Statistics Tutorials
Probability, hypothesis testing, regression, distributions — the math behind data science.
Introduction to Statistics
What statistics is, why it matters, the difference between descriptive and inferential statistics, and how data underpins every business decision.
Data Types & Measurement Scales
Nominal, ordinal, interval, and ratio scales — understand the four levels of measurement and how they determine which statistical methods are valid.
Data Collection & Sampling Methods
How data gets collected — surveys, experiments, observation — and the key sampling methods that determine whether your conclusions are valid.
Descriptive Statistics — Mean, Median & Mode
Summarise the centre of a distribution — arithmetic mean, weighted mean, median, mode, and when to use each measure of central tendency.
Measures of Spread — Variance, SD & IQR
Understand how scattered data is around its centre — range, variance, standard deviation, IQR, and the coefficient of variation.
Data Visualisation for Statistics
Choose the right chart for statistical data — histograms, box plots, scatter plots, QQ plots, and interpreting distribution shape.
Probability Fundamentals
The language of uncertainty — sample spaces, events, probability rules, addition rule, multiplication rule, and combinatorics basics.
Conditional Probability & Bayes' Theorem
How new information updates probability — conditional probability, independence, the law of total probability, and Bayes' theorem with real examples.
Probability Distributions — Binomial & Poisson
Model counting problems with discrete probability distributions — the Binomial distribution for success/failure trials and the Poisson distribution for rare events.
The Normal Distribution & Z-Scores
The bell curve in depth — properties, Z-scores, the empirical rule, and using the standard normal table to solve probability problems.
Sampling Distributions & the Central Limit Theorem
Why averages follow the normal distribution — the sampling distribution of the mean, the Central Limit Theorem, and the standard error.
Confidence Intervals
Build a range of plausible values for a population parameter — constructing, interpreting, and understanding confidence intervals for means and proportions.
Hypothesis Testing — Concepts & p-Values
The formal framework for making data-driven decisions — null and alternative hypotheses, Type I and II errors, p-values, and significance levels.
t-Tests — One-Sample, Two-Sample & Paired
Compare means with the t-test — one-sample t-test, independent two-sample t-test, paired t-test, and checking assumptions.
Chi-Square Tests
Test categorical data — goodness-of-fit to a distribution and independence between two categorical variables using the chi-square statistic.
ANOVA — Analysis of Variance
Compare means across three or more groups — one-way ANOVA, the F-statistic, ANOVA table, post-hoc tests, and effect size (η²).
Correlation — Pearson, Spearman & Causation
Quantify the linear relationship between two variables — Pearson r, Spearman ρ, interpreting r², and why correlation does not imply causation.
Linear Regression & Model Evaluation
Model relationships and make predictions — simple linear regression, OLS estimation, interpreting coefficients, R-squared, residuals, and model assumptions.