ch02 JWBK035-Vince February 12, 2007 6:50 Char Count= 0
Probability Distributions 45a bin for trades that made nothing to$99.99, the next bin would be for
trades that made$100 to$199.99, and so on. There is a loss of information
content in binning this way, yet the profile of the distribution of the trade
profits and losses remains relatively unchanged.Descriptive Measures of Distributions
Most people are familiar with the average, or more specifically thearith-
metic mean. This is simply the sum of the data points in a distribution
divided by the number of data points:A=
(N
∑
i= 1Xi)/
N (2.01)
where: A=The arithmetic mean.
Xi=The ith data point.
N=The total number of data points in the distribution.The arithmetic mean is the most common of the types of measures of
location,orcentral tendencyof a body of data, a distribution. However,
you should be aware that the arithmetic mean is not the only available
measure of central tendency and often it is not the best. The arithmetic
mean tends to be a poor measure when a distribution has very broad tails.
Suppose you randomly select data points from a distribution and calcu-
late their mean. If you continue to do this, you will find that the arithmetic
means thus obtained converge poorly, if at all, when you are dealing with
a distribution with very broad tails.
Another important measure of location of a distribution is themedian.
The median is described as the middle value when data are arranged in an
array according to size. The median divides a probability distribution into
two halves such that the area under the curve of one half is equal to the
area under the curve of the other half. The median is frequently a better
measure of central tendency than the arithmetic mean. Unlike the arith-
metic mean, the median isnotdistorted by extreme outlier values. Further,
the median can be calculated even foropen-endeddistributions. An open-
ended distribution is a distribution in which all of the values in excess of a
certain bin are thrown into one bin. An example of an open-ended distribu-
tion is the one we were compiling when we recorded the finishing position
in horse racing for the horse starting out in the pole position. Any finishes