Law

Ratios do not average

This is arithmetic, not a modeling convention: store the numerator and the denominator, never the ratio.

\frac{1}{n} i \sum \frac{a _{i}}{b _{i}} \neq = \frac{\sum _{i} a _{i}}{\sum _{i} b _{i}}

Worked examples, recomputed

Every number the mechanisms quote for this relationship is recomputed from it, so none of them disagrees with it.

Each mechanism states it in its own names. The general symbol each name stands for is shown with it.

Data Modeling
What does one row mean, who is allowed to change that answer, and what breaks downstream when they do?
$avg (a / b) \neq = Σ a /Σ b$
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Specialized Processing Models
What do you build when a query predicate cannot be reduced to a range over an ordered key?
$\frac{100 + 10}{2} = 55 \neq = \frac{100 + 99 \times 10}{100} = 10.9$
Read it in place →