The supervisor's recommendation doubtless arises from the advice to be found in many contemporary textbooks in elementary statistics: If the (raw) distribution be symmetrical, the mean and standard deviation are adequate for descriptive purposes and are to be preferred. If the distribution be skewed (at least, skewed enough to be visible and worth worrying about) the median and quartiles (or median and hinges: a box plot) are preferred, because while mean & s.d. CANNOT convey any information about asymmetry in the distribution, median and quartiles MAY convey such information (if the quartiles are unequally distant from the median).
Whether the supervisor's advice was "sage" (or even "good") in the current context I cannot say, since there is nothing in the post (as received from Stan -- I haven't seen Tony's original) to indicate what purpose lay behind the decision, nor what further analysis(es) might be contemplated that might use the summary information (rather than the raw data). On Fri, 25 Jul 2003, Stan Brown wrote: > In > sci.stat.edu, Tony <[EMAIL PROTECTED]> wrote: > > >One of these statistics collected was how many weeks did it take to > >fill a vacancy. ... The reply from her supervisor was "if the > >results are normally distributed then use the mean otherwise use the > >median". I am sure this is sage advice, but why? Not so sure the advice was "sage"; and in any case she SHOULD have said, "If the results are approximately symmetrical and unimodal", since NO results are ever normally distributed... > >I would have thought that if the distribution was normally > >distributed then the mean and the median would be roughly similar > > Not just roughly similar, but identical. The same is true for any > symmetric distribution, whether normal or not. > > >since the normal curve has the frequency distributed around > >the mean. As Stan more gracefully pointed out, this subordinate clause is without useful meaning. > > My further thinking about this was that for any > >distribution the mean will always be the upper bound of the median. > >Is this correct? > > No. < snip, discussion of asymmetry > Cheers! -- DFB. ----------------------------------------------------------------------- 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/ . =================================================================
