Which elements are included in the five-number summary of a dataset?

The five-number summary of a dataset is a vital descriptive statistic that provides a quick overview of its distribution. It specifically includes the minimum value (lower extreme), the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value (upper extreme). These five components allow for the identification of the spread and central tendency of the data.

In this case, the correct option lists the lower extreme, lower quartile (Q1), median (Q2), upper quartile (Q3), and upper extreme, which aligns perfectly with the definition of the five-number summary. Each of these elements serves a crucial role: the lower extreme indicates the smallest value, while the upper extreme indicates the largest value, and the quartiles and median provide insight into the data's distribution and central values.

The other answer choices include components that do not fit within the five-number summary framework. For example, options that list the mean, mode, or interquartile range (IQR) stray from the traditional five-number summary, which strictly focuses on minimum and maximum values along with quartiles and the median. Understanding this structure is key to summarizing datasets effectively in statistics.