Mean Deviation (book)
Mean deviation may refer to: Statistics * Mean signed deviation, a measure of central tendency * Mean absolute deviation, a measure of statistical dispersion * Mean squared deviation, another measure of statistical dispersion Other * ''Mean Deviation'' (book), a 2010 non-fiction book by former Metal Maniacs magazine editor Jeff Wagner See also * Deviation (statistics) * Mean difference (other) Mean difference may refer to: * Mean absolute difference, a measure of statistical dispersion * Mean signed difference, a measure of central tendency See also *Mean deviation (other) Mean deviation may refer to: Statistics * Mean signed d ...

Mean Signed Deviation
In statistics, the mean signed difference (MSD), also known as mean signed deviation and mean signed error, is a sample statistic that summarises how well a set of estimates \hat_i match the quantities \theta_i that they are supposed to estimate. It is one of a number of statistics that can be used to assess an estimation procedure, and it would often be used in conjunction with a sample version of the mean square error. For example, suppose a linear regression model has been estimated over a sample of data, and is then used to extrapolate predictions of the dependent variable out of sample after the out-of-sample data points have become available. Then \theta_i would be the ''i''-th out-of-sample value of the dependent variable, and \hat_i would be its predicted value. The mean signed deviation is the average value of \hat_i-\theta_i. Definition The mean signed difference is derived from a set of ''n'' pairs, ( \hat_i,\theta_i), where \hat_i is an estimate of the parameter \th ...
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Mean Absolute Deviation
The average absolute deviation (AAD) of a data set is the average of the Absolute value, absolute Deviation (statistics), deviations from a central tendency, central point. It is a summary statistics, summary statistic of statistical dispersion or variability. In the general form, the central point can be a arithmetic mean, mean, median, mode (statistics), mode, or the result of any other measure of central tendency or any reference value related to the given data set. AAD includes the mean absolute deviation and the median absolute deviation (both abbreviated as MAD). Measures of dispersion Several measures of statistical dispersion are defined in terms of the absolute deviation. The term "average absolute deviation" does not uniquely identify a measure of statistical dispersion, as there are several measures that can be used to measure absolute deviations, and there are several measures of central tendency that can be used as well. Thus, to uniquely identify the absolute deviat ...
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Mean Squared Deviation
In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate. In machine learning, specifically empirical risk minimization, MSE may refer to the ''empirical'' risk (the average loss on an observed data set), as an estimate of the true MSE (the true risk: the average loss on the actual population distribution). The MSE is a measure of the quality of an estimator. As it is derived from the square of Euclidean distance, it is always a positive value that decreases as the error a ...
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Mean Deviation (book)
Mean deviation may refer to: Statistics * Mean signed deviation, a measure of central tendency * Mean absolute deviation, a measure of statistical dispersion * Mean squared deviation, another measure of statistical dispersion Other * ''Mean Deviation'' (book), a 2010 non-fiction book by former Metal Maniacs magazine editor Jeff Wagner See also * Deviation (statistics) * Mean difference (other) Mean difference may refer to: * Mean absolute difference, a measure of statistical dispersion * Mean signed difference, a measure of central tendency See also *Mean deviation (other) Mean deviation may refer to: Statistics * Mean signed d ...

Deviation (statistics)
In mathematics and statistics, deviation is a measure of difference between the observed value of a variable and some other value, often that variable's mean. The sign of the deviation reports the direction of that difference (the deviation is positive when the observed value exceeds the reference value). The magnitude of the value indicates the size of the difference. Types A deviation that is a difference between an observed value and the ''true value'' of a quantity of interest (where ''true value'' denotes the Expected Value, such as the population mean) is an error. A deviation that is the difference between the observed value and an ''estimate'' of the true value (e.g. the sample mean; the Expected Value of a sample can be used as an estimate of the Expected Value of the population) is a residual. These concepts are applicable for data at the interval and ratio levels of measurement. Unsigned or absolute deviation In statistics, the absolute deviation of an element ...
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