This is another example of why "citizen scientists" should not post results of their "investigations" without a review from a qualified expert. It is also another reason to keep scientific instruments out of the hands of amateurs. GM counters are simple to use but problematic when interpreting the results.
His concern and musings over the asymmetry in the count rate distribution are a wasted effort. The distribution is not exactly Gaussian but Poisson which still manifests a slight asymmetry at his count rate. His two distribution hypothesis is fallacious and should not be used for this experiment.
The detector is sensitive to all types of ionizing radiation which in this case have different sources whose radiation comes from different directions. The efficiency is directionally dependent.
The data were accumulated over the complete seasonal cycle. He is at a high elevation so during the winter the house is closed tightly sequestering the air and probably allowing radon to build up to higher levels than in the summer. He merges all the data without any concern for the possibility of seasonal variations.
And finally he states results in uR/hr (a unit of exposure rate) and compares his results to standard values without concern to the units. Environmental dose rates are given in rem/yr. not R/yr. GM detectors are typically used for surveying gamma/xrays and the scales are appropriately labeled in R/min or R/hr. The detector is sensitive to betas and alpha but in the case it is used for these only counts/minute are appropriate since exposure rate is defined only for gamma/xrays. To convert counts/min to rem/minute you must know specifics of each type of radiation and their relative abundance.
I should add for anyone who later reads this thread and may want to buy a Geiger Counter. The source provide with GM counters is what is know as a check source and only used for assuring that the counter is working properly at least on one scale and is NOT a calibration source and to emphasize that the reading in mR/hr is only for gamma/xrays which may also be only correct for a certain energy range of that radiation. Many GM counters will not detect Alpha or Beta radiation.