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It is very common to see no distinction between probability concepts and statistical concepts.Many times material from both of these subjects gets lumped under the heading “probability and statistics,” with no attempt to separate what topics are from which discipline.
Questions of this type would be: If instead, we have no knowledge about the types of socks in the drawer, then we enter into the realm of statistics.
Statistics help us to infer properties about the population on the basis of a random sample.
When it began to flourish, it did so in the context of the “new science” of the 17th-century scientific revolution, when the use of calculation to solve tricky problems had gained a new credibility.
Cardano, moreover, had no great faith in his own calculations of gambling odds, since he believed also in luck, particularly in his own.
Despite these practices and the common ground of the subjects, they are distinct.
What is the difference between probability and statistics?Although we typically do not have complete information about a population, we can use theorems and results from probability to arrive at statistical results. Underlying all of this is the assumption that we are dealing with random processes.This is why we stressed that the sampling procedure we used with the sock drawer was random.Probability has its origin in the study of gambling and insurance in the 17th century, and it is now an indispensable tool of both social and natural sciences.Statistics may be said to have its origin in census counts taken thousands of years ago; as a distinct scientific discipline, however, it was developed in the early 19th century as the study of populations, economies, and moral actions and later in that century as the mathematical tool for analyzing such numbers.More than a century earlier, the Italian mathematician, physician, and gambler Girolamo Cardano calculated odds for games of luck by counting up equally probable cases.His little book, however, was not published until 1663, by which time the elements of the theory of chances were already well known to mathematicians in Europe.The main difference between probability and statistics has to do with knowledge.By this, we refer to what are the known facts when we approach a problem.It will never be known what would have happened had Cardano published in the 1520s.It cannot be assumed that probability theory would have taken off in the 16th century.