solve mathematically.

data point months of the year:

array([12., 10., 8., 9., 8., 5., 3., 4., 12., 5., 6., 10., 8., 1., 1., 3.,1., 10., 7., 5., 6., 2., 12., 10.])

Our definition for time-of-year for patient admission is not truly linear. 12 (December) is followed by 1 (January) - it is much closer in time to January it is to 9 (September).

calculate mean and stdev to more naturally reflect the circular nature of the calendar( how to handle the data to reflect the clock modulo arithmetic.)