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Questions tagged [mean-absolute-deviation]

Mean absolute deviation around the mean. Use [mad] for median absolute deviation around the median.

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Average deviation of a set of 10 random integers from −5 to +5

I calculate the average deviation ($AVD$) of a set of $10$ numbers ($v_{1},v_{2},\cdots,v_{10}$) as follows: calculate the average of the $10$ numbers: $$AVR =\frac{\sum_{n=1}^{10} v_{n}}{10}$$ ...
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What makes the difference between the Mean Absolute Deviation (AAD) and Standard Deviation of a distrubution constant?

We can see very nicely in the normal distribution that the relationship between the mean absolute deviation and standard deviation is a constant ratio (by sqrt(2/pi)). What is it that gives a ...
Kenny's user avatar
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Average deviation from mean of Irwin-Hall distribution

Consider the Irwin-Hall distribution, which for me means $X_n$ is the sum of $n$ uniform iid variables in $[-1/2, 1/2]$. I would like an absolute lower bound for $E[|X_n|]$. By general theory we know ...
Cyclicduck's user avatar
3 votes
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Are there cases where we need to avoid the usage of IQR?

Let's consider the interquartile range (IQR), the standard deviation (SD) and the mean absolute deviation (MAD). We know that "one of the most common robust measures of scale is the interquartile ...
Ommo's user avatar
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Log transformation leading to extremely negative R-squared and extremle values for MSE

I have a set of data and I am using this code on it: ...
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225 views

Upper bound on absolute difference with squares

I'm looking for an upper bound on $E_X\left[\left\vert X^2-(E[X])^2\right\vert\right]$, where $X$ is a nonnegative random variable, with known $E[X]$ and $E[X^2]$, but unknown higher moments. A lower ...
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MAD/Mean Ratio - advantages/disadvantages of using average or sum

The calculation the MAD (Mean Absolute Deviation)/Mean ratio is this, according to the title: $$ \frac{\overline{\left | Forecast - Demand \right |}}{\overline{Demand}}$$ However, the calculation is ...
tktk234's user avatar
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Absolute deviation from the mean using logarithms

I am calculating the absolute deviation from the mean of a strictly positive set $\{x_1, x_2, \ldots, x_n\}$ like: $$\left| x_i - \bar X\right|$$ My analysis makes it appropriate to work in logs ...
AllDoe_1's user avatar
3 votes
1 answer
196 views

Is it incorrect to take the standard deviation of absolute values

Imagine I have a model that predicts a person’s height from a photo (just an example). Each individual has their ground-truth height (H), and the model outputs a predicted height (h). The model error ...
Kurt Newman's user avatar
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127 views

Mean absolute deviation (MAD) analogy to 68-95-99 rule

With MAD, 50% of all values fall within one absolute deviation. How many within two, and three?
status's user avatar
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Show that, for any real numbers a and b such that m ≤ a ≤ b or m ≥ a ≥ b, E|Y − a| ≤ E|Y − b| ,where Y be a random variable with finite expectation

Let $Y$ be a random variable with finite expectation, and $m$ be a median of $Y;$ i.e., $P(Y \le m) \ge 1/2$ and $P(Y \ge m) \ge 1/2.$ Show that, for any real numbers $a$ and $b$ such that $m\le a \le ...
Debarghya Jana's user avatar
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Count the fraction of trials for which the absolute deviation from the mean is larger than the standard deviation?

So, I have a data set containing 99 elements each with their own associated value. I have computed the standard deviation and the mean, but I am a little stumped with how exactly I should proceed with ...
Austin's user avatar
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Deducing $L^1$ Boundary from Mahalanobis Boundary

Assume maximum likelihood estimators $a,b$ of size $p$, with corresponding estimated covariance matrices $V^a,V^b$. In fact $a,b$ are two regression coefficient vectors. Denote $q=a-b$ the vector of ...
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Standard Deviations of Detrended Data vs Original Data

I'am interested to know the opinion on this matter. I have Data of a Financial Security. The goal is to view the Standard Deviations levels of the data to possibly see patterns of behavior of the ...
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measure for deviation/error that is guarantueed to be smaller than the mean

I am presenting some non-negative values by using a mean value with error bars, basically something like this: So the mean values are shown as dots and the error bars are displayed vertically, ...
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Mean Absolute Deviation for AR(1) process

Is there closed-form solution for mean absolute deviation (MAD) for AR(1) process? $X_t = c + \beta X_{t-1} + \epsilon_t $ $\epsilon_t \sim N(0,\sigma^{\epsilon})$ (Similar to the variance and the ...
maril's user avatar
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Least Absolute Values Regression

I have the data: x <- c(0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0) y <- c(2.06, 2.12, 2.32, 2.02, 2.76, 3.04, 2.83, 3.15, 3.36, 3.68, 3.96) I ...
Epsilon Delta's user avatar
1 vote
0 answers
405 views

How do I calculate Correlation Coefficient using Mean Absolute Deviation?

