Data, Statistics & Probability
Advanced statistics, distributions, regression and probability models
Explanation
Regression & Correlation
- Correlation coefficient r: ranges −1 to 1; |r| close to 1 = strong relationship.
- Line of best fit: minimises the sum of squared residuals.
- r² (coefficient of determination): % of variation in y explained by x.
- Correlation ≠ causation.
Distributions
- Normal: symmetric, bell-shaped; mean = median = mode
- Skewed right: long tail to the right; mean > median
- Skewed left: long tail to the left; mean < median
- Binomial distribution: P(X=k) = C(n,k)·pᵏ·(1−p)ⁿ⁻ᵏ
Advanced Probability
- Bayes' theorem: P(A|B) = P(B|A)P(A)/P(B)
- Independence test: A and B are independent iff P(A∩B) = P(A)·P(B)
- Geometric probability: favourable region/total region
Practice Questions
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What does Data, Statistics & Probability cover in the ISEE Upper Level exam?
Advanced statistics, distributions, regression and probability models.
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