Information Technology Reference
In-Depth Information
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Control
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Treatment
FIGURE 7.3
Box and Whiskers Plot.
The box encompasses the middle 50%
of each sample while the “whiskers” lead to the smallest and largest values. The
line through the box is the median of the sample; that is, 50% of the sample is
larger than this value, while 50% is smaller. The plus sign indicates the sample
mean. Note that the mean is shifted in the direction of a small number of very
large values.
normal distribution. This is because the sum of a large number of random
variables each of which makes only a small contribution to the total is a
normally distributed random variable.
9
And in a sample mean based on
n
observations, each contributes only 1/
n
th the total. How close the fit is
to a normal will depend upon the size of the sample and the distribution
from which the observations are drawn.
The distribution of a uniform random number
U
[0,1] is a far cry from
the bell-shaped curve of Figure 7.1. Only values between 0 and 1 have a
positive probability, and in stark contrast to the normal distribution, no
range of values between zero and one is more likely than another of the
same length. The only element the uniform and the normal distributions
have in common is their symmetry about the population mean. Yet to
obtain normally distributed random numbers for use in simulations a fre-
quently employed technique is to generate 12 uniformly distributed
random numbers and then take their average.
9
This result is generally referred to as the Central Limit Theorem. Formal proof can be
found in a number of texts including Feller [1966, p. 253].
