Central Limit Theorem (1 of 2)
The central limit theorem states that given a distribution with a
mean μ and variance σ², the sampling
distribution of the mean
with a mean (μ) and a
variance σ²/N as N, the sample size,
The amazing and counter-intuitive thing about the central limit
theorem is that no matter what the shape of the original
distribution, the sampling distribution of the mean approaches a
normal distribution. Furthermore, for most distributions, a normal
distribution is approached very quickly as N increases. Keep in mind
that N is the sample size for each mean and not the number of
samples. Remember in a sampling
the number of samples is assumed to be infinite. The
sample size is the number of scores in each sample; it is the number
of scores that goes into the computation of each mean.
On the next page are shown
the results of a simulation exercise to demonstrate the central limit theorem.
The computer sampled N scores from a uniform distribution
computed the mean. This procedure was performed 500 times for each of the
sample sizes 1, 4, 7, and 10.