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Quartile
In statistics, quartiles are a type of quantiles which divide the number of data points into four parts, or ''quarters'', of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic. The three quartiles, resulting in four data divisions, are as follows: * The first quartile (''Q''1) is defined as the 25th percentile where lowest 25% data is below this point. It is also known as the ''lower'' quartile. * The second quartile (''Q''2) is the median of a data set; thus 50% of the data lies below this point. * The third quartile (''Q''3) is the 75th percentile where lowest 75% data is below this point. It is known as the ''upper'' quartile, as 75% of the data lies below this point. Along with the minimum and maximum of the data (which are also quartiles), the three quartiles described above provide a five-number summary of the data. This summary is important in statistics because it provides infor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantile
In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities or dividing the observations in a sample in the same way. There is one fewer quantile than the number of groups created. Common quantiles have special names, such as '' quartiles'' (four groups), '' deciles'' (ten groups), and '' percentiles'' (100 groups). The groups created are termed halves, thirds, quarters, etc., though sometimes the terms for the quantile are used for the groups created, rather than for the cut points. -quantiles are values that partition a finite set of values into subsets of (nearly) equal sizes. There are partitions of the -quantiles, one for each integer satisfying . In some cases the value of a quantile may not be uniquely determined, as can be the case for the median (2-quantile) of a uniform probability distribution on a set of even size. Quantiles can also be applied to continuous di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boxplot
In descriptive statistics, a box plot or boxplot is a method for demonstrating graphically the locality, spread and skewness groups of numerical data through their quartiles. In addition to the box on a box plot, there can be lines (which are called ''whiskers'') extending from the box indicating variability outside the upper and lower quartiles, thus, the plot is also called the box-and-whisker plot and the box-and-whisker diagram. Outliers that differ significantly from the rest of the dataset may be plotted as individual points beyond the whiskers on the box-plot. Box plots are non-parametric: they display variation in samples of a statistical population without making any assumptions of the underlying statistical distribution (though Tukey's boxplot assumes symmetry for the whiskers and normality for their length). The spacings in each subsection of the box-plot indicate the degree of dispersion (spread) and skewness of the data, which are usually described using the five-n ... [...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 ''Q''1 (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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Five-number Summary
The five-number summary is a set of descriptive statistics that provides information about a dataset. It consists of the five most important sample percentiles: # the sample minimum ''(smallest observation)'' # the lower quartile or ''first quartile'' # the median (the middle value) # the upper quartile or ''third quartile'' # the sample maximum (largest observation) In addition to the median of a single set of data there are two related statistics called the upper and lower quartiles. If data are placed in order, then the lower quartile is central to the lower half of the data and the upper quartile is central to the upper half of the data. These quartiles are used to calculate the interquartile range, which helps to describe the spread of the data, and determine whether or not any data points are outliers. In order for these statistics to exist, the observations must be from a univariate variable that can be measured on an ordinal, interval or ratio scale. Use and represent ... [...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. The midhinge is defined as \begin \operatorname(X) &= \overline \\ &= \frac \\ &= \frac \\ &= M_(X). \end The midhinge is related to the interquartile range (), the difference of the third and first quartiles (i.e. ), which is a measure of statistical dispersion. The two are complementary in sense that if one knows the midhinge and the , 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 (), which originated in the same context and equals the avera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantile Function
In probability and statistics, the quantile function is a function Q: ,1\mapsto \mathbb which maps some probability x \in ,1/math> of a random variable v to the value of the variable y such that P(v\leq y) = x according to its probability distribution. In other words, the function returns the value of the variable below which the specified cumulative probability is contained. For example, if the distribution is a standard normal distribution then Q(0.5) will return 0 as 0.5 of the probability mass is contained below 0. The quantile function is also called the percentile function (after the percentile), percent-point function, inverse cumulative distribution function (after the cumulative distribution function or c.d.f.) or inverse distribution function. Definition Strictly increasing distribution function With reference to a continuous and strictly increasing cumulative distribution function (c.d.f.) F_X\colon \mathbb \to ,1/math> of a random variable , the quantile function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percentile
In statistics, a ''k''-th percentile, also known as percentile score or centile, is a score (e.g., a data point) a given percentage ''k'' of all scores in its frequency distribution exists ("exclusive" definition) or a score a given percentage of the all scores exists ("inclusive" definition); i.e. a score in the ''k''-th percentile would be above approximately ''k''% of all scores in its set. For example, the 97th percentile of data is a data point below which 97% of all data points exist (by the exclusive definition). Percentiles depends on how scores are arranged. Percentiles are a type of quantiles, obtained adopting a subdivision into 100 groups. The 25th percentile is also known as the first '' quartile'' (''Q''1), the 50th percentile as the ''median'' or second quartile (''Q''2), and the 75th percentile as the third quartile (''Q''3). For example, the 50th percentile (median) is the score (or , depending on the definition) which 50% of the scores in the distribution are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skewness
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution (a distribution with a single peak), negative skew commonly indicates that the ''tail'' is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value in skewness means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution but can also be true for an asymmetric distribution where one tail is long and thin, and the other is short but fat. Thus, the judgement on the symmetry of a given distribution by using only its skewness is risky; the distribution shape must be taken into account. Introduction Consider the two d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Dispersion
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions. Measures of statistical dispersion A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured. In other words, if the measurements are in metres or seconds, so is the measure of dispersion. Examples of dispersion measures include: * Standard deviation * Interquartile ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
