Page 31 - Quality control of pharmaceuticals (07-PA 704)

treating the results in Table 2.1 as ten samples, each containing five
results. Taking each column as one sample, the means are 0.506,
0.504, 0.502, 0.496, 0.502, 0.492, 0.506, 0.504, 0.500 and 0.486.

We can see at once that these means are more closely clustered than the
original measurements. If we took still more samples of five
measurements and calculated their means, those means would have a
frequency distribution of their own.

The distribution of all possible sample means (in this case, an infinite
number) is called the sampling distribution of the mean. Its mean
is the same as the mean of the original population. Its standard
deviation is called the standard error of the mean (SEM). There is
an exact mathematical relationship between the latter and the
standard deviation, σ, of the distribution of the individual
measurements:

For a sample of n measurements, standard error of the mean
= σ/√n

Another property of the sampling distribution of the mean is that,
even if the original population is not normal, the sampling distribution
of the mean tends to the normal distribution as n increases. This result
is known as the central limit theorem. This theorem is oIII great