The interquartile range or the quartile deviation is a better measure of variation in a distribution than the range. Here, avoiding the 25 percent of the distribution at both the ends uses the middle 50 percent of the distribution. In other words, the interquartile range denotes the difference between the third quartile and the first quartile.

Symbolically, interquartile

Range = Q3- Ql

Many times the interquartile range is reduced in the form of semi-interquartile range or quartile deviation as shown below:

Semi interquartile range or Quartile deviation = (Q3 – Ql)/2

When quartile deviation is small, it means that there is a small deviation in the central 50 percent items. In contrast, if the quartile deviation is high, it shows that the central

50 percent items have a large variation. It may be noted that in a symmetrical distribution, the two quartiles, that is, Q3 and QI are equidistant from the median. Symbolically,

M-QI = Q3-M

However, this is seldom the case as most of the business and economic data are asymmetrical. But, one can assume that approximately 50 percent of the observations are contained in the interquartile range. It may be noted that interquartile range or the quartile deviation is an absolute measure of dispersion. It can be changed into a relative measure of dispersion as follows:

Coefficient of QD = Q3 –Q1 /Q3 +Q1

The computation of a quartile deviation is very simple, involving the computation of upper and lower quartiles. As the computation of the two quartiles has already been explained in the preceding chapter, it is not attempted here.


The following merits are entertained by quartile deviation:

  1. As compared to range, it is considered a superior measure of
  2. In the case of open-ended distribution, it is quite
  3. Since it is not influenced by the extreme values in a distribution, it is particularly suitable in highly skewed or erratic


  1. Like the range, it fails to cover all the items in a distribution.
  2. It is not amenable to mathematical
  3. It varies widely from sample to sample based on the same
  4. Since it is a positional average, it is not considered as a measure of
  5. It merely shows a distance on scale and not a scatter around an average.

In view of the above-mentioned limitations, the interquartile range or the quartile deviation has a limited practical utility.