Suppose you are given a box plot that is highly skewed to the right, with the median closer to the lower quartile and a long upper whisker. The distribution that has the box plot shown could be described as which of the following?

• A. $\text{Negatively skewed (left-skewed)}$
• B. $\text{Positively skewed (right-skewed)}$
• C. $\text{Uniform}$
• D. $\text{Symmetric}$

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the characteristics of skewness in a distribution. A distribution is said to be positively skewed (right-skewed) if it has a long tail on the right side, meaning the upper whisker in a box plot is longer than the lower whisker.
2. Step 2: Recognize that in a right-skewed distribution, the median is closer to the lower quartile (Q1) than to the upper quartile (Q3), because the bulk of the data is concentrated on the lower end with a few larger values stretching the upper end.
3. Step 3: Compare this to a negatively skewed (left-skewed) distribution, where the long tail is on the left side, and the median is closer to the upper quartile (Q3) with a longer lower whisker.
4. Step 4: Note that a uniform distribution has roughly equal spread and no skewness, so the median is centered between the quartiles and whiskers are about equal in length.
5. Step 5: Conclude that since the box plot described has the median closer to the lower quartile and a long upper whisker, it matches the characteristics of a positively skewed (right-skewed) distribution.