Merits and Limitation of Quartile Deviation

Merits:

(i)    In certain respects it is superior to range as a measure of dispersion.

(ii)    It has a special utility in measuring variation in case of open-end distributions or one in which the data may be ranked  but measured quantitatively.

(iii)    It is also useful in erratic or badly skewed distributions, where the other measures of dispersion would be warped by extreme values. The quartile deviation is not affected by the presence of extreme values.

Limitations:

(i)    Quartile deviation ignores 50% items, i.e., the first 25% and the last 25%. As the value of quartile deviation does not depend upon every item of the series it cannot be regarded as good method of measuring dispersion.

(ii)    It is not capable of mathematical manipulation.

(iii)    Its value is very much affected by sampling fluctuations.

(iv)    It is in fact not a measure of dispersion as it really does not show the scatter around an average, but t is a positional average. Consequently, some statisticians speak of quartile deviation as a measure of partition rather than as a measure of dispersion. If we really desire to measure variation in the sense of showing the scatter around an average, we must include the deviation of each and every item from an average in the measurement.

Because of the above limitations quartile deviation is not often useful for statistical inference.

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