MONTHSTATS is the jOceans module of jLab.

 MONTHSTATS  Mean month and standard deviation using circular statistics.
 
    [MFBAR,MFSTD]=MONTHSTATS(NUM,DIM) where NUM is an ND array of dates in 
    Matlab's DATENUM format, finds the mean and standard deviation of the
    month number in NUM over dimension DIM using circular statistics.
 
    MFBAR and MFSTD are the mean and standard deviations of the month dot
    fraction, defined such that 1.0 is January first and 12.99999 is the 
    end of December, as computed from YEARFRAC.
 
    MONTHSTATS works by converting month number, computed using YEARFRAC, 
    into angles, finding the circular statistics, and converting back. 
 
    For a complex-valued, unit magnitude quanity z, one can find the 
    statistics of its angles through R e^{1i* Theta} =  where "<>" is
    an averaging operator.  Then Theta is the average angle, and the
    standard deviation of angles is sqrt(-2 ln R).  
 
    See e.g. https://en.wikipedia.org/wiki/Directional_statistics.
 
    Usage: [mfbar,mfstd]=monthstats(num,dim);
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    This is part of JLAB --- type 'help jlab' for more information
    (C) 2020 J.M. Lilly --- type 'help jlab_license' for details