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Almost all biologists who use our center have been convinced that for roughly
normal or log normal distributed signals the arithmetic or geometric mean is an
appropriate measure of central tendency. However, for distributions which vary
greatly from this, the "average" contains very little information regarding
central tendancy. Thus, many researchers here will use order statistics (median,
25th, 75th percentile) to characterize the central tendancy and spread of such a
distribution.
Order statistics have the following characteristics: (1) when data is "normally"
distributed, they agree with the mean. (2) they are not sensitive to outliers,
so gating conditions and off-scale pile-ups affect them less, (3) for list mode
data they are faster to calculate than means.
In a normal distribution, the coefficient of variation (cv) is:
cv = .742 (75th-25th)/median
This quantity also has properties (2) and (3) above, that is, it is less
sensitive than a true "CV" to gating and outliers and provides a very rapid
algorithm for monitoring cv's during machine alignment.
-Marty Bigos
Stanford Shared FACS Facility
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