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A stemplot (also known as a stem-and-leaf plot) and a histogram are both graphical tools used to display the distribution of a quantitative variable. A stemplot is more suitable for smaller data sets and shows exact data points, while a histogram is better for larger data sets and groups data into bins.

Let's analyze each provided option to determine the best reason for choosing a stemplot: (a) *Stemplots allow you to split stems; histograms don't.* While stemplots do allow for splitting stems, this is not their primary advantage over histograms. (b) *Stemplots allow you to see the values of individual observations.* This is a significant advantage because stemplots display actual data points, allowing insights into specific values. (c) *Stemplots are better for displaying very large sets of data.* This is incorrect, as stemplots become cumbersome with large data sets. (d) *Stemplots never require rounding of values.* While stemplots often use exact values, this isn't their primary reason for use over histograms. (e) *Stemplots make it easier to determine the shape of a distribution.* Although both can show distribution shapes, histograms are generally preferred for understanding the overall shape in larger datasets.

Option (b) stands out as the best reason because it highlights a clear advantage of stemplots: the ability to display actual data points, allowing for an immediate understanding of each individual observation. This is crucial in situations where knowing specific data values is important.