Game Development Reference
In-Depth Information
FIGURE 11.4
A generic representation of a normal (Gaussian) distribution showing
the range, mean, median, upper and lower limits, and one standard deviation.
Of course, it could certainly be
smaller
than 100. We must make certain to not
confuse the parameters of the scenario and the reality of the sample. If no one in
our sample guessed 100, the uppermost bound would not be 100. In our example
subset illustrated in Figure 11.2, the range was about 71—from 0 to 70. In this case
the
actual
range differed from the theoretical maximum that the parameters of the
scenario defined.
There are times, however, when there are no parameters that would artificially
constrain a range. For example, the distribution of people's heights has no theoret-
ical maximum—or at least not one that we have found. Therefore, the uppermost
limit of the distribution is the height of the tallest person. Similarly, the lower limit
of the range is pinned at the height of the shortest person in the sample. The result-
ing range is the difference between those two extremes.
We must remember that the range is specific to the population. Two different
populations may have completely different ranges. An obvious example would be the
distribution of the heights of NBA players compared to the heights of the general
population. They each have their own maximums and minimums which, in turn,
yield different ranges.
Mean, Median, and Mode
Another major player in defining a normal distribution is the relative locations of
the
mean,
the
median,
and the
mode
. The mean (represented by the Greek letter
mu
:
) is the average value of all the items in the population. The median is the point
where there are as many items greater than it as less than it. The mode is the point in
the range that has the most samples.
μ
