A researcher conducted a Particle Filtration Efficiency (PFE) test on surgical masks and reusable masks which have been used for 24 hours. The box-and-whisker plots represent the distribution of PFE scores.

1. Find the range of the reusable mask PFE scores

For reusable masks,

maximum PFE score $=75$, minimum PFE score $=62$.

$\text{Range}=75-62=13$

1. Find the interquartile range using $Q_3-Q_1$

For surgical masks, $Q_1=80$ and $Q_3=85$.

$\text{Interquartile range}=Q_3-Q_1=85-80=5$

1. Compare the typical PFE scores using the medians

From the box-and-whisker plots,

• median for surgical masks $=83$,
• median for reusable masks $=68$.

Since $83>68$, surgical masks generally have higher PFE scores than reusable masks.

2. Compare the spread of the PFE scores using interquartile ranges

For surgical masks,
$\text{IQR}=85-80=5.$
For reusable masks,
$\text{IQR}=70-66=4.$
Since $5>4$, the middle $50\%$ of surgical mask PFE scores are slightly more spread out than those of reusable masks. Equivalently, reusable masks have the smaller interquartile range.