Given a histogram that is skewed to the right ($\mathrm{positively}\mathrm{skewed}$), which of the following boxplots best matches the distribution shown in the histogram?

• A. A boxplot where the $\mathrm{median}$ is closer to the left, and the right whisker is noticeably longer than the left whisker.
• B. A boxplot where the $\mathrm{median}$ is closer to the right, and the left whisker is noticeably longer than the right whisker.
• C. A boxplot where the $\mathrm{median}$ is centered and both whiskers are approximately equal in length.
• D. A boxplot with no whiskers, indicating all data points are identical.

Answer: (A)

Verified step by step guidance

1. Understand what it means for a distribution to be skewed to the right (positively skewed). This means that the tail on the right side of the distribution is longer or fatter than the left side, indicating more extreme higher values.
2. Recall how a boxplot represents data: the box shows the interquartile range (IQR), the line inside the box is the median, and the whiskers extend to the smallest and largest values within 1.5 times the IQR from the quartiles.
3. For a right-skewed distribution, the median tends to be closer to the lower quartile (left side of the box), because the bulk of the data is concentrated on the lower end, and the upper whisker is longer due to the extended tail on the right.
4. Compare the options by matching these characteristics: the median closer to the left side of the box and a longer right whisker correspond to a right-skewed distribution.
5. Eliminate options that show the median centered with equal whiskers (which indicate symmetry), median closer to the right with a longer left whisker (which indicates left skew), or no whiskers (which indicates no variability).