For example, for the observation group 1 time 1, the cumulative mean is missing; for observation group 1 time 2, the cumulative mean is the average of previous observations, namely 74; for observation group 1 time 3, the cumulative mean is the average of previous observations, namely avarage of 74 and 85.5.

Thanks a ton in advance!

Code:
* Example generated by -dataex-. For more info, type help dataex
clear
input float group byte time double x
1  1   74
1  2 85.5
1  3 83.3
1  4 83.7
1  5   53
1  6   81
1  7   72
1  8 89.9
1  9 85.3
1 10 87.5
1 12 82.8
1 13 79.2
1 15 80.8
1 16 85.2
2  1   62
2  2   73
2  3   63
2  4   63
2  5   78
2  6   68
end