The grand variance is best described as the variance within which set?

• A. The entire collection of observations.
• B. Each separate group.
• C. Each time point separately.
• D. The average of group variances.

Answer: (A)

Grand variance describes how much all observations in the entire dataset vary around the overall mean. It uses every data point, not just those within a single group or at a single time point. That’s why it represents the variance of the whole collection. If you looked at the variance within each group separately, you’d miss differences between group means, which is captured when you consider the grand variance across all data. In ANOVA terms, the total variance (grand variance) combines the spread within groups and the differences between groups, but its definition is based on all observations together.