Numerical Measures of Central Tendency and Variability

The interquartile range (IQR) is the range of the middle $\mathrm{50\%}$ of the scores in a distribution. It is computed as follows:

For Quiz 1, the $\mathrm{75th}$ percentile is $\mathrm{8}$ and the $\mathrm{25th}$ percentile is $\mathrm{6}$. The interquartile range is therefore $\mathrm{2}$. For Quiz 2, which has greater spread, the $\mathrm{75th}$ percentile is $\mathrm{9}$, the $\mathrm{25th}$ percentile is $\mathrm{5}$, and the interquartile range is $\mathrm{4}$. Recall that in the discussion of box plots, the $\mathrm{75th}$ percentile was called the upper hinge and the $\mathrm{25th}$ percentile was called the lower hinge. Using this terminology, the interquartile range is referred to as the H-spread.

A related measure of variability is called the semi-interquartile range. The semi-interquartile range is defined simply as the interquartile range divided by $\mathrm{2}$. If a distribution is symmetric, the median plus or minus the semi-interquartile range contains half the scores in the distribution.