Data, Statistics & Probability
Advanced statistics, distributions and combinatorics
Explanation
Statistical Inference
- Normal distribution: bell-shaped; 68% of data within 1 SD; 95% within 2 SD; 99.7% within 3 SD.
- Correlation vs causation: a strong correlation does not imply one thing causes the other.
- Bias in sampling: convenience sampling, self-selection bias can skew results.
Combinatorics
- Permutation (order matters): P(n,r) = n!/(n−r)!
- Combination (order doesn't matter): C(n,r) = n!/[r!(n−r)!]
- Binomial theorem: (a+b)ⁿ — the coefficients come from Pascal's triangle (= C(n,r)).
Probability
- Bayes' theorem: P(A|B) = P(B|A)·P(A) / P(B)
- Geometric probability: probability = (favourable area)/(total area)
- Expected value: E(X) = Σ[xᵢ · P(xᵢ)]
Practice Questions
Test your knowledge of Data, Statistics & Probability with a timed quiz.
Take Quiz →Topics in Quantitative Reasoning