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

• A. A $boxplot$ is used to display the distribution of quantitative data.
• B. A $boxplot$ cannot display outliers in a dataset.
• C. A $boxplot$ is best suited for visualizing qualitative data.
• D. A $boxplot$ always shows the $mean$ of the data.

Answer: (A)

Verified step by step guidance

1. Understand what a boxplot represents: A boxplot is a graphical representation used to summarize the distribution of a quantitative dataset by showing its minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.
2. Recall that boxplots are designed for quantitative data because they rely on numerical order and measures of central tendency and spread, which do not apply to qualitative (categorical) data.
3. Recognize that boxplots can display outliers explicitly, often marked as individual points beyond the whiskers, which represent typical data range limits (usually 1.5 times the interquartile range from the quartiles).
4. Note that boxplots typically show the median (Q2) as a line inside the box, not the mean. The mean is not always displayed in a standard boxplot unless specifically added.
5. Conclude that the true statement is: 'A boxplot is used to display the distribution of quantitative data,' because it accurately describes the purpose and nature of boxplots.