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Interquartile Mean
The interquartile mean (IQM) (or midmean) is a statistical measure of central tendency based on the truncated mean of the interquartile range. The IQM is very similar to the scoring method used in sports that are evaluated by a panel of judges: ''discard the lowest and the highest scores; calculate the mean value of the remaining scores''. Calculation In calculation of the IQM, only the data between the first and third quartiles is used, and the lowest 25% and the highest 25% of the data are discarded. : x_\mathrm = \sum_^ assuming the values have been ordered. Examples Dataset size divisible by four The method is best explained with an example. Consider the following dataset: :5, 8, 4, 38, 8, 6, 9, 7, 7, 3, 1, 6 First sort the list from lowest-to-highest: :1, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 38 There are 12 observations (datapoints) in the dataset, thus we have 4 quartiles of 3 numbers. Discard the lowest and the highest 3 values: :1, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 38 We now ... [...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] |
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] |
Everything2
Everything2 (styled Everything2 or E2 for short) is a collaborative Web-based community consisting of a database of interlinked user-submitted written material. E2 is moderated for quality, but has no formal policy on subject matter. Writing on E2 covers a wide range of topics and genres, including encyclopedic articles, diary entries (known as "daylogs"), poetry, humor, and fiction. History The predecessor of E2 was a similar database called Everything (later labeled "Everything1" or "E1") which was started around March 1998 by Nathan Oostendorp and was initially closely aligned with and promoted by the technology-related news website Slashdot (by virtue of various key principals having attended the Holland Christian High School), even sharing (at the time) some administrators. The Everything2 software offered vastly more features, and the Everything1 data was twice incorporated into E2: once on November 13, 1999, and again in January 2000. The Everything2 server used to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust Statistics
Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a parametric distribution. For example, robust methods work well for mixtures of two normal distributions with different standard deviations; under this model, non-robust methods like a t-test work poorly. Introduction Robust statistics seek to provide methods that emulate popular statistical methods, but which are not unduly affected by outliers or other small departures from Statistical assumption, model assumptions. In statistics, classical estimation methods rely heavily on assumpti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume-weighted Average Price
In finance, volume-weighted average price (VWAP) is the ratio of the value of a security or financial asset traded to the total volume of transactions during a trading session. It is a measure of the average trading price for the period. Typically, the indicator is computed for one day, but it can be measured between any two points in time. VWAP is often used as a trading benchmark by investors who aim to be as passive as possible in their execution. Many pension funds, and some mutual funds, fall into this category. The aim of using a VWAP trading target is to ensure that the trader executing the order does so in line with the volume on the market. It is sometimes argued that such execution reduces transaction costs by minimizing market impact costs (the additional cost due to the market impact In financial markets, market impact is the effect that a market participant has when it buys or sells an asset. It is the extent to which the buying or selling moves the price against ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SOFR
Secured Overnight Financing Rate (SOFR) is a secured interbank overnight interest rate. SOFR is a reference rate (that is, a rate used by parties in commercial contracts that is outside their direct control) established as an alternative to LIBOR. LIBOR has been published in a number of currencies and underpins financial contracts all over the world. Because LIBOR is derived from banks' daily quotes of borrowing costs, banks were able to manipulate the rates through lying in the surveys. Deeming it prone to manipulation, UK regulators decided to discontinue LIBOR in 2021. In 2022, the LIBOR Act passed by the U.S. Congress established SOFR as a default replacement rate for LIBOR contracts that lack mechanisms to deal with LIBOR's cessation. The Act also grants a safe harbor to LIBOR contracts that transition to SOFR. Previously, SOFR was seen as the likely successor of LIBOR in the US since at least 2021. SOFR uses actual costs of transactions in the overnight repo market, calcula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
London Interbank Offered Rate
The London Inter-Bank Offered Rate is an interest-rate average calculated from estimates submitted by the leading banks in London. Each bank estimates what it would be charged were it to borrow from other banks. The resulting average rate is usually abbreviated to Libor () or LIBOR, or more officially to ICE LIBOR (for Intercontinental Exchange LIBOR). It was formerly known as BBA Libor (for British Bankers' Association Libor or the trademark bba libor) before the responsibility for the administration was transferred to Intercontinental Exchange. It is the primary benchmark, along with the Euribor, for short-term interest rates around the world. Libor was phased out at the end of 2021, and market participants are being encouraged to transition to risk-free interest rates. As of late 2022, parts of it have been discontinued, and the rest is scheduled to end within 2023; the Secured Overnight Financing Rate (SOFR) is its replacement. Libor rates are calculated for five currenci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trimean
In statistics the trimean (TM), or Tukey's trimean, is a measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles: : TM= \frac This is equivalent to the average of the median and the midhinge: : TM= \frac\left(Q_2 + \frac\right) The foundations of the trimean were part of Arthur Bowley's teachings, and later popularized by statistician John Tukey in his 1977 book which has given its name to a set of techniques called exploratory data analysis. Like the median and the midhinge, but unlike the sample mean, it is a statistically resistant L-estimator with a breakdown point of 25%. This beneficial property has been described as follows: Efficiency Despite its simplicity, the trimean is a remarkably efficient estimator of population mean. More precisely, for a large data set (over 100 points) from a symmetric population, the average of the 20th, 50th, and 80th percentile is the most efficient 3 point L-es ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Midhinge
In statistics, the midhinge is the average of the first and third quartiles and is thus a measure of location. Equivalently, it is the 25% trimmed mid-range or 25% midsummary; it is an L-estimator. : \operatorname(X) = \overline = \frac = \frac = M_(X) The midhinge is related to the interquartile range (IQR), the difference of the third and first quartiles (i.e. IQR = Q_3 - Q_1), which is a measure of statistical dispersion. The two are complementary in sense that if one knows the midhinge and the IQR, one can find the first and third quartiles. The use of the term "hinge" for the lower or upper quartiles derives from John Tukey's work on exploratory data analysis in the late 1970s,Tukey, J. W. (1977) ''Exploratory Data Analysis'', Addison-Wesley. and "midhinge" is a fairly modern term dating from around that time. The midhinge is slightly simpler to calculate than the trimean (TM), which originated in the same context and equals the average of the median (\tilde = Q_2 = P_) and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Mean
In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics, because it helps distinguish it from other means, such as the geometric mean and the harmonic mean. In addition to mathematics and statistics, the arithmetic mean is used frequently in many diverse fields such as economics, anthropology and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population. While the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is greatly influe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Tendency
In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.Weisberg H.F (1992) ''Central Tendency and Variability'', Sage University Paper Series on Quantitative Applications in the Social Sciences, p.2 Colloquially, measures of central tendency are often called ''averages.'' The term ''central tendency'' dates from the late 1920s. The most common measures of central tendency are the arithmetic mean, the median, and the mode. A middle tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution. Occasionally authors use central tendency to denote "the tendency of quantitative data to cluster around some central value."Upton, G.; Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP (entry for "central tendency")Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP for International Statistical Institute. (entry for "ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Outlier
In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set. An outlier can be an indication of exciting possibility, but can also cause serious problems in statistical analyses. Outliers can occur by chance in any distribution, but they can indicate novel behaviour or structures in the data-set, measurement error, or that the population has a heavy-tailed distribution. In the case of measurement error, one wishes to discard them or use statistics that are robust to outliers, while in the case of heavy-tailed distributions, they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
