Welcome to the Statistics portal
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the natural and social sciences to the humanities, government and business.
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.
|Margin of error
The margin of error is a statistic expressing the amount of random sampling error in a survey's results. The larger the margin of error, the less confidence one should have that the poll's reported results are close to the "true" figures; that is, the figures for the whole population.
The margin of error is usually defined as the radius of a confidence interval for a particular statistic from a survey. One example is the percent of people who prefer product A versus product B. When a single, global margin of error is reported for a survey, it refers to the maximum margin of error for all reported percentages using the full sample from the survey. If the statistic is a percentage, this maximum margin of error can be calculated as the radius of the confidence interval for a reported percentage of 50%.
The margin of error has been described as an "absolute" quantity, equal to a confidence interval radius for the statistic. For example, if the true value is 50 percentage points, and the statistic has a confidence interval radius of 5 percentage points, then we say the margin of error is 5 percentage points. As another example, if the true value is 50 people, and the statistic has a confidence interval radius of 5 people, then we might say the margin of error is 5 people.
|A pie chart from Playfair's 1801 "Statistical Breviary"
William Playfair (22 September 1759 – 11 February 1823) was a Scottish engineer and political economist, the founder of graphical methods of statistics. He invented four types of diagrams: in 1786 the line graph and bar chart of economic data, and in 1801 the pie chart and circle graph, used to show part-whole relations. Playfair had a variety of careers: he was in turn a millwright, engineer, draftsman, accountant, inventor, silversmith, merchant, investment broker, economist, statistician, pamphleteer, translator, publicist, land speculator, convict, banker, ardent royalist, editor, blackmailer and journalist. He has been variously described as an "engineer, political economist and scoundrel" and an "ingenious mechanic and miscellaneous writer."
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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 the Cauchy distribution is an example of a distribution which has no mean, variance or higher moments defined?
- ...that according to Benford's law, the first digit from many real-life sources of data is 1 almost one third of the time?
- ...that the Law of Truly Large Numbers of Diaconis and Mosteller states that with a sample size large enough, any outrageous thing is likely to happen?
- ...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?
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