Talk:Median absolute deviation

We need a reference for the 3/4 in the formula relating MAD to standard deviation. —Preceding unsigned comment added by 99.251.254.165 (talk • contribs)

It seems almost obvious that for a continous distribution which is symmetric about 0, half the distribution is further from the centre/median than the 3rd quartile (i.e. above the 3rd quartile or below the 1st quatile) and half is closer.

In other words, if F(x)=1-F(-x) and F(0)=1/2, then both F^-1(3/4)-F^-1(1/2) and F^-1(1/2)-F^-1(1/4) are equal to F^-1(3/4), and Pr(|X-F^-1(1/2)|>F^-1(3/4)) is 1/2, making F^-1(3/4) the median absolute deviation --Rumping (talk) 01:53, 11 December 2009 (UTC)

That much is obvious, but I don't think that's what was being referred to. Take a look at the article. Michael Hardy (talk) 19:40, 15 December 2009 (UTC)

....OK,.... indeed, that is not what is referred to, but what is referred to is similarly obvious. Michael Hardy (talk) 19:47, 15 December 2009 (UTC)

Relationship with absolute deviation?

Is it really worth two articles?. Does MAD stand for Median absolute deviation, or Mean absolute deviation, or both/either? See http://www.google.com/search?q=MAD+%22absolute+deviation%22+-wikipedia --Rumping (talk) 00:03, 11 December 2009 (UTC)

Alternative formula

I have seen some textbooks refer to "Median absolute deviation", but using this formula:

$\operatorname {MAD} ={\frac {1}{N}}\sum _{i=1}^{n}|X_{i}-\operatorname {median} |$

Since I have not much knowledge about statistics I don't know if it is worth mentioning it. --Tgor (talk) 19:05, 17 October 2013 (UTC)

That is not an equivalent measurement to the one that this article is about. Yours would be the mean of the deviation from the median instead of the median of the deviations from the median. 199.34.4.20 (talk) 00:54, 20 January 2018 (UTC)

What you say may be true, but so is the fact that this alternative formula is presented in text books and calculated by R under the name "MAD"... 84.248.202.7 (talk) 21:46, 8 December 2020 (UTC)

Is there a mistake?

Is this statement correct? "For a symmetric distribution with zero mean, the population MAD is the 75th percentile of the distribution." Wouldn't it be the 75th percentile minus the 25th percentile, not merely the 75th percentile? — Preceding unsigned comment added by 98.116.5.5 (talk) 17:44, 7 August 2015 (UTC)

It’s (the 75th percentile minus the 25th percentile) divided by 2, where the 25th percentile equals minus the 75th percentile. So it equals (twice the 75th percentile) divided by 2, which equals the 75th percentile. Loraof (talk) 16:28, 8 May 2018 (UTC)

Source for Geometric median absolute deviation

I cannot find any reference for the section "Geometric median absolute deviation". I added an "Unreferenced section" template, would be good to find where this material comes from. Bedzbedz (talk) 13:36, 22 April 2019 (UTC)

Median does not minimise median absolute deviation

Is it worth mentioning that using the median as the central point does not minimise the median absolute deviation even though it does minimise the mean absolute deviation? For example, with data 0,1,2,3,4,5,6, the median absolute deviation about the median 3 is 2, while the median absolute deviation about 2.5 is the smaller 1.5 (and about 1.5 is also 1.5). Rumping (talk) 15:34, 8 February 2023 (UTC)