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Freedman–Diaconis Rule
In statistics, the Freedman–Diaconis rule can be used to select the width of the bins to be used in a histogram. It is named after David A. Freedman and Persi Diaconis. For a set of empirical measurements sampled from some probability distribution, the Freedman-Diaconis rule is designed roughly to minimize the integral of the squared difference between the histogram (i.e., relative frequency density) and the density of the theoretical probability distribution. The general equation for the rule is: :\text=2\, where \operatorname(x) is the interquartile range In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference ... of the data and n is the number of observations in the sample x. Other approaches With the factor 2 replaced by approximately 2.59, the Freedman-Diaconis rule asy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Histogram
A histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson. To construct a histogram, the first step is to " bin" (or "bucket") the range of values—that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) must be adjacent and are often (but not required to be) of equal size. If the bins are of equal size, a bar is drawn over the bin with height proportional to the frequency—the number of cases in each bin. A histogram may also be normalized to display "relative" frequencies showing the proportion of cases that fall into each of several categories, with the sum of the heights equaling 1. However, bins need not be of equal width; in that case, the erected rectangle is defined to have its ''area'' proportional to the frequency ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David A
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". was, according to the Hebrew Bible, the third king of the United Kingdom of Israel. In the Books of Samuel, he is described as a young shepherd and harpist who gains fame by slaying Goliath, a champion of the Philistines, in southern Canaan. David becomes a favourite of Saul, the first king of Israel; he also forges a notably close friendship with Jonathan, a son of Saul. However, under the paranoia that David is seeking to usurp the throne, Saul attempts to kill David, forcing the latter to go into hiding and effectively operate as a fugitive for several years. After Saul and Jonathan are both killed in battle against the Philistines, a 30-year-old David is anointed king over all of Israel and Judah. Following his rise to power, David ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Persi Diaconis
Persi Warren Diaconis (; born January 31, 1945) is an American mathematician of Greek descent and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University. He is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards. Biography Diaconis left home at 14 to travel with sleight-of-hand legend Dai Vernon, and dropped out of high school, returning to school at age 24 to learn math, motivated to read William Feller's famous two-volume treatise on probability theory, ''An Introduction to Probability Theory and Its Applications''. He attended the City College of New York for his undergraduate work, graduating in 1971, and then obtained a Ph.D. in Mathematical Statistics from Harvard University in 1974), learned to read Feller, and became a mathematical probabilist.Jeffrey R. Young, "The Magical Mind of Persi Diaconis" ''Chronicle of Highe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interquartile Range
In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference between the 75th and 25th percentiles of the data. To calculate the IQR, the data set is divided into quartiles, or four rank-ordered even parts via linear interpolation. These quartiles are denoted by Q1 (also called the lower quartile), ''Q''2 (the median), and ''Q''3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = ''Q''3 − ''Q''1. The IQR is an example of a trimmed estimator, defined as the 25% trimmed range, which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points. It is also used as a robust measure of scale It can be clearly visualized by the box on a Box plot. Use Unlike tota ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Histogram
A histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson. To construct a histogram, the first step is to " bin" (or "bucket") the range of values—that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) must be adjacent and are often (but not required to be) of equal size. If the bins are of equal size, a bar is drawn over the bin with height proportional to the frequency—the number of cases in each bin. A histogram may also be normalized to display "relative" frequencies showing the proportion of cases that fall into each of several categories, with the sum of the heights equaling 1. However, bins need not be of equal width; in that case, the erected rectangle is defined to have its ''area'' proportional to the frequency ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rules Of Thumb
In English, the phrase ''rule of thumb'' refers to an approximate method for doing something, based on practical experience rather than theory. This usage of the phrase can be traced back to the 17th century and has been associated with various trades where quantities were measured by comparison to the width or length of a thumb. A modern folk etymology holds that the phrase is derived from the maximum width of a stick allowed for wife-beating under English common law, but no such law ever existed. This belief may have originated in a rumored statement by 18th-century judge Sir Francis Buller that a man may beat his wife with a stick no wider than his thumb. The rumor produced numerous jokes and satirical cartoons at Buller's expense, but there is no record that he made such a statement. English jurist Sir William Blackstone wrote in his '' Commentaries on the Laws of England'' of an "old law" that once allowed "moderate" beatings by husbands, but he did not mention thumbs or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Charts And Diagrams
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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