Final answer:
Comparisons between groups involve analyzing differences across datasets, while calculations within groups assess data distributions within a single dataset. Pie charts are suitable for parts of a whole, and bar graphs compare quantities. Certain statistical operations are exclusive to either within or between group analyses.
Step-by-step explanation:
Comparisons between groups involve analyzing differences across distinct sets of data, such as comparing average test scores from students in different classrooms. Calculations within groups focus on the distribution and relationships of data points within a single group, such as finding the average or range of test scores within one classroom. Operations within group data may include calculating averages, ranges, modes, and other descriptive statistics. Operations between group data typically involve comparative measures like t-tests or ANOVA to determine statistical significance.
In considering chart types, a pie chart is useful when showing how parts contribute to a whole, such as the percentage of total hours played by students in a gaming study. A bar graph is more appropriate when comparing quantities, such as the number of students in different categories of hours played or analyzing population sizes of various countries.
The operations not allowed in between-group analyses are those that could combine or confuse distinct sets of data, like averaging scores from different groups without considering the groups' separateness. Within-group analyses should not employ statistical tests meant for comparing different datasets.