Question

which of the following box plots is an example of skewed right distribution?

Explanation:

Analyze box plot skewness

Using the Data Distribution Shape and Skewness Direction knowledge points

A box plot shows skewness through the relative lengths of its whiskers and the position of the median line within the box:

• Symmetric: The median is centered in the box, and the whiskers are of roughly equal length.
• Skewed Right (Positive Skew): The right whisker is longer than the left whisker, and/or the right side of the box (from median to \(Q_3\)) is wider than the left side (from \(Q_1\) to median).
• Skewed Left (Negative Skew): The left whisker is longer than the right whisker, and/or the left side of the box is wider than the right side.

Evaluate the options

Using the Box Plot Symmetry knowledge point

• First Option:
• The median line is shifted to the left side of the box.
• The right side of the box is noticeably wider than the left side.
• The right whisker is longer than the left whisker.
• This indicates a right-skewed distribution.

• Second Option:
• The median line is located directly in the middle of the box.
• Both whiskers are of equal length.
• This indicates a symmetric distribution.

Answer:

• (A) The first box plot, where the median is shifted to the left and the right whisker is longer. (Correct answer)
• (B) The second box plot, where the median is centered and the whiskers are symmetric.