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I'm looking for an umbrella term for the maximum, the minimum, the median and the average of a sequence of numbers.

For the maximum and the minimum, such a term would, for example, be the extremum (Term for minimum or maximum).

For the median and the average, one could use measure of central tendency (http://www.quickmba.com/stats/centralten/).

A very generic term for all four words would be just measure.

Is there a more specific term?

Mitch
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user55190
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    How about statistics? – Weather Vane Feb 07 '19 at 18:31
  • ... and this would typically include deviation too. – Weather Vane Feb 07 '19 at 18:44
  • These are examples of set functions: https://en.wikipedia.org/wiki/Set_function – jejorda2 Feb 07 '19 at 18:48
  • @jejorda2 My question is about sequences, not sets. Is there a corresponding term for sequences? – user55190 Feb 07 '19 at 19:06
  • The maximum, minimum, median, average and deviation will be the same regardless of their sequence. The data might just as well be an unordered set. – Weather Vane Feb 07 '19 at 19:09
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    @WeatherVane The median of the sequence (1,3,1,1,1,2,1) is different from the median of the set {1,2,3}. Sequences can contain the same number more than once, sets cannot. See https://en.wikipedia.org/wiki/Sequence – user55190 Feb 07 '19 at 20:18
  • @user55190 uh, multiset then. – Weather Vane Feb 07 '19 at 20:21
  • @WeatherVane But the term "set function" is commonly only used with respect to sets, not multisets (http://mathworld.wolfram.com/SetFunction.html). – user55190 Feb 07 '19 at 20:28
  • @user55190 it was not my suggestion to use terms for sets. I meant "set" in the non-mathematical sense - "bag". – Weather Vane Feb 07 '19 at 20:37
  • The median of a collection of numbers is one of several averages which are all calculated differently, by average do you mean arthmetic mean? – BoldBen Feb 07 '19 at 22:45
  • @BoldBen "The arithmetic mean of a set of values is the quantity commonly called 'the' mean or the average" (http://mathworld.wolfram.com/ArithmeticMean.html). I used average in this sense. – user55190 Feb 07 '19 at 23:10
  • @user55190 I tend to use 'average' for 'arithmetic mean' as well when it's free standing. I just found it a bit odd to have 'median' and 'average' in the same sentence when a median is a type of average. – BoldBen Feb 08 '19 at 05:51
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    In databases, the term aggregate function is used. https://en.wikipedia.org/wiki/Aggregate_function – jejorda2 Feb 08 '19 at 15:12

2 Answers2

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Each one of these, max, min, mean, median, mode, variance, kurtosis, correlation coefficient, etc etc, and so on, is a

statistic.

a function of a sample of data.

Mitch
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The functions you list are all examples of aggregate functions.

Common aggregate functions include:

  • Average (i.e., arithmetic mean)
  • Count
  • Maximum
  • Median
  • Minimum
  • Mode
  • Range
  • Sum

Unlike set functions, aggregate functions can work with multisets or sequences:

Formally, an aggregate function takes input a set, a multiset (bag), or a list from some input domain I and outputs an element of an output domain O. The input and output domains may be the same, such as for SUM, or may be different, such as for COUNT.

The term aggregate function is more common in programming (especially databases) than in mathematics.

jejorda2
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