Statistical methods are used to summarize and describe a collection of data; this is called descriptive statistics. In addition, patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and then used to draw inferences about the process or population being studied; this is called inferential statistics.
Statistics arose no later than the 18th century from the need of states to collect data on their people and economies, in order to administer them. The meaning broadened in the early 19th century to include the collection and analysis of data in general.
A correlation, (often measured as a correlation coefficient), indicates the strength and direction of a linear relationship between two random variables. In general statistical usage, correlation or co-relation refers to the departure of two variables from independence. In this broad sense there are several coefficients, measuring the degree of correlation, adapted to the nature of data. A number of different coefficients are used for different situations. The best known is the Pearson product-moment correlation coefficient, which is obtained by dividing the covariance of the two variables by the product of their standard deviations. Despite its name, it was first introduced by Francis Galton.
A polar area diagram by Florence Nightingale. The polar area diagram is similar to a pie chart, except that the sectors are each of an equal angle and differ rather in how far each sector extends from the centre of the circle, enabling multiple comparisons on one diagram. This "DIAGRAM of the CAUSES of MORTALITY in the ARMY in the EAST" was published in Notes on Matters Affecting the Health, Efficiency, and Hospital Administration of the British Army and sent to Queen Victoria in 1858. It shows the number of deaths due to preventable diseases (blue), wounds (red), and other causes (black).
...that one result of the birthday problem is that among a group of 23 (or more) randomly chosen people, there is more than 50% probability that some pair of them will both have been born on the same day of the year?
...that the term bias is not necessarily pejorative in statistics, since biased estimators may have desirable properties (such as a smaller mean squared error than any unbiased estimator), and that in extreme cases the only unbiased estimators are not even within the convex hull of the parameter space?
...that William Sealy Gosset published under the pseudonym Student in order to avoid detection by his employer, and so his most famous achievement is now referred to as Student's t-distribution, which might otherwise have been Gosset's t-distribution?
...that in 1747, by dividing 12 men suffering from scurvy into six pairs and giving each group different additions to their basic diet for a period of two weeks, the surgeon James Lind conducted one of the first controlled experiments?
...that for the number of shuffles needed to randomize a deck, Persi Diaconis concluded that for good shuffling technique, the deck did not start to become random until five good riffle shuffles, and was truly random after seven, in the precise sense of variation distance described in Markov chain mixing time?
...that for many standard probability distributions, there are infinitely many outcomes in the sample space, so that attempting to define probabilities for all possible subsets of such spaces would cause difficulties for 'badly-behaved' sets such as those which are nonmeasurable?