stats

Statistics is the science concerned with collecting, analyzing, interpreting, presenting, and organizing data. It provides methods for describing data, quantifying uncertainty, and supporting evidence-based decision making. The term originates from the study of state data and governance, with roots in European statistics and probability theory.

Statistics has two broad aims: descriptive statistics, which summarizes data using measures such as mean, median, mode, variance, and graphical displays; and inferential statistics, which uses samples to draw conclusions about populations, incorporating likelihood and uncertainty through probability theory.

Key concepts include populations and samples, sampling methods, experimental design, bias, variability, correlation and causation, and the distinction between parameter and statistic. Statistical practice relies on models and assumptions, and uses estimation and hypothesis testing, confidence intervals, regression and analysis of variance, time-series analysis, and nonparametric methods to analyze data.

Data collection, quality, and ethics are central. Data are subject to measurement error, missing values, and biases, requiring cleaning, validation, and transparent reporting to support reproducibility. Statistical results are expressed with measures of uncertainty, such as p-values, confidence intervals, and effect sizes.

Applications span science, medicine, engineering, economics, public policy, sports, and business. Statistical thinking underpins data science, analytics, and machine learning, providing foundations for model selection, validation, and interpretation. Popular tools include programming languages and software such as R, Python libraries, SAS, SPSS, and Excel.