The law of large numbers states (informally) that as the number of independent observations drawn from a population with finite mean
increases, the mean of those observed values approaches
. This Demonstration illustrates that behavior by plotting the sample mean as a function of the current sample size
, for
to
. Random samples can be drawn from a population of 0's and 1's (with any proportion of 1's), a normal population (with a range of
and
available), or from the (first 100,000) digits of
. The first 100 digits of
are available as a population, with samples of size
consisting of the first
digits, to allow for classroom illustration with a familiar and frequently referred to as random set of digits.
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