Foundation in Business Analytics Notes

Establishes the foundational concepts of business analytics and statistical data summarization. Topics include defining business analytics; descriptive, predictive, and prescriptive analytics paradigms; data types (qualitative vs quantitative, cross-sectional vs time-series, structured vs unstructured data); data collection and frequency distributions; measures of central tendency: arithmetic mean, weighted average, median, mode, geometric mean, and harmonic mean (properties, mathematical calculations, managerial suitability); and measures of dispersion: absolute and relative measures, range, quartile deviation, variance, standard deviation, and coefficient of variation (CV) for comparing enterprise risk and performance consistency.

Covers the mathematical principles of probability and uncertainty modeling in business decision-making. Topics include fundamental probability concepts (random experiments, sample space, events, mutually exclusive, exhaustive, and independent events); approaches to probability (classical, empirical, subjective); basic probability theorems: addition theorem for mutually exclusive and non-mutually exclusive events, multiplication theorem for independent and dependent events, conditional probability, and Bayes' Theorem for revising prior probabilities based on new commercial information; random variables: discrete and continuous random variables; and probability mass functions (pmf) and probability density functions (pdf).

Delivers comprehensive mathematical training in discrete and continuous theoretical probability models. Binomial Distribution covers assumptions, probability mass function, mean (np), variance (npq), properties, and commercial applications in quality control and success-failure trials; Poisson Distribution covers assumptions, probability mass function, parameter lambda (mean = variance), and applications in customer queue arrivals, defect rates, and rare operational events; and Normal Distribution covers characteristics of the Gaussian curve, standard normal distribution (Z transformation: Z = (X - mu) / sigma), properties of the bell curve (symmetry, empirical rule: 68-95-99.7%), and reading standard normal probability area tables to solve practical business risk and quality assessment problems.

Examines sampling methodologies, sample size determination, and statistical estimation principles. Topics include census inquiry versus sample inquiry; advantages and limitations of sampling; probability sampling designs: simple random sampling (lottery method, random numbers), stratified random sampling (proportionate vs disproportionate), systematic sampling, cluster sampling, and multi-stage sampling; non-probability sampling designs: convenience, quota, judgment, and snowball sampling; sampling errors versus non-sampling errors; the Central Limit Theorem and sampling distribution of the mean; and standard error concepts.

Provides rigorous predictive modeling techniques to evaluate bivariate numerical relationships. Correlation Analysis covers the concept and types of correlation (positive, negative, linear, non-linear); scatter plots; Karl Pearson's coefficient of correlation ('r' - mathematical calculation, properties, coefficient of determination r^2); Spearman's rank correlation coefficient (for tied and untied qualitative ranks). Regression Analysis covers distinction between correlation and regression; simple linear regression model; principle of least squares; derivation of regression equations (Y on X and X on Y); calculating regression coefficients (byx and bxy) and their mathematical properties; and using regression lines for corporate sales forecasting and economic trend projection.