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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.

Jeremy Leipzig
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  • How about global (affected by entire data set) versus local (not affected by entire data set)? – Adrian Keister Jun 20 '18 at 15:06
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    That's not really a math question - you didn't specify what it means to 'change' the result, for example the result of applying roots also changes when you change single element.

    What you might find interesting though is the notion of morphisms of F-algebras, for example catamorphisms vs anamorphisms (consider fold vs map from functional programming languages)

     – Jakub Bartczuk Jun 20 '18 at 15:16
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    In this context, I think that the term you are looking for is a sample statistic, which can be thought of as a function that takes a set as input, and outputs some value. More generally, perhaps you might like the term set function, which is a function that takes a set as input. In any event, I am not sure that you need terms for these functions; instead, you need to be more careful about describing the domains and codomains of your functions (functions on sets vs functions on $\mathbb{R}$, for example). – Xander Henderson Jun 20 '18 at 15:16
  • If I am understanding the question correctly, you are trying to distinguish between (a) a function whose input is a set, and (b) a function whose input is an element of the set. Is that right? – mweiss Jun 20 '18 at 15:53

2 Answers2

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Aggregating: "formed or calculated by the combination of many separate units or items; total."

More details here.

JonathanZ
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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.

badjohn
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