Question

the box plots show the average wind speeds, in miles per hour, for two different islands. average wind speeds on island a average wind speeds on island b which explains, on a given day, which island is more likely to have a wind speed close to its median? o island a because the median is closer to one end of the box in the box plot. o island b because the median is closer to the center of the box in the box plot. o island a because it has a smaller interquartile range. o island b because it has a larger interquartile range.

Explanation:

Step1: Understand the concept of interquartile range (IQR)

The interquartile range (IQR) is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$), i.e., $IQR = Q_3 - Q_1$. A smaller IQR means the data is more concentrated around the median.

Step2: Analyze the box - plots

In a box - plot, if the median is closer to one end of the box, it indicates that the data is more spread out on the other end. But when we want to know which island has wind speeds more likely to be close to its median (more consistent around the median), we look at the interquartile range. A smaller IQR means the middle 50% of the data is more concentrated around the median.
Looking at the box - plots, Island A has a smaller interquartile range.

Answer:

Island A because it has a smaller interquartile range.