Statistics

Counting principles, probability, regression

Counting Principles, Probability and Regression

Grade 12 statistics combines counting principles (permutations and combinations), advanced probability (dependent/independent events, tree diagrams, contingency tables) and regression analysis (interpreting r and ŷ = a + bx).

Example

Permutations and Factorial

How many ways can 5 people sit in a row? 5! = 5 × 4 × 3 × 2 × 1 = 120 How many 3-letter codes from A, B, C, D, E (no repetition)? 5P3 = 5!/(5−3)! = 120/2 = 60

Example

Regression and Correlation

Given data: x (hours studied) and y (mark %). Regression equation: ŷ = 12.5 + 8.2x, r = 0.92 Interpretation: • Strong positive correlation (r = 0.92 close to 1) • For each extra hour studied, mark increases by ≈ 8.2% • Predicted mark for 6 hours: ŷ = 12.5 + 8.2(6) = 61.7%

Note

Remember

Permutations: order matters (nPr). Combinations: order doesn't matter (nCr). |r| > 0.8 = strong correlation. Regression predictions are most reliable within the given data range (interpolation), not outside it (extrapolation).

Key Vocabulary

PermutationAn arrangement where order matters

CombinationA selection where order does not matter

Factorialn! = n × (n−1) × ... × 2 × 1

RegressionThe statistical relationship between two variables expressed as an equation

InterpolationPredicting within the range of given data

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