If I have a data set which has three sub groups, each of a different size and with a different mean can I index the means to adjust for the sub-sample size?

For example if I have:


sub group 1: 1900 observations with a mean of 8.9

sub group 2: 2184 observations with a mean of 9

and

sub group 3: 2210 observations with a mean of 9.7

can I use sub group 1 as a 'base group' and calculate the percentage differences in the size of the groups and adjust the means accordingly?

so sub group one would be itself

sub group two would be (2184/1900) times 8.9 which is aprox 10.4

sub group three would be (2210/1900) times 9.7 which is aprox 11.3

is that acceptable or does it give incorrect information?

thanks!