Question

question 1 points 1
in a box plot, if the median is in the center of the box, and the left and right whiskers are roughly of the same length, then the distribution is said to be ______.

skewed right
symmetric

Explanation:

Analyze box plot components

A box plot displays a five-number summary of a dataset: minimum, first quartile \(Q_1\), median \(Q_2\), third quartile \(Q_3\), and maximum. The "box" represents the middle \(50\%\) of the data between \(Q_1\) and \(Q_3\), with a line inside representing the median. The "whiskers" extend from the box to the minimum and maximum values.

Evaluate symmetry conditions

If the median is located exactly in the center of the box, the distance from \(Q_1\) to the median equals the distance from the median to \(Q_3\). This indicates that the middle \(50\%\) of the data is distributed evenly. Furthermore, if the left and right whiskers are roughly of the same length, the spread of the lower \(25\%\) of the data matches the spread of the upper \(25\%\) of the data.

Determine distribution shape

When both halves of a box plot are mirror images of each other—meaning the median is centered and the whiskers are equal in length—the data is balanced on both sides of the center. This balanced shape indicates that the underlying data distribution is symmetric.

Answer:

• skewed right
• symmetric (Correct answer)