Principle of Statistics & Probability - NU

1. Descriptive StatisticsData Classifications: Distinguishing between qualitative (categorical) and quantitative (numerical) variables, as well as discrete vs. continuous measurements.Data Presentation: Organizing raw data using frequency distributions, histograms, bar charts, and pie charts.Measures of Central Tendency: Calculating and comparing the mean, median, and mode for both ungrouped and grouped data.Measures of Dispersion: Evaluating variance, standard deviation, range, and the coefficient of variation to understand data spread.2. Introduction to Probability & CountingBasic Concepts: Defining sample spaces, random events, mutually exclusive events, and independent events.Counting Rules: Applying permutations, combinations, and the fundamental counting principle to compute sample sizes.Probability Rules: Using addition and multiplication rules to compute the likelihood of complex events.Conditional Probability: Setting up conditional equations and using Bayes' Theorem to update basic probabilities.3. Random Variables and Probability DistributionsDiscrete Distributions: Defining probability mass functions and working with standard models like the Binomial and Poisson distributions.Continuous Distributions: Introduction to probability density functions, with an intensive focus on the Normal (Gaussian) Distribution and reading Z-score tables.4. Elements of Statistical InferenceSampling Distributions: Introduction to how sample means behave, rooted in the Central Limit Theorem.Estimation: Constructing point estimations and basic Confidence Intervals (CIs) for population means and proportions.Hypothesis Testing: Formulating null (H₀) and alternative (H₁) hypotheses; running basic one-sample Z-tests and t-tests to make data-driven decisions