Aggregate function

In database management, an aggregate function or aggregation function is a function where multiple values are processed together to form a single summary statistic.

Common aggregate functions include:

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

Others include:

• Nanmean (mean ignoring NaN values, also known as "nil" or "null")
• Stddev

Formally, an aggregate function takes as input a set, a multiset (bag), or a list from some input domain I and outputs an element of an output domain MAX, AVERAGE (tracking sum and count, dividing at the end) and MEDIAN, and ⁠⁠SUM⁡(x)=x, for a singleton;

COUNT⁡(X⊎Y)=COUNT⁡(X)+COUNT⁡(Y).

MAX⁡(X⊎Y)=max⁡(MAX⁡(X),MAX⁡(Y)).

MIN⁡(X⊎Y)=min⁡(MIN⁡(X),MIN⁡(Y)).

Note that self-decomposable aggregation functions can be combined (formally, taking the product) by applying them separately, so for instance one can compute both the f as one that can be expressed as the composition of a final function f=g∘h,f(X)=g(h(X)). For example, COUNT, SUM in OLAP, since these can be computed for each cell of the OLAP cube and then summarized ("rolled up"), but it is difficult to support AVG⁡(X⊎Y)=(SUM⁡(X)+SUM⁡(Y))/(COUNT⁡(X)+COUNT⁡(Y)) or, only if COUNT(X)=COUNT(Y)
STDDEV⁡(X⊎Y)=(SUM⁡(X2)+SUM⁡(Y2))/(COUNT⁡(X)+COUNT⁡(Y))−((SUM⁡(X)+SUM⁡(Y))/(COUNT⁡(X)+COUNT⁡(Y)))2

• Cross-tabulation a.k.a. Contingency table
• Data drilling
• Data mining
• Data processing
• Extract, transform, load
• Fold (higher-order function)
• Group by (SQL), SQL clause
• OLAP cube
• Online analytical processing
• Pivot table
• Relational algebra
• Utility functions on indivisible goods#Aggregates of utility functions
• XML for Analysis
• AggregateIQ
• MapReduce