Data Cube: Sales by Region, Month and Product Category

Dimensions: Region = 4, Month = 12, Product category = 5. Measure: total sales.

(i) Total number of possible multidimensional cells

Each combination of (region, month, category) is one cell:

Cells = 4 x 12 x 5 = 240

(ii) Cells required for one region across all months and products

Fix the region (1 value) and vary the other two dimensions:

Cells = 1 x 12 x 5 = 60

(iii) OLAP operations on this cube

Operation	What it does	Example on this cube	Result
Roll-up	Aggregate to a higher level of a dimension hierarchy (or remove a dimension)	Months to quarters (12 to 4); sales then shown per region, quarter and category	4 x 4 x 5 = 80 cells
Drill-down	Go from summary to more detailed data	Quarter to month, or month to day; Region to city	More cells than before (e.g. back to 240)
Slice	Select one value on one dimension, giving a sub-cube with one dimension fewer	Region = "North": a 2-D table of month x category	12 x 5 = 60 cells
Dice	Select ranges/values on two or more dimensions, giving a smaller cube	Regions {North, South}, months Jan to Mar, categories {Electronics, Clothing}	2 x 3 x 2 = 12 cells
Pivot (rotate)	Rotate axes to see the data from another view	Swap month and category axes	Same cells, new view

Extra: number of cuboids

With 3 dimensions and no hierarchies, the cube has 2^3 = 8 cuboids: the base cuboid (region, month, category), three 2-D cuboids, three 1-D cuboids and the apex (grand total).

Conclusion

The cube holds 240 base cells; one region slice needs 60 cells; roll-up, drill-down, slice and dice let a user move between summary and detail views.