#mean absolute deviation

MAD Deviation

Mathober Day 2: Deviation.

I made a GeoGebra guessing game for the most underappreciated statistic, mean absolute deviation.

Here's two examples:

So what would you guess these have?

To have a meaningful insights from the deviations from the mean, the negative values are ignored so that only positive values are considered. Hence we talk about the absolute values from the mean.

Sometimes measures of central tendency does not give the actual picture of the data in question. For example if we were to determine the average income per home of a certain country, we may obtain a high value and fail to deduce that majority of people have been living below poverty line but are dominated by few individuals that earns extremely high incomes. The few people earning high raises the…

To have a meaningful insights from the deviations from the mean, the negative values are ignored so that only positive values are considered. Hence we talk about the absolute values from the mean.

Sometimes measures of central tendency does not give the actual picture of the data in question. For example if we were to determine the average income per home of a certain country, we may obtain a high value and fail to deduce that majority of people have been living below poverty line but are dominated by few individuals that earns extremely high incomes. The few people earning high raises the…

To have a meaningful insights from the deviations from the mean, the negative values are ignored so that only positive values are considered. Hence we talk about the absolute values from the mean.

Sometimes measures of central tendency does not give the actual picture of the data in question. For example if we were to determine the average income per home of a certain country, we may obtain a high value and fail to deduce that majority of people have been living below poverty line but are dominated by few individuals that earns extremely high incomes. The few people earning high raises the…

A Simple yet Interesting Question in Statistics.

Originally published on RandomPearls.com on 14 July 2020.

TL;DR

Mean ⟹ around which number the observations are centered. But a set can have its observations quite far from the mean, on an average, as compared to another set having the same mean. In order to get that information (i.e. the average distance of observations from its mean), we move to MAD.

MAD ⟹ how far each observation individually is from the mean of all observations, but it doesn't tell how the observations are arranged in relation to one another. To get that information (i.e. the average distance of the set itself from its mean, which depends upon how the observations are arranged in relation to one another), we move to σ.

σ ⟹ how far the complete set is from its mean (or, how far the observations are from each other).

And two sets having their individual observations equally distant (on an average) from their respective means (i.e. having the same MAD) can be, as a whole, at different distances from their respective means (i.e. can have different σ’s)!

In the sets — check RandomPearls.com for complete context — A(1,1,7) and B(0,2,7), each observation in A is, on an average, equally distant from its mean as each observation in B is from its own mean (which happens to be the same as A’s). This is shown by the MAD being same for the two sets. But, observations in B are farther apart from each other compared to how those are in A, and this fact is indicated by their different σ’s.

Thus, we see that by looking at these two statistical concepts (MAD and σ) from a geometrical point of view, we get some insight into the arrangement of observations — not only in relation to the mean, but also in relation to one another.

TS; WM

Assurer un niveau satisfaisant de fiabilité des prévisions est un objectif essentiel pour tout Supply Chain Manager qui doit anticiper la mobilisation de moyens et de ressources.

La mesure de la fiabilité a pour objectif de vérifier la qualité du processus de prévision qui dépend principalement du choix des paramètres et des données de la prévision.

Il existe plusieurs méthodes d’évaluation de…

A Procedure for Starting Values for Sine Fitting (IEEE1057)Stephen Neil Summary: The four type sine fitting procedure IEEE1057 provides an accurate and fast method for fitting a sine lay out to noisy data. In any case, the lines requires certainly starting value anent low frequency (the incomparable parameters from a 3 parameter sine fit) to guard convergence. The procedure described here provides a simple robust course being obtaining starting values. The procedure is easily described passageway simple stairs from a starting data series. 0. remove the mean value from the unexpended data 1. calculate the cumulative continuum excepting the conceptive data 2. take account of the average of the firsthand series 3. estimate the additional humble it's average. Call this series 'the integral' 4. quantize the first difference series of the inspired dataseries. Call this series 'the derivative' 5. compute the foul absolute deviation of the monistic: MAD1 6. calculate the mean transcendent whimsy of the derivative: MAD2 7. compute square root as regards MAD2\MAD1: our estimate of the frequency<\p>

An elementary knowledge of calculus only is imperative towards see how replacing A.Sin(w*t+p) we are estimating the integral, -(A\w).Cos(w*t+p), and the development, A.Cos(w*t+p). Problems of form and sign are avoided by in virtue of the mean absolute deviation of these series, their ratio being w^2 Some simple tests by the author apprehend revealed this procedure is rugged assumed at least 2 cycles, frequency between.01 and.5 and noise of amplitude widen to half the sine amplitude. The contrivance is thus and thus simple it can be there readily tested in a simple spreadsheet Another behavioral norm more robust to sonorous report but only suitable for frequencies infra 0.1 is the 'twice integral' method The procedure is besides easily described in simple steps from a starting data pursuance. 0. cast aside the mean substance from the original series 5. meter the fairish absolute obliqueness of the original series: MAD1 1. count on the cumulative series without the original series 2. calculate the equatorial as to the cumulative series 3. sound the cumulative less it's average. Call this series 'the integral' 1. build on the cumulative series from the integral coming after 2. rationalize the average of the cumulative dogging 3. calculate the certain less it's average. Preconization this succession 'twice integral' 6. calculate the mean absolute transition in point of the twice monadic: MAD2 7. calculate square smell around with regard to MAD2\MAD1: our estimate of the frequency<\p>