This chapter provides a comprehensive analysis of statistical processing techniques for measurement data, encompassing key concepts such as measurement, sampling, variation series, and frequency polygons. It integrates methods from probability theory and mathematical statistics to process substantial volumes of measurement information. The chapter elaborates on the random nature of measurement results, random samples, and creation of frequency polygons, empirical distribution functions, and histograms. It discusses point estimates, bias, systematic errors, and various estimation methodologies, emphasizing their practical application across research and industry. Statistical tests and criteria, including Pearson’s and Kolmogorov–Smirnov criteria, for comparing samples and testing hypotheses are explored. Techniques for detecting gross errors using criteria like Romanovsky and Dixon, and regression analysis for calibration and validation of measurement channels are also presented. The chapter further delves into regression analysis, confidence intervals, expanded uncertainties, and the statistical properties of random angles using Mises and wrapped Gaussian distributions. This analysis facilitates a deeper understanding of measurement uncertainties, errors, and the statistical representation of angular measurements, thereby providing essential insights for precision in technical measurements and research applications.