Aggregate Functions, Relational Algebra

Aggregate functions are functions that define an operation which consumes values from multiple records to a produce a single output. Aggregate functions in SQL are typically used in GROUP BY functions. Aggregate functions are similar to scalar functions and function signatures with a small set of different properties.

Aggregate function signatures contain all the properties defined for scalar functions. Additionally, they contain the properties below:

In database management an aggregate function is a function where the values of multiple rows are grouped together as input on certain criteria to form a single value of more significant meaning.

Various Aggregate Functions

1) Count()

2) Sum()

3) Avg()

4) Min()

5) Max()

Id     Name     Salary

———————–

1       A        80

2       B        40

3       C        60

4       D        70

5       E        60

6       F        Null

Count():

Count(*): Returns total number of records .i.e 6.

Count(salary): Return number of Non Null values over the column salary. i.e 5.

Count(Distinct Salary):  Return number of distinct Non Null values over the column salary .i.e 4

Sum():

sum(salary):  Sum all Non Null values of Column salary i.e., 310

sum(Distinct salary): Sum of all distinct Non-Null values i.e., 250.

Avg():

Avg(salary) = Sum(salary) / count(salary) = 310/5

Avg(Distinct salary) = sum(Distinct salary) / Count(Distinct Salary) = 250/4

Min():

Min(salary): Minimum value in the salary column except NULL i.e., 40.

Max(salary): Maximum value in the salary i.e., 80.

Relational Algebra

Relational algebra is a procedural query language, which takes instances of relations as input and yields instances of relations as output. It uses operators to perform queries. An operator can be either unary or binary. They accept relations as their input and yield relations as their output. Relational algebra is performed recursively on a relation and intermediate results are also considered relations.

The fundamental operations of relational algebra are as follows:

• Select
• Project
• Union
• Set different
• Cartesian product
• Rename