Advanced Statistics
Normal distribution, hypothesis testing and regression
University-level statistics including normal distribution, standard deviation and hypothesis testing.
📖 Understanding Advanced Statistics
Standard deviation (σ) measures how spread out data is from the mean. A small σ means data is clustered closely; large σ means widely spread. Variance = σ².
The Normal Distribution is a symmetric bell-shaped curve. Mean, median and mode are equal. 68% of data lies within 1σ, 95% within 2σ, 99.7% within 3σ (Empirical Rule).
Z-score measures how many standard deviations a value is from the mean: Z = (X − μ)/σ. Use Z-tables to find probabilities.
Hypothesis Testing: Set up null hypothesis H₀ and alternative H₁. Calculate test statistic, find p-value. If p < significance level α, reject H₀.
🔑 Key Points to Remember
- ✓σ = √(Σ(x−μ)²/n) for population
- ✓Normal distribution: symmetric, μ=median=mode
- ✓Z = (X − μ) / σ
- ✓68-95-99.7 rule
- ✓p < 0.05 → reject null hypothesis (usually)
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