# Questions tagged [mean-absolute-deviation]

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

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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 $k\in\{1,\... 0answers 128 views ### Statistical test for comparing the performance of two methods using absolute differences I am doing a study where I have to compare tumor sizes measured using two different methods with the real tumor size. What I want to prove is that the absolute difference between method 1 and real ... 2answers 74 views ### Rephrasing Statistics using MAD I just got done reading Gorard's "Revisiting a 90-year-old debate: the advantages of the mean deviation." (https://www.leeds.ac.uk/educol/documents/00003759.htm) I'm no expert at statistics; in fact, ... 2answers 126 views ### Verbal Description Of The RSE I'm reading An Introduction to Statistical Learning, currently on page 69, the chapter on Simple Linear Regression. The text says: In the case of the advertising data, we see from the linear ... 2answers 1k views ### Why does Mean deviation = Standard deviation = Range/2? We know that mean deviation and standard deviation are two different things but why are both of them equal to Range/2? Range ($R$) = Highest value - lowest value Mean deviation ($\text{MD}$) = ... 2answers 3k 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}(... 0answers 114 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$a$... 1answer 519 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 ... 0answers 30 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. 1answer 405 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 ... 1answer 1k views ### Is mean deviation the same as mean absolute difference? Do both terms mean the same thing or are they different? 1answer 46 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$|X-\mathbb{E}[X]|$? 1answer 709 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. 0answers 8k views ### 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\...
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 ...