Comparing Medians in Box Plots
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The Metropolitan Museum of Art has plates on display from the Roman Empire and ancient Greece. The box plots shown summarize the distributions of the diameters, in centimeters, of all the museum's plates from each region. How does the median diameter of the plates from the Roman Empire, $r$, compare to the median diameter of the plates from ancient Greece, $g$ ?
A) $r < g$
B) $r > g$
C) $r = g$
D) There is not enough information to compare the medians.
This question includes visual content: Two horizontal box plots aligned over a single numerical axis labeled 'Diameter (cm)' ranging from 0 to 40 with major ticks every 5 units. The top box plot is labeled 'Roman Empire'. Its whisker begins at approximately 5, the first quartile (Q1) is at 10, the median line is at approximately 13, the third quartile (Q3) is at approximately 17, and the right whisker ends at approximately 28. The bottom box plot is labeled 'Ancient Greece'. Its whisker begins at approximately 2, Q1 is at approximately 16, the median line is at 19, Q3 is at approximately 28, and the right whisker ends at approximately 38.
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In this problem, we are looking at two box plots representing the diameters of plates from the Roman Empire and ancient Greece. We need to compare their median diameters.
Comparing Medians from Box Plots
Recall that in a box plot, the vertical line located inside the box represents the median of the data set.
The median is represented by the vertical line inside the rectangular box.
Let's find the median diameter for the Roman Empire plates, labeled as r. Looking at the first box plot, the vertical line is aligned with thirteen on the number line.
Now, let's find the median for the ancient Greece plates, labeled as g. In the second box plot, the vertical line is aligned with nineteen on the number line.
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