In order to compute some graph plots in multidimensional space, we often need to judge if a measure is algebraic, distributive, or holistic, where
distributive: if the result derived by applying the function to n aggregate values is the same as that derived by applying the function on all the data without partitioning. E.g., count(), min(), max(), sum()
algebraic: if it can be computed by an algebraic function with M arguments (where M is a bounded integer), each of which is obtained by applying a distributive aggregate function. E.g., avg(), std()
holistic: if there is no constant bound on the storage size needed to describe a sub aggregate. E.g., median(), mode(), rank().
Judge which category each of the following measures (or set of measures) belongs to and explain your judgment briefly. (
1) Boxplot (2) Bottom-10 (among all the objects in the corresponding k-dimensional space) (3) linear regression line
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