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Re: Mean, Median and Mode  the threeheaded monster
Posted:
Apr 10, 2014 3:32 PM


> It is math. For example, if I were to choose 10 houses at random and take the mean price of those 10 houses, would it be closer to the median price of all houses, or the mean price of all houses?
Got me.
Did a single person understand what I made perfectly clear in my web page?
The median is worthless. When told the median, all you can conclude is that it falls somewhere within the range of values, maybe at one extreme or the other. If you're not given the range, then the median is less than worthless.
If it were reported that the median number of Beatle records in the houses on a certain block is 3, what could you conclude? We're probably pretty safe setting a lower bound of 0. The upper bound might be... well, who knows?
> If you want to go beyond trying to argue what is the best metric, then the raw data itself is the only real metric.
I do not. I only wanted to demonstrate the worthlessness of the median and mode, and reaffirm the beauty, simplicity, intuitiveness and usefulness of the average. If we were totally honest with ourselves, we would admit that when we hear, "The median is such and such," our next thought is, "Well, I sure hope that's somewhere around the average!"
http://www.donaldsauter.com/meanmedianmode.htm
Donald Sauter
> On Jan 25, 2014, at 12:46 PM, Donald Sauter > <donaldsauter@gmail.com> wrote: > > > I thought my example disproved that. Doesn't the > word "skewed" imply an extramathematical judgment > imposed on simple numbers? When we say "skewed > data," doesn't that imply, "Even though this is the > _raw_ data, we know that it's _really_ trying to say > such and such"? > > > > I am not touching that situation. I am only > addressing the problem, given a bunch of raw data for > which you do not have "insider information", what is > the best "measure of central tendency"? If you know > the answer you want, and the median happens to hit > closest, go ahead and trumpet the median. But that's > not math. > > It is math. For example, if I were to choose 10 > houses at random and take the ?mean? price of those > 10 houses, would it be closer to the ?median? price > of all houses, or the ?mean? price of all houses? > > The ?median? gives a better ?probable" mean than the > ?mean? when the data is skewed. That is often more > useful than the mean of all houses. > > If you want to go beyond trying to argue what is the > ?best? metric, then the raw data itself is the only > real metric. > > Bob Hansen



