Question

in a box plot, if the median is to the left of the center of the box and the right whisker is substantially longer than the left whisker, the distribution is ______.

skewed right
symmetric

Explanation:

Analyze box plot components

Using the Box Plot Symmetry knowledge point

• The median line is positioned to the left of the center of the box.
• This indicates that the data values in the lower half of the middle \(50\%\) are more concentrated, while the upper half is more spread out.

Evaluate whisker lengths

Using the Data Distribution Shape knowledge point

• The right whisker is substantially longer than the left whisker.
• A longer right whisker shows that the top \(25\%\) of the data spans a much wider range, indicating a long tail on the right side.

Determine distribution skewness

Using the Skewness Direction knowledge point

• Both a median shifted to the left and a longer right whisker are classic indicators of a tail extending to the right.
• Therefore, the distribution is skewed right (positively skewed).

Answer:

• Skewed right (Correct answer)
• Symmetric