Which statement is true about box plots when visualizing data?

• A. Box plots cannot show information about the spread or variability of data.
• B. Box plots are used to display the distribution of quantitative data, showing the $\mathrm{median}$, $\mathrm{quartiles}$, and possible outliers.
• C. Box plots are primarily used to visualize qualitative data categories.
• D. Box plots are only useful for displaying the $\mathrm{mean}$ of a dataset.

Answer: (B)

Verified step by step guidance

1. Understand that a box plot is a graphical representation used to summarize the distribution of a quantitative dataset.
2. Recall that a box plot displays key statistics such as the median (the middle value), the first quartile (Q1), and the third quartile (Q3), which together show the spread and variability of the data.
3. Recognize that the 'box' in the box plot represents the interquartile range (IQR), which is the range between Q1 and Q3, indicating the middle 50% of the data.
4. Note that box plots also often show 'whiskers' extending to the smallest and largest values within 1.5 times the IQR from the quartiles, and any points outside this range are considered outliers.
5. Conclude that box plots are not used for qualitative data or just the mean; instead, they provide a visual summary of the distribution, spread, median, quartiles, and potential outliers of quantitative data.