[Geysers] More on Old Faithful and Descriptive Statistics in General

[Lynn Stephens]

THIS POST IS FOR THE PERSONAL USE OF THE READERS OF THIS LISTSERV AND IS NOT TO BE REPRODUCED FOR ANY OTHER PURPOSE, INCLUDING PUBLICATION IN THE TRANSACTIONS OR THE SPUT. RE Old Faithful's "average" interval.  I examined intervals from the OFVEC logbook for January 1 through March 15.  The 444 intervals varied from a minimum of 56 minutes to a maximum of 112 minutes, with a mean of 88 minutes and a median of 89 minutes.   Eyeballing the data from 2011 and 2012, Old Faithful's durations do not appear to have changed. I also looked at descriptive statistics shown for Old Faithful on geysertimes.org.  When I used the "view latest data for geyser" retrieve function, the mean was 2h40m, and the median was 90m.  I knew the geysertimes calculation of the mean was not useful for most geysers because geysertimes uses the last 21 intervals between reports, so the "intervals" used in the calculation often include multiple intervals treated as a single interval.  For example, when I removed the three intervals that involved missing data, the mean dropped to 88 minutes.  I was more interested in the "stability" (how much of a change occurred when the multiple intervals were removed) of the median.  When the three multiple intervals were removed, the median remained at 90m. Just for fun, I decided to examine the "stability" of the median calculated by geysertimes for some other selected geysers.   At the time I looked at the data, the only two geysers with multiple intervals were Grand and Great Fountain.  Thus, both the mean and median for the time period were "actual" values. Castle had 4 missing data points, assuming intervals over 20 hours were not closed intervals.  Elimination of the 4 multiple intervals dropped the mean from 16h37m to 12h44m, but the median was "stable," dropping only 12 minutes from 14h26m to 14h14m.  Note that these means and medians do not distinguish between intervals between minor and major eruptions. Daisy also had only 4 multiple intervals, assuming intervals over 3 hours were not closed intervals.  Elimination of the 4 multiple intervals dropped the mean from 4h44m to 2h28m, but the median was quite stable, decreasing by only one minute from 2h32m to 2h31m. Only 9 of the 21 intervals used in geysertimes calculations for Riverside were closed intervals.  Because the multiple intervals included 1 double, 5 triples, 4 quadruples, one interval of 1d11h, and one interval of 2d5h, neither the geysertimes mean of 16h15m and median of 16h39m were close approximations of the actual mean and median.  The nine closed intervals had a mean of 5h55m and a median of 6h01m. I eliminated the 10 intervals over 24 hours from the calculations of geyser statistics for Beehive.  The geysertimes mean was 21h04m, the adjusted mean was 14h21m.  The geysertimes median was 16h06m, the adjusted median was 14h59m.  Thus, the median only moved 1 hour. Statistics for Fan & Mortar included the 238d9h dormancy.  Removing it significantly changes the mean, but doesn't change the median.  The dormancy period will drop out of the calculations after three more eruptions of F&M.   All intervals of Fountain Geyser for the last 21 reports were double intervals, so division of the mean and median by two would yield a good approximation of the "actual" mean and median for the period involved.  Lion had only 3 "missing data" (probably involving some time frame including time between one series and the next) amounts included in the geysertimes calculations, so the geysertimes median of 1h10m was a good approximations of the median between eruptions within a series.   Interestingly, the geyser I had not realized would show stability in the median was Pink Cone.  Because the last set of eruptions included the string of reports from my visit to the Park, there were only three multiple intervals so the median of 23h44m closely approximated the "actual" median for that time period. Comments about stability of the mean and medians shown on geysertimes.org are relevant only to the last 21 reports shown as of about midnight September 27. With decreasing daylight hours for webcam viewing and decreased numbers of gazers in the park, intervals between reports on geysertimes will begin to include more multiple intervals, thus decreasing the stability of the mean and median reported on geysertimes for most geysers. Lynn Stephens   		 	   		  
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