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.
