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

• A. A $boxplot$ cannot display outliers in the data.
• B. A $boxplot$ is used to display the distribution of quantitative data.
• C. A $boxplot$ is primarily used to visualize qualitative data.
• D. A $boxplot$ shows the frequency of each category in a dataset.

Answer: (B)

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 through its five-number summary (minimum, first quartile, median, third quartile, and maximum).
2. Recall that boxplots can display outliers by marking data points that fall outside the typical range (usually 1.5 times the interquartile range above the third quartile or below the first quartile). This means the statement 'A boxplot cannot display outliers' is false.
3. Recognize that boxplots are designed for quantitative data, not qualitative data. Therefore, the statement 'A boxplot is primarily used to visualize qualitative data' is incorrect.
4. Note that boxplots do not show frequencies or counts of categories; instead, they show the spread and central tendency of numerical data. Hence, the statement 'A boxplot shows the frequency of each category in a dataset' is false.
5. Conclude that the true statement is: 'A boxplot is used to display the distribution of quantitative data,' as it effectively summarizes and visualizes the distribution characteristics of numerical datasets.