Regarding the computation of measures in a data cube:

a. Enumerate three categories of measures, based on the kind of aggregate functions used in computing a data cube.

b. For a data cube with the three dimensions time, location, and item, which category does the function variance belong to? Describe how to compute it if the cube is partitioned into many chunks.

Hint: The formula for computing variance is \(\frac{1}{N} \sum_{i=1}^{N}\left(x_{i}-\bar{x}_{i}ight)^{2}\), where \(\overline{x_{i}}\) is the average of \(x_{i} \mathrm{~s}\).

c. Suppose the function is "top 10 sales." Discuss how to efficiently compute this measure in a data cube.