Rates, underlying distributions, and measuring things When comparing two metrics, say visitors and time spent on a website, by just taking the ratio (time on site)/(visitors) can this be misleading?  And if so how can we describe this problem mathematically or with statistics.
More context, the vanilla interpretation of such a ratio is that the "typical" visitor spends t minutes on a site.  What if we look at the actual Time on Site by Visitor, and this distribution is hypothetically multimodal, or heavily skewed, basically something that would not lend itself to being interpreted as having a typical visitor?
What I'm curious about is functionally describing what's going on here.
I feel the answer is in the realm of these are actually random processes that we're taking a ratio of and hence the dynamics of each process should dictate the dynamics of the ratio of the processes...right?
In physical problems this is probably not often an issue as the randomness is probably mostly measuring errors but in other systems that are inherently noisy maybe this should be a consideration.
 A: This ratio is simply the arithmetic mean. It can indeed be misleading for skewed distributions but there are other measures of central tendency. It does also make sense to consider the (hypothesized) generating process when choosing a measure of central tendency. For example, normal distributions result from additive processes (that's the central limit theorem) whereas multiplicative processes commonly create log-normal distributions. The geometric mean (not the arithmetic mean) is a natural way to describe the central tendency in a log-normal distribution.
However, I am not so sure that physical processes are fundamentally different from social processes (if that's the distinction you want to make) in this respect. The Wikipedia article on the log-normal distribution gives several examples across the biological and physical sciences.
I am also not entirely convinced that this invalidates the idea of a “typical visitor” any more than variance in a normal distribution. Even with a perfectly normal distribution, the “typical visitor” is an abstraction and individual times can vary a lot (what counts as “a lot” depends on your purpose and the nature of the variable). With a distribution skewed to the right, the median time can still be thought as the typical visit duration, even if a handful of visits can be expected to last much longer.
A: Google "Little's Law" for literature that may help e.g. 
http://en.wikipedia.org/wiki/Little's_law
For a review in a statistical context see 
M.F. Ramalhoto, J.A. Amaral, and M.T. Cochito. 1983. A survey of J. Little's formula. International Statistical Review 51: 255- 278.
