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Olympic Average
A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an equal amount of both. This number of points to be discarded is usually given as a percentage of the total number of points, but may also be given as a fixed number of points. For most statistical applications, 5 to 25 percent of the ends are discarded. For example, given a set of 8 points, trimming by 12.5% would discard the minimum and maximum value in the sample: the smallest and largest values, and would compute the mean of the remaining 6 points. The 25% trimmed mean (when the lowest 25% and the highest 25% are discarded) is known as the interquartile mean. The median can be regarded as a fully truncated mean and is most robust. As with other trimmed estimators, the main advantage of the trimmed mean is rob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "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. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...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 statistics, 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, wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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 arithmetic mean 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 18th, 50th, and 82nd percentile is the most efficient 3-p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Winsorising
Winsorizing or winsorization is the transformation of statistics by limiting extreme values in the statistical data to reduce the effect of possibly spurious outliers. It is named after the engineer-turned-biostatistician Charles P. Winsor (1895–1951). The effect is the same as clipping in signal processing. The distribution of many statistics can be heavily influenced by outliers, values that are 'way outside' the bulk of the data. A typical strategy to account for, without eliminating altogether, these outlier values is to 'reset' outliers to a specified percentile (or an upper and lower percentile) of the data. For example, a 90% winsorization would see all data below the 5th percentile set to the 5th percentile, and all data above the 95th percentile set to the 95th percentile. Winsorized estimators are usually more robust to outliers than their more standard forms, although there are alternatives, such as trimming (see below), that will achieve a similar effect. Examp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Libor
The London Inter-Bank Offered Rate (Libor ) was an interest rate average calculated from estimates submitted by the leading Bank, banks in London. Each bank estimated what it would be charged were it to borrow from other banks. It was the primary benchmark, along with the Euribor, for short-term interest rates around the world. Libor was phased out at the end of 2021, with market participants encouraged to transition to risk-free interest rates such as SOFR and SARON. LIBOR was discontinued in the summer of 2023. The last rates were published on 30 June 2023 before 12:00 pm UK time. The 1 month, 3 month, 6 month, and 12 month Secured Overnight Financing Rate (SOFR) is its replacement. In July 2023, the International Organization of Securities Commissions (IOSCO) said four unnamed United States dollar, dollar-denominated alternatives to LIBOR, known as "credit-sensitive rates", had "varying degrees of vulnerability" that might appear during times of market stress. Libor rates w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sport
Sport is a physical activity or game, often Competition, competitive and organization, organized, that maintains or improves physical ability and skills. Sport may provide enjoyment to participants and entertainment to spectators. The number of participants in a particular sport can vary from hundreds of people to a single individual. Sport competitions may use a team or single person format, and may be Open (sport), open, allowing a broad range of participants, or closed, restricting participation to specific groups or those invited. Competitions may allow a "tie" or "draw", in which there is no single winner; others provide tie-breaking methods to ensure there is only one winner. They also may be arranged in a tournament format, producing a champion. Many sports leagues make an annual champion by arranging games in a regular sports season, followed in some cases by playoffs. Sport is generally recognised as system of activities based in physical athleticism or physical de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R (programming Language)
R is a programming language for statistical computing and Data and information visualization, data visualization. It has been widely adopted in the fields of data mining, bioinformatics, data analysis, and data science. The core R language is extended by a large number of R package, software packages, which contain Reusability, reusable code, documentation, and sample data. Some of the most popular R packages are in the tidyverse collection, which enhances functionality for visualizing, transforming, and modelling data, as well as improves the ease of programming (according to the authors and users). R is free and open-source software distributed under the GNU General Public License. The language is implemented primarily in C (programming language), C, Fortran, and Self-hosting (compilers), R itself. Preprocessor, Precompiled executables are available for the major operating systems (including Linux, MacOS, and Microsoft Windows). Its core is an interpreted language with a na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Student's T-test
Student's ''t''-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It is any statistical hypothesis test in which the test statistic follows a Student's ''t''-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known (typically, the scaling term is unknown and is therefore a nuisance parameter). When the scaling term is estimated based on the data, the test statistic—under certain conditions—follows a Student's ''t'' distribution. The ''t''-test's most common application is to test whether the means of two populations are significantly different. In many cases, a ''Z''-test will yield very similar results to a ''t''-test because the latter converges to the former as the size of the dataset increases. History The term "''t''-statistic" is abbreviated from " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when the random errors are assumed to have normal distributions with the same variance. From the perspective of Bayesian inference, ML ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Statistics
In statistics, the ''k''th order statistic of a statistical sample is equal to its ''k''th-smallest value. Together with rank statistics, order statistics are among the most fundamental tools in non-parametric statistics and inference. Important special cases of the order statistics are the minimum and maximum value of a sample, and (with some qualifications discussed below) the sample median and other sample quantiles. When using probability theory to analyze order statistics of random samples from a continuous distribution, the cumulative distribution function is used to reduce the analysis to the case of order statistics of the uniform distribution. Notation and examples For example, suppose that four numbers are observed or recorded, resulting in a sample of size 4. If the sample values are :6, 9, 3, 7, the order statistics would be denoted :x_=3,\ \ x_=6,\ \ x_=7,\ \ x_=9,\, where the subscript enclosed in parentheses indicates the th order statistic of the sam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
