Question

choosing the set with the greatest mad
which box plot represents a set of data that has the greatest mean absolute deviation?
three box plots are shown, each with a radio button next to it

Explanation:

To determine which box plot has the greatest mean absolute deviation (MAD), we analyze the spread of data:

1. Understand MAD and Spread: The mean absolute deviation measures how spread out data is from the mean. A larger spread (wider range, more dispersed data points) generally means a greater MAD.
2. Analyze the Box Plots:

• The first box plot has a relatively narrow interquartile range (IQR) but check the overall spread (whiskers). Wait, no—wait, the second box plot (middle one) has a very long left whisker, meaning data points are far from the median/mean. Wait, no, let’s re-express: The key is that the second box plot (middle) has the most dispersed data (longest whiskers, especially the left whisker, showing data points far from the center). Wait, no—actually, the middle box plot’s data is spread over a much wider range (the whiskers are longer, especially the left one, and the overall range is larger). Wait, no, let's correct: The middle box plot (second one) has the data spread out the most. Wait, no—wait, the first box plot? No, wait, the middle box plot: Let's see the number line. The middle box plot has a left whisker that extends far left, meaning data points are far from the median, so the MAD (average distance from mean) would be largest. Wait, no—actually, the middle box plot (second) has the greatest spread. Wait, no, let's recheck:

Wait, the middle box plot (second) has a long left whisker, so data points are more spread out. The MAD depends on how far data is from the mean. The more spread out (wider range, more extreme values), the higher the MAD. So the middle box plot (second one) has the greatest MAD.

The mean absolute deviation (MAD) measures data spread from the mean. A greater spread (wider range, more extreme values) increases MAD. The middle box plot has the most dispersed data (longest whiskers, especially the left whisker, indicating extreme values far from the center), so it has the greatest MAD.

Answer:

The middle box plot (the second one, with the long left whisker)