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In order to calculate the average and standard deviation from aggregate data, it is necessary to have available for each group: the total of values (Σx i = SUM(x)), the number of values (N=COUNT(x)) and the total of squares of the values (Σx i 2 =SUM(x 2)) of each groups.
Examples of sources for these US aggregate data include the United States Census Bureau, Statistical Abstract of the United States, and Social Explorer. International Monetary Fund data, World DataBank, and Penn World Table are examples of transactional and international aggregate data sources. [11]
The aggregate navigation essentially examines the query to see if it can be answered using a smaller, aggregate table. [5] Implementations of aggregate navigators can be found in a range of technologies: OLAP engines; Materialized views; Relational OLAP services; BI application servers or query tools
External tables (in Informix [3] or Oracle, [4] [5] for example) can also be thought of as views. In many systems for computational statistics, such as R and Python's pandas, a data frame or data table is a data type supporting the table abstraction. Conceptually, it is a list of records or observations all containing
Shuffling can also be implemented by a sorting algorithm, namely by a random sort: assigning a random number to each element of the list and then sorting based on the random numbers. This is generally not done in practice, however, and there is a well-known simple and efficient algorithm for shuffling: the Fisher–Yates shuffle .
The second meaning of "aggregation problem" is the theoretical difficulty in using and treating laws and theorems that include aggregate variables. A typical example is the aggregate production function. [2] Another famous problem is Sonnenschein-Mantel-Debreu theorem. Most of macroeconomic statements comprise this problem.
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
For example, a table of 128 rows with a Boolean column requires 128 bytes a row-oriented format (one byte per Boolean) but 128 bits (16 bytes) in a column-oriented format (via a bitmap). Another example is the use of run-length encoding to encode a column.