Question

question 29 points 2

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

skewed left

skewed right

Explanation:

Analyze the box plot components

Using the Box Plot Symmetry knowledge point, we look at the relative positions of the median and the whiskers. A box plot consists of a central box from the first quartile \(Q_1\) to the third quartile \(Q_3\), with a line representing the median \(Q_2\) inside. Whiskers extend from the box to the minimum and maximum values (excluding outliers).

Determine the direction of skewness

Using the Data Distribution Shape knowledge point, we evaluate the asymmetry:

• The median is to the right of the center of the box, meaning the left side of the box (from \(Q_1\) to the median) is wider than the right side (from the median to \(Q_3\)).
• The left whisker is substantially longer than the right whisker.

Both of these features indicate that the data is stretched out further on the lower (left) end of the scale. This long tail on the left side corresponds to a left-skewed (or negatively skewed) distribution.

Answer:

• Skewed left (Correct answer)
• Skewed right