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Grand Mean
The grand mean is most often used in the computation of the F value in analysis of variance, or ANOVA. It is the overall mean from which group means are subtracted when computing the between-group variance. The between-group variance and the within-group variance are the two variance estimates that are used to create the F ratio. The grand mean can also be used as an estimate of the average of all the scores in a group.
| Table 1 Sample Data for Computing the Means and Grand Mean | |||
|---|---|---|---|
| Group 1 | Group 2 | Group 3 | |
| 6 | 7 | 8 | |
| 4 | 6 | 7 | |
| 5 | 5 | 6 | |
| 6 | 3 | 5 | |
| 5 | 4 | 6 | |
| 4 | 5 | 5 | |
| 3 | 3 | 4 | |
| 4 | 2 | 4 | |
| 5 | 3 | 3 | |
| 6 | 3 | 3 | |
| Group Average | 4.8 | 4.1 | 5.1 |
| Grand Mean | 4.7 | ||
For example, Table 1 shows three sets of 10 scores along with the mean for each of the groups. The grand, or overall, mean is shown in this table as well.
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