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 ...
165 views

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 ...
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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 ...
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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: ...
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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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 ...
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135 views

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 ...
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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 ...
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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?
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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 ...
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107 views

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 ...
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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|...
1 vote
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 ...
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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 ...
1 vote
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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 ...
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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 ...
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1 vote
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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 ...
111 views

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, ...
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189 views

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 ...
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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 ($\text{MD}$) = ...
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}(...
1 vote
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 $a$...
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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 ...
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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.
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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 ...
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Is mean deviation the same as mean absolute difference?

Do both terms mean the same thing or are they different?
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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 $|X-\mathbb{E}[X]|$ ?
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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.
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