Mean Absolute Deviation — Quiz

Question 6 • Concepts in Probability and Statistics

Which box plot represents a set of data that has the greatest mean absolute deviation?

Answer

Image with description A box plot has a number line that has 10 tick marks. The endpoint for its left whisker is at the first tick mark. The left side of its box is at the second tick mark. A vertical segment through the box is at the third tick mark. The right side of its box is at the fourth tick mark. The endpoint for its right whisker is at the sixth tick mark.

Image with description A box plot has a number line that has 10 tick marks. The endpoint for its left whisker is at the first tick mark. The left side of its box is at the second tick mark. A vertical segment through the box is at the fourth tick mark. The right side of its box is a little past the fifth tick mark. The endpoint for its right whisker is a little past the sixth tick mark.

Image with description A box plot has a number line that has 10 tick marks. The endpoint for its left whisker is at the first tick mark. The left side of its box is at the second tick mark. A vertical segment through the box is at the fourth tick mark. The right side of its box is a little before the fifth tick mark. The endpoint for its right whisker is at the seventh tick mark.

Image with description A box plot has a number line that has 10 tick marks. The endpoint for its left whisker is at the first tick mark. The left side of its box is at the second tick mark. A vertical segment through the box is at the fourth tick mark. The right side of its box is at the ninth tick mark. The endpoint for its right whisker is at the tenth tick mark.

Explanation

Mean absolute deviation measures how far data values typically lie from the mean, so a wider spread suggests a greater MAD. Choice D spans from tick 1 to tick 10, with its box stretching from tick 2 to tick 9; the other plots have much shorter boxes and ranges. Therefore, D represents the greatest spread and is the best choice for the greatest mean absolute deviation.

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