standard deviation for digits

The std. dev. for the set 1-2-3 is 1 and so is the std.dev. for the
sets 4-4-6 and 7-8-9. But the overall std.dev. for the total set
from 1 to 9 is 2. 49. By what formula could this value be predicted?
It looks like the mean of each set must be part of any formula.

Stig Holmquist
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