Outliers and running medians
Since medians are less sensitive to outliers than means, a more robust alternative to running means replaces each value by the median of it and adjacent values. A 3-point running median is:
and higher-order running medians will use more adjacent values.
Comparison of means and medians
Running medians, followed by moving averages
To take advantage of the best features of both moving averages and running medians, these two techniques are often applied sequentially.