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Intuitively, for each sailor we check that there is no boat that has not been reserved by this sailor

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In addition to simply retrieving data, we often want to perform some computation or summarization As we noted earlier in this chapter, SQL allows the use of arithmetic expressions We now consider a powerful class of constructs for computing aggregate values such as MIN and SUM These features represent a signi cant extension of relational algebra SQL supports ve aggregate operations, which can be applied on any column, say A, of a relation: 1 COUNT ([DISTINCT] A): The number of (unique) values in the A column 2 SUM ([DISTINCT] A): The sum of all (unique) values in the A column 3 AVG ([DISTINCT] A): The average of all (unique) values in the A column 4 MAX (A): The maximum value in the A column 5 MIN (A): The minimum value in the A column Note that it does not make sense to specify DISTINCT in conjunction with MIN or MAX (although SQL-92 does not preclude this) (Q25) Find the average age of all sailors SELECT AVG (Sage) FROM Sailors S On instance S3, the average age is 374 Of course, the WHERE clause can be used to restrict the sailors who are considered in computing the average age: (Q26) Find the average age of sailors with a rating of 10 SELECT AVG (Sage) FROM Sailors S WHERE Srating = 10 There are two such sailors, and their average age is 255 MIN (or MAX) can be used instead of AVG in the above queries to nd the age of the youngest (oldest) sailor

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However, nding both the name and the age of the oldest sailor is more tricky, as the next query illustrates (Q27) Find the name and age of the oldest sailor Consider the following attempt to answer this query: SELECT Ssname, MAX (Sage) FROM Sailors S The intent is for this query to return not only the maximum age but also the name of the sailors having that age However, this query is illegal in SQL if the SELECT clause uses an aggregate operation, then it must use only aggregate operations unless the query contains a GROUP BY clause! (The intuition behind this restriction should become clear when we discuss the GROUP BY clause in Section 551) Thus, we cannot use MAX (Sage) as well as Ssname in the SELECT clause We have to use a nested query to compute the desired answer to Q27: SELECT Ssname, Sage FROM Sailors S WHERE Sage = ( SELECT MAX (S2age) FROM Sailors S2 ) Observe that we have used the result of an aggregate operation in the subquery as an argument to a comparison operation Strictly speaking, we are comparing an age value with the result of the subquery, which is a relation However, because of the use of the aggregate operation, the subquery is guaranteed to return a single tuple with a single eld, and SQL converts such a relation to a eld value for the sake of the comparison The following equivalent query for Q27 is legal in the SQL-92 standard but is not supported in many systems: SELECT Ssname, Sage FROM Sailors S WHERE ( SELECT MAX (S2age) FROM Sailors S2 ) = Sage We can count the number of sailors using COUNT This example illustrates the use of * as an argument to COUNT, which is useful when we want to count all rows (Q28) Count the number of sailors SELECT COUNT (*) FROM Sailors S We can think of * as shorthand for all the columns (in the cross-product of the fromlist in the FROM clause) Contrast this query with the following query, which computes the number of distinct sailor names (Remember that sname is not a key!)

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