Final answer:
The best graphical representations for comparing quantitative data across groups are bar graphs and pie charts, with bar graphs being more suitable for comparing total numbers and pie charts for showing percentage distributions.
Step-by-step explanation:
The two graphical representations that are best for comparing quantitative data across groups are bar graphs and pie charts. Bar graphs are effective for displaying the relationships between the sizes of multiple groups, and can also show detailed breakdowns within a population. In contrast, pie charts are best for illustrating parts of a whole and showing the percentage distribution across different categories.
When deciding between these two types of graphs, the choice often depends on the nature of the data and the specific aspects one wishes to emphasize. For instance, a bar graph would be more suitable for comparing the total numbers of individuals across different categories, as it displays values along an axis which can be easily compared. On the other hand, a pie chart represents data as a circular whole, divided into slices to represent a proportion of the total, which can be ideal for visualizing percentages or fractions of a dataset.