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Quartile Coefficient Of Dispersion
In statistics, the quartile coefficient of dispersion is a descriptive statistic which measures dispersion and is used to make comparisons within and between data sets. Since it is based on quantile information, it is less sensitive to outliers than measures such as the coefficient of variation. As such, it is one of several robust measures of scale. The statistic is easily computed using the first (''Q''1) and third (''Q''3) quartiles for each data set. The quartile coefficient of dispersion is: : . Example Consider the following two data sets: : ''A'' = :: ''n'' = 7, range = 12, mean = 8, median = 8, ''Q''1 = 4, ''Q''3 = 12, quartile coefficient of dispersion = 0.5 : ''B'' = :: ''n'' = 7, range = 1.2, mean = 2.4, median = 2.4, ''Q''1 = 2, ''Q''3 = 2.9, quartile coefficient of dispersion = 0.18 The quartile coefficient of dispersion of data set ''A'' is 2.7 times as great (0.5 / 0.18) as that of data set ''B''. See also * Robust measures of scale * Coefficient of ... [...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] |
Statistical Dispersion
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a Probability distribution, 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 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 of measurement, 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 deviat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient Of Variation
In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage, and is defined as the ratio of the standard deviation \sigma to the mean \mu (or its absolute value, The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R, by economists and investors in economic models, and in neuroscience. Definition The coefficient of variation (CV) is defined as the ratio of the standard deviation \ \sigma to the mean \ \mu , c_ = \frac. It shows the extent of variability in relation to the mean of the population. The coefficient of variation should be computed only for data measured on scales that have a meaningful zer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust Measures Of Scale
In statistics, robust measures of scale are methods that quantify the statistical dispersion in a sample of numerical data while resisting outliers. The most common such robust statistics are the ''interquartile range'' (IQR) and the ''median absolute deviation'' (MAD). These are contrasted with conventional or non-robust measures of scale, such as sample variance or standard deviation, which are greatly influenced by outliers. These robust statistics are particularly used as estimators of a scale parameter, and have the advantages of both robustness and superior efficiency on contaminated data, at the cost of inferior efficiency on clean data from distributions such as the normal distribution. To illustrate robustness, the standard deviation can be made arbitrarily large by increasing exactly one observation (it has a breakdown point of 0, as it can be contaminated by a single point), a defect that is not shared by robust statistics. IQR and MAD One of the most common robust mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quartile
In statistics, a quartile is a type of quantile which divides 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 main quartiles are as follows: * The first quartile (''Q''1) is defined as the middle number between the smallest number (minimum) and the median of the data set. It is also known as the ''lower'' or ''25th empirical'' quartile, as 25% of the data is below this point. * 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 middle value between the median and the highest value (maximum) of the data set. It is known as the ''upper'' or ''75th empirical'' 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 provid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust Measures Of Scale
In statistics, robust measures of scale are methods that quantify the statistical dispersion in a sample of numerical data while resisting outliers. The most common such robust statistics are the ''interquartile range'' (IQR) and the ''median absolute deviation'' (MAD). These are contrasted with conventional or non-robust measures of scale, such as sample variance or standard deviation, which are greatly influenced by outliers. These robust statistics are particularly used as estimators of a scale parameter, and have the advantages of both robustness and superior efficiency on contaminated data, at the cost of inferior efficiency on clean data from distributions such as the normal distribution. To illustrate robustness, the standard deviation can be made arbitrarily large by increasing exactly one observation (it has a breakdown point of 0, as it can be contaminated by a single point), a defect that is not shared by robust statistics. IQR and MAD One of the most common robust mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient Of Variation
In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage, and is defined as the ratio of the standard deviation \sigma to the mean \mu (or its absolute value, The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R, by economists and investors in economic models, and in neuroscience. Definition The coefficient of variation (CV) is defined as the ratio of the standard deviation \ \sigma to the mean \ \mu , c_ = \frac. It shows the extent of variability in relation to the mean of the population. The coefficient of variation should be computed only for data measured on scales that have a meaningful zer ... [...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] |
Median Absolute Deviation
In statistics, the median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data. It can also refer to the population parameter that is estimated by the MAD calculated from a sample. For a univariate data set ''X''1, ''X''2, ..., ''Xn'', the MAD is defined as the median of the absolute deviations from the data's median \tilde=\operatorname(X) : : \operatorname = \operatorname( , X_i - \tilde, ) that is, starting with the residuals (deviations) from the data's median, the MAD is the median of their absolute values. Example Consider the data (1, 1, 2, 2, 4, 6, 9). It has a median value of 2. The absolute deviations about 2 are (1, 1, 0, 0, 2, 4, 7) which in turn have a median value of 1 (because the sorted absolute deviations are (0, 0, 1, 1, 2, 4, 7)). So the median absolute deviation for this data is 1. Uses The median absolute deviation is a measure of statistical dispersion. Moreover, the MAD is a robus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Deviation And Dispersion
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 exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
