Renáta Németh, Dávid Simon
So far we have discussed five measures of variability: the IQV, the range, the IQR, the variance and the standard deviation. Which one to choose in a given situation?
If the distribution of an interval-ratio variable is highly skewed, the mean is an ambiguous measure of central tendency, so variance and standard deviation (based on the mean) may be also ambiguous,
IQV loses some information used with ordinal variables, since it does not take the ordering of the categories into account,
Use of IQR with ordinal variables is questionable, since it is based on the distance between two quartiles, and distance is not defined for the categories of an ordinal variable. The compromise is to interpret the IQR as the range that includes the “middle half” of the ordered observations, and to use with caution for comparing variabilities (only if the variables being compared measure similar things on the same scale, e.g. attitude questions with Strongly agree–Strongly disagree scaled responses).
Note that these are purely methodological considerations, not always followed in research practice. E.g. income data are usually skewed; however, the standard deviation for income is frequently used.