One problem with Jason's suggestion (and this applies equally to the interquartile range and the semi-interquartile range) is that the resulting value tells you nothing about the asymmetry of the data. Since John's original reason for considering the median (&c) at all was that some of his variables are (or at least appear to be!) strongly enough skewed to worry about, I would rather suppose that it were preferable to report both quartiles (or other symmetric percentiles), so as to make the degree of asymmetry at least retrievable if not necessarily visible (depending on the form of the reportage).
To answer John's P.S.: Q == semi-interquartile range = 1/2(interquartile range) and can be construed as the average (over both directions) of the median distance of data points from the median. I believe (but am not certain, not having taken the time to do the algebra) that Jason's suggestion may sometimes generate Q, but only for some distributions. (Jason's measure is constrained to be either an observed deviation or a value midway between two adjacent observed absolute deviations; Q is not so constrained.) (I myself would prefer Q to Jason's median of absolute deviations from the median, I think.) On 28 Feb 2003, Jason wrote in part: > If your data is x1,x2,...,xn with mean m, then the SD is the square > root of the mean of (x1-m)^2,(x2-m)^2,...,(xn-m)^2. It takes this > form for computational reasons, but in principle you can think of it > as the mean of |x1-m|,|x2-m|,...,|xn-m|. > > So if the median in M, the analog would be to look at the median of > |x1-M|,|x2-M|,...,|xn-M|. Whether or not anyone actually uses this, > I don't know. ----------------------------------------------------------------------- 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/ . =================================================================
