Central Tendency

Mean = Sum / n | Median = middle value (sorted); even n → avg of n/2 and n/2+1 positions | Mode = most frequent

Use mean when all values are needed; median when outliers are present; mode for the most common value.

Dispersion

Range = Max − Min | Variance = Σ(xᵢ − Mean)² / n | Standard Deviation = √Variance

Range gives a quick spread estimate; SD/Variance are used when the question asks about consistency or variation.

Basic Probability

P(E) = Favourable outcomes / Total outcomes | 0 ≤ P(E) ≤ 1 | P(E') = 1 − P(E) | P(A∪B) = P(A) + P(B) − P(A∩B)

Apply P(E) = favourable/total for single-event problems; use P(E') = 1 − P(E) as the complement shortcut for complex events.

Combined & Conditional Probability

Independent: P(A and B) = P(A) × P(B) | Mutually exclusive: P(A or B) = P(A) + P(B) | Conditional: P(A|B) = P(A∩B) / P(B)

Multiplication rule for independent events (coin tosses, dice); addition rule for mutually exclusive outcomes; conditional when one event has already occurred.

Permutations & Combinations

nPr = n! / (n−r)! | nCr = n! / ((n−r)! × r!) | nCr = nC(n−r)

Use nPr when order matters (arrangements, rankings); use nCr when order doesn't matter (selections, committees).