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What is the mean and the median?

If you divide the sum of the mean, median, and mode of a data set by 3 (averaging them)? What could you understand from the result?

  • Take a relatively large and evenly distributed data set, lets say 500 values from 300,000 to 1,000,000, and you arrive at Mean = 529,804, Median = 472,637, Mode = 425,000. If you average those three results, you get 475,814.  If you continue averaging, you will always have a result of 475,814: (x+y+z)/3=A, (x+y+z+A)/4=A, (x+y+z+A+A)/5=A... and on and on. How about for an unevenly distributed dataset? Suppose Mean = 25, median = 65, and mode = 17. (25+65+17)/3=36 If you keep averaging, your result is constant. (25+65+17+36)/4=36, (25+65+17+36+36)/5=36... I have no training in statistics (or anything other than algebra and baisic trig), so I'm sure this number has a meaningful purpose in stats or somewere else. But what does it accomplish that mean, median and mode do not?

  • Answer:

    As Prathab Kali states correctly, there is nothing special about the fact that the averages always equal the same number, since [x + y + z + (x + y + z)/3]/4 = (x + y + z)/3 = A. Firstly, this number means nothing. And you cannot tell anything about a distribution that you cannot tell from knowing the mean, median, and mode. Secondly, your first example is self-contradictory because with that mean and median, it is fairly clear that your distribution is not evenly distributed.

Brian Chu at Quora Visit the source

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Yes, you will get the same result. There is no significance in what you are doing. (x+y+z)/3=A, (x+y+z+A)/4=A, (x+y+z+A+A)/5=A... (x+y+z)/3 = A                                          ; x+y+z = 3A (x+y+z+A)/4 = A        ; x+y+z+A = 4A      ; x+y+z = 4A - A = 3A (x+y+z+A+A)/5 = A    ; x+y+z+A+A = 5A  ; x+y+z = 5A - A - A = 3A You are indirectly just adding and subtracting on both the sides which will always result in same number.

Prathab Kali

Well yes, there is no significance in continuing to averaging the mean median and mode, ad nauseam. I was illustrating your own point, perhaps less eloquently stated. My question was "If you divide the sum of the mean, median, and mode of a data set by 3 (averaging them)? What could you understand from the result?" I am questioning the implication and relevance of the first result of averaging the mean, median and mode of a set of data. (mean + median + mode)/3=?. Mean = 529,804, Median = 472,637, Mode = 425,000. If you average those three results, you get 475,814. This is a number which is unique from the mean, median or mode, yet seems to follow quite closely within the range of averages from a set of relatively consistent data. Does the result of  (mean + median + mode)/3 tell us anything that mean, median and mode do not in a consistent data set

Chris Sylvester

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