Numerical Measures of Central Tendency and Variability

Measures of Variability

Interquartile Range

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

$\mathrm{IQR} = \mathrm{75th} \, \; \text{percentile} - \mathrm{25th} \; \text{percentile}$

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.

Callback before_footer in local_aigrade component should be migrated to new hook callback for core\hook\output\before_footer_html_generation

line 7225 of /lib/moodlelib.php: call to debugging()
line 7292 of /lib/moodlelib.php: call to {closure}()
line 71 of /lib/classes/hook/output/before_footer_html_generation.php: call to get_plugins_with_function()
line 987 of /lib/classes/output/core_renderer.php: call to core\hook\output\before_footer_html_generation->process_legacy_callbacks()
line 97 of /mod/book/tool/print/index.php: call to core\output\core_renderer->footer()