Statistics & Probability

Statistics tests your grasp of central tendency (mean, median, mode) and dispersion (range, variance, SD), while probability problems measure how well you count favorable outcomes. SSC CGL Tier 2 and banking mains routinely combine both areas in a single paper. Drill the complement shortcut P(at least one) = 1 \u2212 P(none) and the Sum = Mean \u00d7 n back-calculation to cover the highest-frequency patterns.

Key Idea

For statistics: Sum = Mean × n — use this to work backwards from a given average. For probability: P(at least one) = 1 − P(none) is almost always faster than direct counting.

Core Formulas

Central Tendency

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

Pick mean for aggregate calculations, median when data has outliers, and mode when the question asks for the most frequent value.

Dispersion

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

Compute range for a quick spread check; switch to SD or variance when the question asks about consistency or data spread.

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).

Relevant Exams

SSC CGLSSC CGL Tier 2IBPS POSBI POCDSUPSC CSAT

Statistics & Probability is high-yield in SSC CGL Tier 2 and banking exams — expect 3–5 questions per paper combining central tendency, probability of card/dice/ball problems, and nCr-based selection problems.