Comparison of Median Values in Box Plots
Published:
Roman Empire
Ancient Greece
[Box plots image]
0 5 10 15 20 25 30 35 40
Diameter (cm)
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: The image contains two horizontal box plots stacked vertically against a common horizontal scale labeled 'Diameter (cm)'. The scale runs from 0 to 40 with major tick marks every 5 units. The top box plot is labeled 'Roman Empire'. Its whisker starts at 5, the lower quartile (Q1) is at 10, the median (Q2) line is at approximately 13, the upper quartile (Q3) is at 17, and the right whisker ends at 28. The bottom box plot is labeled 'Ancient Greece'. Its whisker starts at 2.5, Q1 is at 16, the median (Q2) line is at approximately 19, Q3 is at 28, and the right whisker ends at 38.
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Step by Step Written Solution
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 Median Diameters
In a box plot, the median is represented by the vertical line section inside the box.
Key Concept: The median is the line inside the box.
Let's identify the median for the Roman Empire plates, labeled small r.
Looking at the scale, the median for the Roman Empire is exactly at thirteen centimeters. So, r equals thirteen.
Now, let's look at the box plot for Ancient Greece to find its median, labeled small g.
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