Variation in radiation counts

What to make of the variation in radiation counts?

Statistics:

  • Min 5 at 363; Max 33 at 1447
  • Mean 16.28; Median 16
  • Std. dev. 4.095 $\approx$ 4.1

Standard deviation

Here are the first 20 1-minute counts for the "all day" GC counting:

  • "Mean" = average
  • "Median": Half the measurements are above this value, half are below.
  • The "deviation" for one particular measurement is
      dev= Counts - average(Counts).
  • Why is the average of the deviations not useful for talking about how much variation there is in the data?
  • The "Standard deviation", $\sigma$, for our purposes is: $$\sigma = \sqrt{\text{Average(}\text{dev}^2\text{)}}.$$

In a course on probability and statistics, you would find that for many kinds of random processes:

  • 68% of measurements are between $\text{ave}-\sigma$ and $\text{ave}+\sigma$.
  • 95% of measurements are between $\text{ave}-2\sigma$ and $\text{ave}+2\sigma$.
  • 99.7% of measurements are between $\text{ave}-3\sigma$ and $\text{ave}+3\sigma$.
  • ...

GC data

Here are the histograms from the 1 minute counts and the 10-minute averages for the GC data:

There is a trick we can use to connect the standard deviation of the 1-minute counts with the width of the 10-min average histogram....