How is a box plot useful in statistics?

A box plot, also known as a whisker plot, is particularly useful in statistics as it provides a visual representation of the distribution of a dataset through five summary statistics: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

By visualizing these five statistics, a box plot effectively highlights the central tendency of the data (represented by the median) and the spread or variability (indicated by the interquartile range between Q1 and Q3). Furthermore, it can showcase potential outliers, giving a quick overview of how data is distributed, whether it is skewed, and how it varies. This makes it easier for statisticians and data analysts to compare distributions between different groups or datasets.

The other options provided do not accurately reflect the specific function of a box plot in statistical analysis. For instance, illustrating relationships between variables requires different types of graphs, and trends over time usually necessitate time series analysis rather than a box plot. Probability of events involves different statistical tools and concepts outside the scope of what a box plot is designed to convey.