I understand that the standard deviation of a population is derived by
using N = population in the denominator, and that the standard
deviation of a sample is derived by using N-1 in the denominator (at
least I think that's right), but a number of the books I'm currently
studying have raised questions in my mind as to when a set of data is
considered to be a sample and when it is a population.
Example (from the REA AP statistics test prep guide):
The average monthly rainfall in inches in Birmingham, England, is
shown in the table below:
Jan 2.3
Feb 1.9
Mar 2.1
Apr 1.8
May 2.2
June 2.2
Jul 2.0
Aug 2.8
Sep 2.2
Oct 2.1
Nov 2.5
Dec 2.6
Compute the variance and standard deviation of the monthly rainfall.
The answer provided uses N-1 (= 11) in the denominator, not N. Is
this due to the fact that these 12 months are a sample of all possible
months?
And in "How to Calculate Statistics," a book designed for teachers, it
is claimed that when calculating the standard deviation and variance
of an entire class, one uses N-1 in the denominator. But that doesn't
make sense to me because the population of the class is its own
population, and no sample of the population is involved if every test
score is used in the statistical analysis. Am I to understand that
the class itself is a sample of all people of that age, and hence
since not all (say) 14-year olds took the test in question, by
definition the class is not a population but only a sample?
Is there a widely agreed to rule of thumb as to when one uses N and
when one uses N-1 for the purpose of calculating variance and standard
deviation?
Thanks in advance,
Henry Sun
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