Why can't you mix Aggregate values and Non-Aggregate values in a single SELECT?

Question

I know that if you have one aggregate function in a SELECT statement, then all the other values in the statement must be either aggregate functions, or listed in a GROUP BY

Answer 1

Aggregates doesn't work on a complete result, they only work on a group in a result.

Consider a table containing:

Person   Pet
-------- --------
Amy      Cat
Amy      Dog
Amy      Canary
Dave     Dog
Susan    Snake
Susan    Spider

If you use a query that groups on Person, it will divide the data into these groups:

Amy:
  Amy    Cat
  Amy    Dog
  Amy    Canary
Dave:
  Dave   Dog
Susan:
  Susan  Snake
  Susan  Spider

If you use an aggreage, for exmple the count aggregate, it will produce one result for each group:

Amy:
  Amy    Cat
  Amy    Dog
  Amy    Canary    count(*) = 3
Dave:
  Dave   Dog       count(*) = 1
Susan:
  Susan  Snake
  Susan  Spider    count(*) = 2

So, the query select Person, count(*) from People group by Person gives you one record for each group:

Amy    3
Dave   1
Susan  2

If you try to get the Pet field in the result also, that doesn't work because there may be multiple values for that field in each group.

(Some databases, like MySQL, does allow that anyway, and just returns any random value from within the group, and it's your responsibility to know if the result is sensible or not.)

If you use an aggregate, but doesn't specify any grouping, the query will still be grouped, and the entire result is a single group. So the query select count(*) from Person will create a single group containing all records, and the aggregate can count the records in that group. The result contains one row from each group, and as there is only one group, there will be one row in the result.