[pct-l] ...Statistics

[JoAnn M. Michael]

"...Statistics" ????  Oh good heavens, I barely got out of Algebra  alive!!!!!   lol

are we there yet
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I wrote yesterday:
> I suppose you could do the math, but the probability of 15% of hikers
> (45 out of 300) randomly choosing the same exact day to start seems
> remote. Any statistician out there?

I dug into this a bit.  I assumed that hiker start dates followed
a normal (bell curve) distribution with or without the ADZPCTKO.
I also assumed that the vast majority of hikers all start within
a one month window.

With those assumptions you find that a standard deviation of 8 days
results in 95% of the hikers starting within a 32 day window.  That
is two standard deviations from the mean start date (whatever that
may be).

Based on those assumptions and assuming 300 total hikers:

   %   hikers  window
95%   286     32.0
68%   204     16.0
38%   114     8.0
20%    59     4.0
10%    28     1.9

That first row represents my statement that 95% of hikers will start
within a 32 day window with an 8 day standard deviation.

For comparison, 7 day deviation results in a 28 day window for 95%
of hikers and a 9 day deviation results in a 36 day window for 95%
of hikers.

The more interesting number though is the expected number of hikers
near the mean of the distribution.  In the table above you can see
that 10% of the hikers (28) would be expected to start within two
days of the mean (14 hikers per day).

It has been reported that 40-45 hikers started out from Morena
on the Sunday after the last kickoff.  We can ask the question:
What standard deviation would cause us to expect 40 hikers out of
300 to start out right around the mean?

The answer is that you have to drop the standard deviation down
to 3 before you even get close.  The departure table looks like
this in that case:

   %  hikers window
95%   286    12.0
68%   204     6.0
38%   114     3.0
20%    59     1.5
10%    28     0.7

The first row says that 95% of the hikers start within a single
12 day window.  The remaining 14 hikers are before or after that
window.

That last row represents 40 hikers/day.

I believe my numbers are mathematically correct given my assumptions
but it is certainly reasonable to challenge those assumptions.  The
biggest assumption is that hikers choose departure dates in a
uniform normal distribution.  Weekends are probably the biggest
argument against that assumption.

Gary Wright (Radar)