Anomaly Probability Distributions for the Months and the Year

  We can fit histograms to the monthly data to estimate the standard deviation of a normal distribution for each month and combine these to get a distribution for the entire year. The combined distribution does not appear to be a normal distribution.

  This is why there was a problem fitting a normal distribution to the data for the difference between the land northern hemisphere temperature anomaly and the 5-year average.

Supplemental (Oct 2): For a more accurate distribution for year one can replace the equal weight of 1/12 by multiplying each monthly probability distribution in the sum by a statistical weight equal to the number of days in the month divided by the number of days in the year. Since there is a leap day in Feb roughly every four years one could use 28.25 days for Feb and 365.25 for the number of days in the year. The resulting changes to the yearly distribution are very small.