Grand Mean

Authors

Affiliations

Nate Yomogida, B.S., SPT

Doctor of Physical Therapy

B.S. in Kinesiology

Chloë Kerstein, B.S., SPT

Doctor of Physical Therapy

B.A. in Neuroscience

Grand mean is the mean of all observations: every data point, divided by the joint sample size.

Calculation

Tip

If all the subsamples have the same number of points, the grand mean is simply a mean of the subsample means.

Example

• Sample 1: (6, 6, 3, 3)
• Sample 2: (1, 5, 0, 14)
• Sample 3: (9, 10, 11, 12)
• Sample 4: (0, 4, 0, 20)

Step 1: Find the sample means of each group: (4.5, 5, 10.5, 6).

Step 2: Take the mean of the results from Step 1: (4.5, 5, 10.5, 6) / 4 = 26 / 4 = 6.5.