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g.Mean absolute deviation (MAD) measures the accuracy of an estimate by averaging the estimated error (the value of each error). MAD is required to measure prediction errors in the same unit as in the original series [5] [6]. The true MAD can be calculated using the following formula.

 

 

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In statistics, mean absolute deviation (MAD) is probably a reliable measure of the variability of a univariate sample of quantitative data. It can also refer to the expansion parameter estimated by the MAD, calculated from the sample.

For one-dimensional data adjustment X ₁ , X ₂ , …, X _n MAD is defined as in median absolute deviations from the median of this data :

That is, if you start with residuals (deviations)from the median of our own data, MAD is the median that refers to their absolute values.

Example

Consider dates (1, a, 2, 2, 4, 6, 9). Its median is 2. The final deviations of about 2 are (1, 1, 2, 0, 2, 4, of which 7) in rotation have a median value (since the sorted absolute deviations are (0, three, 1, 1, 2, 4, 7)). The mean absolute deviation for this data is certainly 1.

Usage

The mean absolute deviation is the amount of statistical deviation. In addition, MAD was a robust statistic that was more robust to outliers in the dataset than this standard deviation. At standard deviation, distances from the mean are usually squared over a large area, so deviations are heavier or outliers can have a strong effect on them. In MAD, deviations of a from too few emissions are negligible.

Because MAD is a more reliable means of assessing the scale than sample variance or standard alternative, it works best with distributions without mean or variance.rsii such as the Cauchy distribution.

Standard Deviation To Deviation Ratio

MAD can be used in the same way as deviation for mean.To help you, use MAD as a reliable scoring tool to estimate the standard big difference , takes

where is a constant growth rate that depends on the distribution. ^[1]

i.e. quantile stripped function Known (also I would say the inverse of the cumulative distribution function) for each standard normal distribution . ^{[2] [3]} Argument 3/4 is indeed 50% covers (between 1/4 and therefore 3/4) the normal cumulative expansion function, i.e.

we get that from which we resize the factor .

Another way to establish a romantic relationship The value is if Equals distorted a part of the median of the half-normal distribution:

Absolute Geometrically Typical Separation

Just like a typical generalization of the geometric median only in multidimensional data, you can create a geometric MAD that generalizes the MAD. In the case of a paired two-dimensional data record (X ₁ , Y ₁ ), (X ₂ , Y ₂ ), … .., (X _n , Y _n ) a and calculated accordingly geometrically typical , most of the absolute geometric median is taken into account:

This gives the same result as a one-dimensional MAD in one dimension and can easily be transferred to higher dimensions. For complex values ​​(X + iY), the ratio of MAD to standard deviation for normalThe altered data does not change.

Population MAD

The MAD set is defined similarly to the MAD model, but based on a maximum distribution rather than a sample. In a symmetric distribution with a mean of zero, the MAD for most of the population is the 75th percentile of the distribution.

Unlike variance, which can be unlimited or indefinite, the MAD population has always been a finite number. For example, the standard Cauchy distribution usually has indefinite variance, but unfortunately its MAD is 1.

The first known list of the concept of the mentally ill appeared in 1816 in an article by Karl Friedrich Gauss on determining the accuracy of numerical observations. ^{[4] [5]}

See Also

• Difference (statistics)
• Interquartile range
• Probable error
• Reliable measuring scale
• Compared to the real average difference.
• Mean absolute deviation
• Small absolute deviations

Notes

Links

• Hoglin, David K ​​.; Friedrich Mosteller; John W. Tukey (1983). Understand reliable and exploratory data analysis. John Wiley & Sons. S. 404-414. ISBN 978-0-471-09777-8 .
• Russell, Roberta C .; Bernard W. Taylor III (2006). Operational leadership. John Wiley & Sons. S. 497-498. ISBN 978-0-471-69209-6 .
• Venables, W.N.; B.D. Ripley (1999). State-of-the-art applied statistics with S-PLUS. Jumper. S. 128. ISBN 978-0-387-98825-2 .

 

 

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