In probability theory and statistics, what is a measure of the variability or dispersion of a population, a data set, or a probability distribution?
Statistical dispersion be ranked as having more dispersion than the other, or alternatively neither may be ranked as having more dispersion. Statistical dispersion In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions. A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become
Shape of a probability distribution an exponential distribution has exponential tails and a Pareto distribution has long tails. Shape of a probability distribution In statistics, the concept of the shape of a probability distribution arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population. The shape of a distribution may be considered either descriptively, using terms such as "J-shaped", or numerically, using quantitative measures such as skewness and kurtosis. Considerations of the shape of a distribution arise in statistical data analysis, where simple quantitative descriptive statistics and plotting techniques such as