
Shape measures describe common characteristics of distribution appearance: skewness, kurtosis, percentile.
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