Dispersions are estimates of the variability of measurements in a given distribution. Range The range defines the distribution's width from the minimum to the maximum and is defined as follows: Range = x_{max}  x_{min} Percentiles The nth percentile is the value which cuts n% of the distribution. Variance and standard deviation Variance and standard deviation are most commonly used to describe the variability of a given distribution. Requirements: The individual measures must be at least interval scaled. Calculation: For the estimation of a population variance the variance of a sample distribution must be corrected as follows: The same holds for the estimated standard deviation of a population Standard error of the mean This is a measure for the accuracy of the estimated population mean. if is estimated from the sample: Skewness Skewness is a measure for the symmetry of a given distribution. A negative skew means that the left tail of the distribution is elongated (AM > Median > Mode) A positive skew means that the right tail of the distribution is elongated (AM < Median < Mode) Examples: Calculation: Skewness is the third standardized moment of the distribution and is computed as follows: Sample skewness: The estimation of the population skewness from a given sample is: Kurtosis Kurtosis is a measure of the “peakedness” of a given distribution. Higher kurtosis means more of the variance is due to infrequent extreme deviations, as opposed to frequent modestlysized deviations. Calculation: Sample kurtosis: The estimation of the population kurtosis is as follows:
