On Fri, 30 May 2003, Stan Brown wrote in part: > I realized that > I could think of lots of examples of symmetric distributions and of > distributions that are skewed right, but I went blank trying to > think of a straightforward real-life example of a distribution that > is skewed left. > Anyone care to contribute the obvious answer that I can't think of?
(1) Achievement test scores, post-instruction, where most students have mastered the material tested. Sometimes referred to as a "ceiling effect". (2) Diameters of gravel that has been put through a series of graduated screens to produce different degrees of fineness. The smallest size will (assuming an overall distribution that has a left tail) tend to cluster near the mesh size of the smallest screen, and tail off toward zero. (3) A sample drawn from any unimodal distribution that has a left tail subject to an upper cutoff that is at or less than the mode (like the smallest gravel size). E.g., IQ measures of persons labelled "mentally handicapped" or "retarded" or some equivalent locution (depending on the political correctness of the day), when the persons are selected by having an IQ score of 85 or less (or any other cutoff value lower than the mode). (4) Any right-skewed distribution, when the variable X is transformed to its reciprocal 1/X, or to its negative (C-X) for any real constant C. [For an example where a reciprocal is moderately interesting, think of automobile fuel economy measured as in the U.S. in <miles per gallon> and as in Europe in <liters per hundred kilometers>. The one is the reciprocal of the other (multiplied by a constant to convert the units from US measure to metric measure). I have no idea which of these distributions is/are skewed, nor in which direction(s); but even if one of them is approximately symmetric, its reciprocal will almost certainly not be.] ----------------------------------------------------------------------- Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
