What do boxplots display in statistics?

Boxplots, also known as box-and-whisker plots, display a 5-number summary of a dataset, which includes the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value. This summary effectively highlights the central tendency and variability within the data, as well as potential outliers.

By visually representing these key statistics, boxplots allow for a quick assessment of how data points are spread and help in comparing distributions between different groups. Each component of the boxplot offers insight into the data's structure, including how much variability there is and where most values lie in relation to the median.

In contrast, the other options do not align with the purpose of boxplots. A histogram illustrates data distribution through bars, focusing on frequency counts for intervals of data, whereas boxplots present summary statistics instead. The variance and standard deviation are measures of data dispersion but are not illustrated in a boxplot. Lastly, a frequency distribution of categorical data is better represented with bar charts or pie charts, indicating how categorical variables are distributed rather than providing a summary of numerical data. Thus, the option describing the 5-number summary is the most accurate representation of what boxplots display.