Biology Reference
In-Depth Information
absolute but relative to the individual or population level in which
one is situated.
A random phenomenon is therefore statistically reproducible for
a population of events. This reproducibility is described using two
parameters, mean and variance. Everyone is familiar with the con-
cept of a mean. Variance is a measure of the variability of a vari-
able compared with its mean.
Figure 1 shows examples of distribution of a random variable
with different variances. In such distributions, if the variance is
very small, a phenomenon can seem to behave like a deterministic
phenomenon even though it is probabilistic. Indeed, each time it is
produced, the results, which are very close to the mean, seem iden-
tical. This is all the more true when the law of large numbers is
applied, if it is a phenomenon itself composed of a very great num-
ber of random events. The variance of a phenomenon composed of
a series of random events is in fact reduced as the number of events
d
3
d
2
d
1
v
2
v
1
v
3
m
1
m
2
m
3
F
IGURE
1. A random phenomenon is statistically reproducible.
In a population, a
random variable describing a probabilistic phenomenon is distributed according to
a statistical distribution shown by the mean
m
of the variable in the population
and its variance
v
which shows its variability around this mean.
d
1
,
d
2
and
d
3
are
statistical distributions of this type and have different means and variances. Two
distributions may nevertheless have the same mean but different variances. This
would be the case with two classes where the mean of the grades obtained by the
pupils for their maths homework is 10. In one of the classes however, the grades
range from 2 to 18 while in the other they only range from 9 to 11. The variance
in the first class is greater than in the second. A probabilistic phenomenon with a
small variance, such as that shown by
d
3
, may seem deterministic because each
time it occurs its variance is close to the same mean value.
