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Re: A question about describing distributions (fwd)
Posted:
Jan 12, 1997 7:24 PM


 Forwarded message from Albyn Jones 
Bob Hayden writes
>In that situation I would describe it as "symmetric with high >outliers". However, it is very common to be uncertain whether you >have an outlier problem or a skewness problem, especially with small >samples. It helps to use (real and) realistic size datasets rather >than the small datasets in most textbooks. Fortunately, there is >often no need to decide whether you have outliers or skewness. For >example, a median is to be prefered to a mean if you have EITHER >problem.
Why? If i need to know the mean of the distribution, then I might want to use the sample mean (or some other estimate of the mean) rather than the sample median, which estimates the median of the distribution, even if the distribution is skewed.
The method should be appropriate to the data *and* to the question you wish to answer.
albyn
 End of forwarded message from Albyn Jones 
But why would you WANT to know the population mean if the population is skewed? I don't mean to suggest that that could NEVER happen. Sometimes what we really need is the total, which is directly related to the mean and not to the median. However, generally speaking, medians are more apropriate for skewed data or data with outliers, while means are more appropriate for things that are approximately normally distributed. I meant to describe a ruleofthumb of statistics, not a theorem of mathematics!)
_   Robert W. Hayden   Department of Mathematics /  Plymouth State College MSC#29   Plymouth, New Hampshire 03264 USA  *  Rural Route 1, Box 10 /  Ashland, NH 032179702  ) (603) 9689914 (home) L_____/ hayden@oz.plymouth.edu fax (603) 5352943 (work)



