GROUP BY combined with ORDER BY

The bold text from your quote is incorrect (it's probably an oversimplification that is true in many common use cases, but it is not strictly true as a requirement). For instance, this statement executes just fine, although AVG(val) is not in the select list:

WITH DATA AS (SELECT mod(LEVEL,3) grp, LEVEL val FROM dual CONNECT BY LEVEL < 100)SELECT grp,MIN(val),MAX(val)FROM DATAGROUP BY grpORDER BY AVG(val)

The expressions in the ORDER BY clause simply have to be possible to evaluate in the context of the GROUP BY. For instance, ORDER BY val would not work in the above example, because the expression val does not have a distinct value for each row produced by the grouping.

As to your second question, you may care about the ordering but not about the value of the ordering expression. Excluding unneeded expressions from the select lists reduces the amount of data that must actually be sent from the server to the client.

Actually the statement is not entirely true as Dave Costa's example shows.

The Oracle documentation says that an expression can be used but the expression must be based on the columns in the selection list.

expr - expr orders rows based on their value for expr. The expression is based on columns in the select list or columns in the tables, views, or materialized views in the FROM clause. Source: Oracle® Database SQL Language Reference 11g Release 2 (11.2) E26088-01 September 2011. Page 19-33

From the the same work page 19-13 and 19-33 (Page 1355 and 1365 in the PDF)

http://docs.oracle.com/cd/E11882_01/server.112/e26088/statements_10002.htm#SQLRF01702

http://docs.oracle.com/cd/E11882_01/server.112/e26088/statements_10002.htm#i2171079

First:

The implementation of group by is one which creates a new resultset that differs in structure to the original from clause (table view or some joined tables). That resultset is defined by what is selected.

Not every SQL RDBMS has this restriction, though it is a always requirement that what is ordered by be either an aggregate function of the non-grouped columns (AVG, SUM, etc) or one of the columns grouped by, or functions upon more than one of those results (like adding two columns), because this is a logical requirement of the result of the grouping operation.

Second:

Because you only care about that column for the ordering. For example, you might have a list of the top selling singles without giving their sales (the NYT Bestsellers keeps some details of their data a secret, but do have a ranked list). Of course, you can get around this by just selecting that column and then not using it.