Proof for Mean-Mode=3(Mean-Median)

[Raghav Gupta]

Can anybody give proof of the above relationship algebraically?I have not seen the derivation of it.

 

[DrDu]

I don't think that this is a generally valid relationship. I would guess that it holds for a PDF expressed in terms of a lowest order Edgeworth series.

 

[Raghav Gupta]

I don't think that this is a generally valid relationship. I would guess that it holds for a PDF expressed in terms of a lowest order Edgeworth series.

I was in a hurry and when one is not familiar with the derivation ,often one messes the formula.
Yeah the correct relationship is Mode=3Median-2Mean.What is the derivation for it?

 

[DrDu]

That's the same formula you wrote before, only solved for Mode. It is not a general valid equation. For example, there are distributions which don't even have a mode, but a median and a mean.
I suppose you can get it using an Edgeworth expansion including the skewness and the curtosis:
http://en.wikipedia.org/wiki/Edgeworth_series

 

[DrDu]

I found also this interesting discussion:
http://stats.stackexchange.com/questions/3787/empirical-relationship-between-mean-median-and-mode

 

[Raghav Gupta]

Okay I got it.It is an empirical formula.
http://statistics.about.com/od/Desc...tionship-Between-The-Mean-Median-And-Mode.htm
Well then what's the derivation for empirical formula?

 

[Raghav Gupta]

I found also this interesting discussion:
http://stats.stackexchange.com/questions/3787/empirical-relationship-between-mean-median-and-mode

Oh sorry we posted at the same time just seconds delay.Can you give the proof using algebraic manipulation other than using variance or standard deviation?

 

[DrDu]

I hardly know more about this relation than you. In the link I found there are all the references to original articles you need.

 

[Raghav Gupta]

I hardly know more about this relation than you. In the link I found there are all the references to original articles you need.

I have seen that link in Mathematics stack exchange before and I did't get it that's why I have posted it here.When you first posted that it is not a valid relationship I thought that modification in statistic may have came for this formula.

 

[Raghav Gupta]

No problem if you don't know but if you can help for some initial steps It would help me.

 

[statdad]

Karl Pearson (I believe) developed that guideline (not a rule) from observations of many slightly to moderately skewed data sets and distributions. The equality you've written really should be taken as "approximately equal to", since the intent of the relationship was to have a quick way to approximate values. I don't know whether he published a derivation or simply mentioned it in an aside or lecture.