Interquartile Range Semi-Difference
The interquartile range semi-difference is a measure of variability calculated by halving the difference between the third quartile (Q3) and the first quartile (Q1). $$ \delta = \frac{Q_3 - Q_1}{2} $$
The semi-difference provides an indication of how data is spread around the median (second quartile).
The larger the semi-difference, the greater the data spread.
What are quartiles? Quartiles are values that divide an ordered dataset into quarters. The first quartile marks the point below which the lowest 25% of the data falls, while the third quartile (Q3) marks the point above which the top 25% of the data lies.
Why is the interquartile semi-difference useful?
It helps measure data dispersion while excluding potential outliers, exceptional values, or random data points (outliers) caused by measurement errors or data entry mistakes, which often occur at the extremes of a distribution.
A practical example
Consider a dataset where the first quartile (Q1) is 18 and the third quartile (Q3) is 27.
$$ Q_1 = 18 $$
$$ Q_3 = 27 $$
In this case, the semi-difference is 4.5.
$$ \delta = \frac{Q_3 - Q_1}{2} = \frac{27 - 18}{2} = \frac{9}{2} = 4.5 $$
This is exactly half of the interquartile range.
And so forth.
