Which of the following is a true statement about a boxplot?

• A. A boxplot shows the $\mathrm{mean}$ and $\mathrm{standard} \mathrm{deviation}$ of the data.
• B. A boxplot is best used to visualize categorical or qualitative data.
• C. A boxplot cannot be used to identify $\mathrm{skewness}$ in a data set.
• D. A boxplot displays the $\mathrm{median}$, $\mathrm{quartiles}$, and possible outliers of quantitative data.

Answer: (D)

Verified step by step guidance

1. Understand what a boxplot represents: A boxplot is a graphical summary of a quantitative data set that displays the median, quartiles, and potential outliers.
2. Recall the components of a boxplot: It includes the median (the middle value), the first quartile (Q1), the third quartile (Q3), and whiskers that extend to the smallest and largest values within 1.5 times the interquartile range (IQR).
3. Recognize that a boxplot does not show the mean or standard deviation explicitly; these are different summary statistics often shown in other plots like histograms or error bars.
4. Note that boxplots are designed for quantitative (numerical) data, not categorical or qualitative data, because they rely on ordering and numerical summaries.
5. Understand that boxplots can indicate skewness by the relative lengths of the whiskers and the position of the median within the box, so the statement that they cannot identify skewness is false.