Request for Question Clarification by
mathtalk-ga
on
14 Jun 2004 18:15 PDT
Hi, dstew-ga:
Let's make sure we have a clear framework for your Question before
attempting an Answer.
Often in statistics one is trying to understand the characteristics of
a large Population of values/instances from a relatively small subset
of observations, which for the sake of clarity we will call the Sample
to distinguish it from the overall Population.
Now the standard deviation and variance can be defined for both a
Sample set of values and the entire Population. But in the case we
are limited to observing only the Sample, we may ask what can
reasonably be inferred about the Population.
For example, a useful estimate of the mean of the Population is
obtained by using the mean (arithmetic average) of the Sample.
The standard deviation and the variance are (like the mean) statistics
(single numbers that summarize properties of a set of values). The
standard deviation and variance are (given the size of the set)
interchangeable from manipulation of their definitions; in fact the
standard deviation is usually defined in terms of the variance.
Given that, either the standard deviation or the variance may be said
to be a statistical measure of volatility in the intuitive meaning,
i.e. a measure of how far apart a pair of observations from set are
apt to be.
What we can do is review the definitions of standard deviation,
variance, and mean, and show:
1) How the Sample statistics are useful in estimating the Population
statistics, and
2) How the standard deviation (for example) might be used to estimate
"volatility" in the narrow sense of the average distance between two
observations (chosen independently).
Please let me know if this would be satisfactory as an Answer.
regards, mathtalk-ga
