I need some glossary guidance here.
What do you call measures or operations, such as sample standard deviation, which may change the result of existing elements in a data set when new data is added?
Conversely, what do you call operations such as square root, which can be applied independently to elements even if they reside in a sample set?
Twitter suggested coherent or on-line. Not sure if those are appropriate.
On
They are both just functions but they have different domains.
The domain of the square root function is the positive real numbers. Its input is a single positive real number.
The domain of the standard deviation is the set of finite subsets of the real numbers. Its input is a finite set if real numbers.
In some contexts, both functions might have other domains sometimes but I am guessing that these are the contexts which interest you.
If you are a programmer then you might know the database language SQL. This would call SQRT a scalar function and STDDEV a column function. However, that is not the usual mathematical view. There is some similarity and overlap of terms in mathematics and computing but you should not assume that they are the same.
Aggregating: "formed or calculated by the combination of many separate units or items; total."
More details here.