Question

one statistic calculated for pitchers in baseball is called the earned run average, or era. the following boxplots summarize the era for pitchers in two leagues, a and b. league a |----| | |----| league b |----| | |----| 0.0 2.5 5.0 7.5 10.0 12.5 era based on the boxplots, which of the following statistics is the same for both leagues? a the range b the interquartile range c the median d the minimum e the maximum

Explanation:

Step1: Recall box - plot components

A box - plot shows the minimum, first quartile ($Q_1$), median, third quartile ($Q_3$), and maximum. The inter - quartile range (IQR) is $Q_3 - Q_1$. The range is $max - min$.

Step2: Analyze the box - plots

For the range: The maximum and minimum values for League A and League B are different, so the ranges are different.
For the inter - quartile range: The length of the box (which represents the IQR) is the same for both League A and League B. The box starts at $Q_1$ and ends at $Q_3$. Visually, the distance between the start and end of the boxes is equal for both leagues.
For the median: The position of the line inside the box (which represents the median) is different for the two leagues.
For the minimum: The starting points of the whiskers (which represent the minimums) are different for the two leagues.
For the maximum: The ending points of the whiskers (which represent the maximums) are different for the two leagues.

Answer:

B. The interquartile range