I am trying to calculate Pearson's Correlation Coefficient using the product of the Mean Absolute Deviations (MADs) of my two lists as denominators instead of the Standard Deviations. Effectively, ...
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Estimate the error bound of a histogram based mean absolute deviation approximation

Given a sequence of numbers $A = a_1, a_2, \cdots, a_n$. One way to calculate the mean absolute deviation of $A$ is by $G(A)= \sum_{i=0}^n |a_i - median(A)|$. yet, there can be an alternative, by ...
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Why is there no improvement when training Xgboost with pseudo-Huber loss?

In this StackOverflow post I asked if there was something wrong with my syntax when training an XGboost model (in R) with the native pseudo-Huber loss ...
PaulG's user avatar
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4 votes
1 answer
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How to calculate the running mean absolute deviation

I wish to calculate the running mean absolute deviation (MAD) without storing the previous n data points. This calculation is for a continuous stream of data, i.e. infinite length. I am trying to ...
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For multivariate linear regression, what is the partial derivative for Mean Absolute Error?

What is the partial derivative for MAE for multivariate linear regression? I understand that for mean squared error (MSE) the partial derivative with respect to some $\theta_1$ would be $-\theta_1 \...
BullardLA's user avatar
9 votes
1 answer
843 views

an upper bound of mean absolute difference?

Let $X$ be an integrable random variable with CDF $F$ and inverse CDF $F^*$. $Y$ is iid with $X$. Prove $$E|X-Y| \leq \frac{2}{\sqrt{3}}\sigma,$$ where $\sigma=\sqrt{Var(X)} = \sqrt{E[(X-\mu)^2]}$. I ...
Tan's user avatar
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What are the drawbacks of aggregating regression results if error decreases?

I am trying to predict Total National Sales in dollars for a major retailer. However, the data I'm using exists at the state level, and includes several features around specific brands and foot ...
KidMcC's user avatar
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Why isn't absolute deviation used [duplicate]

If the reason that standard deviation is used is that it's easier to just square the distance every time than find the absolute value. Then why is √(E(x-m)^2)/n not used because if I'm not mistaken |x|...
Bob Ross's user avatar
1 vote
2 answers
79 views

Ho do I determine the probability of price reversals using linear regression?

In the screenshot, you will see the daily prices of Nasdaq. Each candle has a High, Low, Open and Close price. I have drawn a regression line with a 2 standard deviation channel on either side. How ...
Grantx's user avatar
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We square at the variance and SD is it due a link with to Gaussian function? [duplicate]

I had almost same question as "Why square the difference instead of taking the absolute value in standard deviation?". But I also noticed the $\sigma$ or population standard deviation is ...
Always Confused's user avatar
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1 answer
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Alternative error measure--maximize data to have residuals less than given threshold

I am looking for a method which finds a linear model (2 input variables, everything reasonably close enough to normally distributed), but with an alternative measure of error. Every error measure I ...
Paul's user avatar
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5 votes
2 answers
119 views

Random variables $(X,Y)$ with $\text{Var}(X)<\text{Var}(Y)$ and $\mathbb{E}(|X-\mu_X|)>\mathbb{E}(|Y-\mu_Y|)$

I am looking for an example of a pair of random variables $(X,Y)$ with expected values $(\mu_X,\mu_Y)$ satisfying the following relationships: $$ \text{Var}(X)<\text{Var}(Y) $$ and $$ \mathbb{E}(|X-...
Richard Hardy's user avatar
1 vote
0 answers
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How to derive this MAE error bound on the central limit theorem?

Is this derived from Chebyshev's inequality or a tail bound theorem? If not, how was it derived? Does this require the existence of the third moment? Does this bound suggest the normal approximation ...
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how to detect a 5% deviation between more than 2 numbers

Dear StackExchange Team in the industry there are GAs generators that have hundreds of instrument measuring process values, such as pressure, temperatures, etc. we have a simple case where a ...
racekiller's user avatar
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1 answer
1k views

How to fix heteroscedasticity (funnel shape)?

I am running a mlr in python on a dataset with 2D feature vectors, X1 and X2 on a single response, Y. The data ends up being funnel-shaped, as below: X1 v Y, with the colors being X2. It was ...
Tuomas Talvitie's user avatar
10 votes
2 answers
445 views

Is mean absolute deviation smaller than standard deviation for $n\ge 3$?

