Problem

For box A with \(Q_{1}=10\), median \(14\), and \(Q_{3}=18\) and box B with \(Q_{1}=14\), median \(18\), and \(Q_{3}=22\), calculate \(\text{both}~\text{IQRs}\), the box intersection and overlap fraction, and the median difference. State the supported comparison and identify claims the summaries do not support.

Source distribution display: Box A has Q1=10, median14,Q3=18; Box B has Q1=14,median18,Q3=22. No requested comparison or interpretation is annotated.

Big Picture

What this problem is really about

Overlap and center describe different features of two distributions, so measure them separately. Treat each box as an interval, find the common segment and compare it with each box width, then compare the medians; substantial overlap prevents claims of complete separation, while equal widths do not imply identical distributions.

Answer choices

Choose your path.

Preview only

IQRs=A8,B8; box intersection=[14,18] length4, overlap fraction=4/8=0.5 for each; medians B>A by4; supported=every B value is higher; unsupported=median ordering proves universal separation

IQRs=A8,B8; box intersection=[14,18] length4, overlap fraction=0.5 for each; medians difference=0 because IQRs match; supported=same IQR means same median; unsupported=spread and center are independent

IQRs=A8,B8; box intersection=[14,18] length4, overlap fraction=4/8=0.5 for each; medians B>A by4; supported=B has higher median but middle halves overlap substantially; unsupported=every B value exceeds every A value or distributions are identical

IQRs=A8,B8; box intersection=[14,18] length4, overlap fraction=4/8=0.5 for each; medians B>A by4; supported=the distributions are identical because boxes overlap; unsupported=overlap proves all values match

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.