Mathematics of Data Management

Counting methods

Organized counting avoids missed outcomes and distinguishes when order matters.

_{n} P_{r} = \frac{n !}{( n - r )!}

Permutations

_{n} C_{r} = \frac{n !}{r ! ( n - r )!}

Combinations

A distribution assigns probabilities to possible values of a random variable.

P (A ∣ B) = \frac{P ( A \cap B )}{P ( B )}

Conditional probability

Centre, spread, and association summarize data without replacing context.

z = \frac{x - μ}{σ}

Z-score

A strong investigation moves from a focused question to transparent evidence and a qualified conclusion.

question \to data \to analysis \to claim

Investigation flow