The table gives the function names and descriptions.
Mean absolute deviation
Central moment of all orders
The range (the difference between the maximum and minimum values) is the simplest measure of spread. But if there is an outlier in the data, it will be the minimum or maximum value. Thus, the range is not robust to outliers.
The standard deviation and the variance are popular measures of spread that are optimal for normally distributed samples. The sample variance is the minimum variance unbiased estimator (MVUE) of the normal parameter σ2. The standard deviation is the square root of the variance and has the desirable property of being in the same units as the data. That is, if the data is in meters, the standard deviation is in meters as well. The variance is in meters2, which is more difficult to interpret.
Neither the standard deviation nor the variance is robust to outliers. A data value that is separate from the body of the data can increase the value of the statistics by an arbitrarily large amount.
The following example shows the behavior of the measures of dispersion for a sample with one outlier.
x = [ones(1,6) 100] x = 1 1 1 1 1 1 100 stats = [iqr(x) mad(x) range(x) std(x)] stats = 0 24.2449 99.0000 37.4185