Quartile Deviation and Coefficient of Quartile Deviation

Quartile Deviation (Q.D.), also called the semi-inter-quartile range, is based on the middle 50% of the data — it ignores the extreme 25% of values on each end, which makes it more stable than the Range.

where $Q_1$ (the lower quartile) and $Q_3$ (the upper quartile) are computed as follows:

Individual series (n observations, arranged in ascending order): locate $Q_1$ at the $\dfrac{n+1}{4}$-th item and $Q_3$ at the $\dfrac{3(n+1)}{4}$-th item, using linear interpolation when the position falls between two items.

Continuous series (grouped frequency distribution, total frequency $N$):

where $L$ = lower limit of the quartile class (the class in which the cumulative frequency $\frac{N}{4}$ or $\frac{3N}{4}$ falls), $cf$ = cumulative frequency of the class just before the quartile class, $f$ = frequency of the quartile class, and $h$ = class width. …