Descriptive (also known
as 'enumerative') statistics are used to
provide information about the specific data
that is being analyzed. For example the
mean of the three values 4, 8 and 9 is 7.
Analytical (also known as 'inferential')
statistics are used to draw conclusions
('inferences') about a population based
on sample data.
Suppose the three values 4, 8 and 9 referred
to the ages of three children surveyed in
a toy shop. Analytical statistics would
be used to infer that the mean age of all
the children who frequented that toy shop
was 7. Clearly it would not be wise to make
that inference from such a small sample.
A proper study would involve making sure
that the sample size was
sufficient, and that proper sampling
methods were used to give confidence
that the sample was representative of the
population being studied.
Refer also to Hypothesis
Testing and Confidence
Intervals for related topics.