In a lengthy list of measures (which are all in the same units), I am reporting both the Mean and the Median because some of the measures have a skewed distribution and others do not (I might also list the skewness and kurtosis, but that may be overkill). To index the dispersion of each measure, I am including the Standard Deviation (which seems most relevant in relation to the Mean) but am wondering what is best to use in relation to the Median.
as don suggested, it is hard to know how to advise if we don't know the level of the audience
but, as a general rule ... NONE of these summary statistics really tell you about the distribution so, my first question is: can you show a picture of the distributions ... like dotplots?
if you can ... then, doing something like what minitab does with its describe command should be more than sufficient ... gives mean and median ... Q1 and Q3 ... low and hi values ... and with the actual shape shown by the dotplot ... what else would you need?
don suggested boxplots but ... the difficulty with those is that they do NOT adequately show you the distributional shape and ... that seems to be of concern to you... and, some distributions if they are radically skewed ... showing a dotplot ... histogram ... or some other "graph" of the data would be useful ALONG with basic summary statistics ...
don't worry about trying to find some variability measure that goes along with the median ... while the semi interquartile range is sometimes used ... there is nothing inherently connected between it and the median ...
. . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
