Statistics: Probability, Inference, and Modeling

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## TL;DR
Statistics is the discipline of learning from data under uncertainty. It combines data description, probability, inference, modeling, and communication so that claims can be evaluated rather than guessed.

## Core Explanation
Descriptive statistics summarize samples with quantities such as means, medians, variability, and correlation. Probability models uncertainty. Statistical inference uses sample data to reason about broader populations, estimate effects, test hypotheses, and express uncertainty with intervals or posterior distributions.

## Detailed Analysis
Frequentist and Bayesian methods answer related questions with different interpretations of probability. In either framework, p-values, confidence intervals, priors, likelihoods, model assumptions, effect sizes, and study design all matter. A strong statistical conclusion depends on context, not a single threshold.

## Further Reading
- OpenStax Introductory Statistics 2e
- Britannica on Bayes's theorem
- ASA statement on p-values

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