Question

which box plot best represents data that are skewed to the right?

Explanation:

Step1: Recall Right - Skewed Box - Plot Properties

A right - skewed (positively skewed) data set in a box - plot has the following characteristics: The median is closer to the lower quartile (Q1) than to the upper quartile (Q3), and the whisker on the right (upper whisker) is longer than the whisker on the left (lower whisker). Also, the box (which represents the inter - quartile range, IQR = Q3 - Q1) is shifted towards the left side of the number line, and the tail of the data (represented by the whisker) is on the right.

Step2: Analyze Each Box - Plot

• For the first box - plot: The box is centered or shifted towards the right. The median is not closer to Q1, and the left whisker seems relatively long. So, it is not right - skewed.
• For the second box - plot: The box is in the middle - right, but the median position and whisker lengths do not match the right - skewed pattern.
• For the third box - plot: The box is centered, and the whiskers seem relatively equal in length (or the distribution is symmetric). So, it is a symmetric distribution, not right - skewed.
• For the fourth box - plot: The box is shifted towards the left (median closer to Q1), the left whisker is short, and the right whisker is long. This matches the characteristics of a right - skewed distribution.

Answer:

The fourth box - plot (the one in the bottom right) best represents data that are skewed to the right.