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221 For each of the SQL aggregate functions sum, count, min and max, show how to compute the aggregate value on a multiset S1 S2 , given the aggregate values on multisets S1 and S2 Based on the above, give expressions to compute aggregate values with grouping on a subset S of the attributes of a relation r(A, B, C, D, E), given aggregate values for grouping on attributes T S, for the following aggregate functions: a sum, count, min and max b avg c standard deviation 222 Show how to express group by cube(a, b, c, d) using rollup; your answer should have only one group by clause 223 Give an example of a pair of groupings that cannot be expressed by using a single group by clause with cube and rollup 224 Given a relation S(student, subject, marks), write a query to nd the top n students by total marks, by using ranking 225 Given relation r(a, b, d, d), Show how to use the extended SQL features to generate a histogram of d versus a, dividing a into 20 equal-sized partitions (that is, where each partition contains 5 percent of the tuples in r, sorted by a)
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226 Write a query to nd cumulative balances, equivalent to that shown in Section 2225, but without using the extended SQL windowing constructs 227 Consider the balance attribute of the account relation Write an SQL query to compute a histogram of balance values, dividing the range 0 to the maximum account balance present, into three equal ranges 228 Consider the sales relation from Section 222 Write an SQL query to compute the cube operation on the relation, giving the relation in Figure 222 Do not use the with cube construct 229 Construct a decision tree classi er with binary splits at each node, using tuples in relation r(A, B, C) shown below as training data; attribute C denotes the class Show the nal tree, and with each node show the best split for each attribute along with its information gain value (1, 2, a), (2, 1, a), (2, 5, b), (3, 3, b), (3, 6, b), (4, 5, b), (5, 5, c), (6, 3, b), (6, 7, c) 2210 Suppose there are two classi cation rules, one that says that people with salaries between $10,000 and $20,000 have a credit rating of good, and another that says that people with salaries between $20,000 and $30,000 have a credit rating of good Under what conditions can the rules be replaced, without any loss of information, by a single rule that says people with salaries between $10,000 and $30,000 have a credit rating of good 2211 Suppose half of all the transactions in a clothes shop purchase jeans, and one third of all transactions in the shop purchase T-shirts Suppose also that half of the transactions that purchase jeans also purchase T-shirts Write down all the (nontrivial) association rules you can deduce from the above information, giving support and con dence of each rule 2212 Consider the problem of nding large itemsets a Describe how to nd the support for a given collection of itemsets by using a single scan of the data Assume that the itemsets and associated information, such as counts, will t in memory b Suppose an itemset has support less than j Show that no superset of this itemset can have support greater than or equal to j 2213 Describe bene ts and drawbacks of a source-driven architecture for gathering of data at a data-warehouse, as compared to a destination-driven architecture 2214 Consider the schema depicted in Figure 229 Give an SQL:1999 query to summarize sales numbers and price by store and date, along with the hierarchies on store and date 2215 Compute the relevance (using appropriate de nitions of term frequency and inverse document frequency) of each of the questions in this chapter to the query SQL relation
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