Game Development Reference
In-Depth Information
FIGURE 11.5
A skewed probability distribution has the bulk of
the population on one side and a tail on the other.
As a result, the mean, median, and mode are no longer co-located.
Standard Deviation
Another measurement that gives us valuable information about the makeup of the
distribution is
standard deviation
(represented by the Greek letter
sigma
:
). It tells
us how spread out the bulk of the population is—also known as “dispersion.� A
probability distribution can have exactly the same range, mode, median, and mean,
and yet many different standard deviations (Figure 11.6). This is important to
remember because it is the standard deviation that determines the “character� of the
population. When most of the population is clustered tightly around the mean,
the standard deviation is small. If the standard deviation is high, then we can assume
that there is a wide dispersion of the population. A normal distribution with
Σ
Σ
= 1
is considered a
standard normal distribution
.
There are actually multiple layers of standard deviations for the same curve.
They lie outside each other. For a normal distribution, about 68% of the data is
within the
first standard deviation
—34% on each side of the mean. The
second
standard deviation
is significantly wider than the first—encompassing 95% of the
population. For any normally distributed population, 99.7% lie within
three standard
deviations
of the mean. It is important to note that this is the case for
all
normal
distributions. No matter what the shape of the curve, 68% of the population will be
within that first standard deviation. This is known as the
68-95-99.7 rule
—the rule
being that, in a normal distribution, almost all the data is within three standard
deviations of the mean.