I want to compare the mean absolute deviation with standard deviation in general case with this definition: $$MAD = \frac{1}{n-1}\sum_1^n|x_i - \mu|, \qquad SD = \sqrt{\frac{\sum_1^n(x_i-\mu)^2}{n-1}}...
Lisbeth's user avatar
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Compare variables with zeta-score

Assume the calculation of a physical quantity $x$ from a given formula i.e. $$x=\dfrac{a*b}{c}$$ where $a, b$ and $c$ are experimental observables, therefore $x$ is a quantity derived from ...
Thanos's user avatar
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1 vote
1 answer
687 views

Why do we use squared deviations to compute the SD, given that it amplifies the effect of outliers? [duplicate]

Suppose I have the following hypothetical data: One thousand times value 15 (i.e., 15 occurs 1000 times) and a single outlier value - 115 (i.e., 115 occurs just once - an outlier) Thus the mean is: $...
VISHAL DAGA's user avatar
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566 views

Estimating Expected Order Statistics

I have a fairly basic question that I'm looking for a reference for. First, a couple definitions. Let's say $X_1,\ldots,X_n$ are IID samples from a distribution $F$ over $[0,1]$. For any $k\in\{1,\...
Lemke's user avatar
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1 vote
0 answers
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Statistical test for comparing the performance of two methods using absolute differences

I am doing a study where I have to compare tumor sizes measured using two different methods with the real tumor size. What I want to prove is that the absolute difference between method 1 and real ...
Paulo Maia's user avatar
5 votes
2 answers
111 views

Rephrasing Statistics using MAD

I just got done reading Gorard's "Revisiting a 90-year-old debate: the advantages of the mean deviation." (https://www.leeds.ac.uk/educol/documents/00003759.htm) I'm no expert at statistics; in fact, ...
Somniad's user avatar
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1 vote
2 answers
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Verbal Description Of The RSE

I'm reading An Introduction to Statistical Learning, currently on page 69, the chapter on Simple Linear Regression. The text says: In the case of the advertising data, we see from the linear ...
fweth's user avatar
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-1 votes
2 answers
3k views

Why does Mean deviation = Standard deviation = Range/2?

We know that mean deviation and standard deviation are two different things but why are both of them equal to Range/2? Range ($R$) = Highest value - lowest value Mean deviation ($\text{MD}$) = ...
user55439's user avatar
6 votes
2 answers
4k views

Why not use modulus for variance? [duplicate]

I am trying to wrap my mind around the variance definition. Given a set of values S and n = #(S), the variance is defined as: $$ \operatorname{var}(S) = \frac{\sum_{i=1}^n( S_i - \operatorname{mean}(...
Bitcoin Cash - ADA enthusiast's user avatar
1 vote
0 answers
219 views

An efficient algorithm for sliding mean deviation

I'm searching for a computationally efficient algorithm to calculate the sliding mean deviation from sample $x_a$ to sample $x_b$ belonging to a large set $x_0, x_1 ... x_n$ with the condition that $a$...
davide's user avatar
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1 vote
1 answer
887 views

Best way to describe changes in performance through time.

I'm wondering how to explain changes in production/performance metrics quarter to quarter. In the example below, one can see that the average processing time for "widgets" has decreased substantially ...
Mr. Geologist's user avatar
0 votes
0 answers
33 views

Is standard deviation always larger than mean deviation? [duplicate]

If yes why is it the case that it have this property? There must be some mathematical proof or intuitive understanding in that case.
ankit's user avatar
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2 votes
1 answer
467 views

Why don't dispersions like median deviation and mode deviation exists on the lines of mean deviation?

Or to say in the formula MD=$\frac{1}{N}\sum_{i=1}^{N}|x_i-\overline{x}|$ why can't we have median or mode instead of mean($\overline{x}$) and as a result speak about additional possible measures of ...
ankit's user avatar
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3 votes
1 answer
2k views

Is mean deviation the same as mean absolute difference?

Do both terms mean the same thing or are they different?
ankit's user avatar
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2 votes
1 answer
98 views

Variance of Binomial total deviation

I have a Binomial random variable $X \sim B(n,p)$. Is there a closed form expression or an upper bound for the variance of the absolute deviation $|X-\mathbb{E}[X]|$ ?
K. Lakshmanan's user avatar
5 votes
1 answer
1k views

Mean Absolute Deviation of Student t distributions?

I could only find these two formulae, both apparently with some issues. Which is the correct one? Online references and derivation would be especially appreciated.
Quartz's user avatar
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8 votes
0 answers
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Relative Mean Deviation [closed]

The Mean Deviation, also referred to as Absolute Average Deviation, is sometimes preferred to the Standard Deviation (Cf. Gorard 2004). For a sample, it can be expressed as: $MD = \frac{1}{n} \sum\...
Ismael Ghalimi's user avatar
2 votes
1 answer
341 views

Difference between absolute deviation to population median and sample mean

I have independent variables $X_i\in[0;1]$ and suppose they are uniformly distributed. If you want to minimize the total absolute deviation to a fixed number, how much can you gain from using the ...
Gere's user avatar
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