Uncertainty and Statistics:
A main goal of statistics is to quantify or measure uncertainty; this branch of statistics is called "inferential statistics." classical statistics measures uncertainty using fundamental concepts and theories of probability and randomness. Modern statistics often applies Monte Carlo simulation as well.
For example, suppose you know the incomes of 100 individuals. If you consider these 100 figures only as a given fact about the 100 people, then there is no any uncertainty and, hence, we do not have any need for inferential statistics. A table with 100 entries like "John Smith - 50,000" will be sufficient.
Now suppose you wish to learn something about incomes in the whole population of a large city, say, the average income. It is also known that the 100 individuals have been selected randomly from the city population. The 100 values of income do not reflect the income of the whole population exactly - i.e. some uncertainty is present. At the same time knowledge of these 100 figures still reduces the uncertainty about the average income in the city. Here statistics can help quantify the uncertainty, e.g using point estimator s of the population mean , confidence interval s for the obtained estimates, and statistical test s to test hypotheses about the population mean.