Designing and analysing market surveys, opinion surveys and censuses. Estimating the ore reserves of a mine, planning the mining strategy for extracting the ore and monitoring the production figures. Establishing quality control procedures for a factory and estimating the reliability of a manufactured product. Designing experiments aimed at improving the performance of a manufacturing processes. Interpreting satellite images and analysing the frequencies of variable stars.
Statistics is the mathematical science of making precise statements about uncertain possibilities.
These statements are in terms of probability or chance. For example, in evaluating a gambling system, the statistician will calculate the probabilities of the various outcomes of the gambling strategy - often with the help of a computer. From this he can predict the expected long-term winnings and losses from applying this strategy. Similarly, the statistician can analyse the performance of automatic teller machines from data on the arrival rates of customers and on the lengths of time they took to do their transactions. From this he can estimate the probability of a customer having to queue for service as well as her expected waiting time.