What is the grand mean in statistics?

• A. The mean of an entire set of observations.
• B. The average of the group means.
• C. The mean of all scores within each time point.
• D. The standard deviation of all scores.

Answer: (A)

The grand mean is the overall average of every observation in the dataset. You combine all scores from all groups and compute one mean, giving the single value that represents the entire data set.

When data are divided into groups, the grand mean still reflects all data combined. It equals a weighted average of the group means, with weights equal to how many observations are in each group. If all groups have the same size, the grand mean also equals the simple average of the group means. For example, if one group has 5 scores averaging 10 and another has 15 scores averaging 20, the grand mean is (5×10 + 15×20) / 20 = 17.5.

This concept is not the standard deviation, which measures dispersion, nor is it simply the mean of scores within a single time point or the unweighted average of group means when group sizes differ.