Measures of Dispersion


The table gives the function names and descriptions.

Function Name



Interquartile range


Mean absolute deviation


Central moment of all orders




Standard deviation








Compare Measures of Dispersion

This example shows how to compute and compare measures of dispersion for sample data that contains one outlier.

Generate sample data that contains one outlier value.

x = [ones(1,6),100]
x = 1×7

     1     1     1     1     1     1   100

Compute the interquartile range, mean absolute deviation, range, and standard deviation of the sample data.

stats = [iqr(x),mad(x),range(x),std(x)]
stats = 1×4

         0   24.2449   99.0000   37.4185

The interquartile range (iqr) is the difference between the 75th and 25th percentile of the sample data, and is robust to outliers. The range (range) is the difference between the maximum and minimum values in the data, and is strongly influenced by the presence of an outlier.

Both the mean absolute deviation (mad) and the standard deviation (std) are sensitive to outliers. However, the mean absolute deviation is less sensitive than the standard deviation.

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