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

  1. Dec 22, 2014 #1
    Can anybody give proof of the above relationship algebraically?I have not seen the derivation of it.
     
  2. jcsd
  3. Dec 22, 2014 #2

    DrDu

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    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.
     
  4. Dec 22, 2014 #3
    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?
     
  5. Dec 23, 2014 #4

    DrDu

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    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
     
  6. Dec 23, 2014 #5

    DrDu

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  7. Dec 23, 2014 #6
  8. Dec 23, 2014 #7
  9. Dec 23, 2014 #8

    DrDu

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    I hardly know more about this relation than you. In the link I found there are all the references to original articles you need.
     
  10. Dec 23, 2014 #9
    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.
     
  11. Dec 23, 2014 #10
    No problem if you don't know but if you can help for some initial steps It would help me.
     
  12. Dec 23, 2014 #11

    statdad

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    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.
     
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