Probability and Statistics for Business and Data Science

Explore levels of measurement from nominal to ratio and learn key notation for probability and statistics, including X bar, mu, sigma, and sigma summations, plus sample mean examples.

Explore the three core measures of central tendency—mean, median, and mode—and how they locate data. Understand mean calculations, median rules for odd/even sets, and how outliers can shift the mean.

Explore dispersion in data by examining range, variance, and standard deviation, distinguishing sample from population calculations and applying Bessel's correction to improve variance estimates.

Explore quartiles and the interquartile range, visualize data with a box plot, and learn to compute Q1, Q2 (the median), Q3, and detect outliers with 1.5 times the IQR.

Explore bivariate data by comparing two variables with scatter plots, and learn covariance and correlation, including positive and negative relationships and the distinction from causality.

Learn how the Pearson correlation coefficient normalizes covariance to a -1 to 1 scale, enabling comparison of linear relationships, with a business example and notes on causality.

Learn the basics of probability as a value between 0 and 1, and explore events, trials, independent outcomes, and the sample space through fair coins and six-sided dice.

Define combinations as unordered selections from a set, using the n choose r formula to count groups where order does not matter, and contrast without and with repetition.

Explore intersections, unions, and complements in probability with a ball-and-pattern example, and learn to compute A and B, A or B, and not A, laying groundwork for further probability concepts.

Examine independent and dependent events, using coin flips and drawing red marbles without replacement to illustrate how probabilities multiply and how conditioning changes outcomes.

Learn how conditional probability links events A and B with P(A|B)=P(A∩B)/P(B), using dependent draws and examples like on-time vs under-budget projects to set up Bayes theorem and rules.

Formalize the addition and multiplication rules and illustrate them with unions, mutually exclusive events, and Bayes theorem, plus examples like projects on time or under budget and drawing four aces.

Explore the concept of distributions, distinguishing discrete probability mass functions from continuous distributions, and examine key families like uniform, binomial, Poisson, and normal distributions.

Explore the discrete uniform distribution with a fair six‑sided die, where six outcomes are equally probable and each occurs with probability 1/6.

Explore the binomial distribution by modeling Bernoulli trials with two outcomes and a constant probability of success across independent trials, using coin flips and dice as examples.

Learn the Poisson distribution, counting occurrences per a continuous unit such as time or distance using lambda. See its PMF and examples like cars per hour and hydrants per kilometer.

Explore continuous normal distributions and their bell-curve shapes used in business data. Learn how area under the curve and standard normal concepts—mean, standard deviation, and z-table—enable inferences.

Learn to standardize a normal distribution with z scores, map any value to the standard normal, and compute percentiles using z tables with real world examples.

Explore what statistics is and how it uses population and sample concepts to infer parameters from data, and distinguish variables, discrete versus continuous data, and the parameter and statistic relationship.

Learn how to sample data and avoid biases in surveys, including random, stratified random, and clustering methods. Examine selection bias, under coverage, self-selection, healthy-user, and survivorship biases with practical examples.

Learn how the central limit theorem makes sample means normally distributed around the population mean, with 95% within two standard deviations, even when the population is not normal.

Explore how the standard error relates the sample mean to the population mean, compute it as sigma divided by the square root of n, and construct 95% confidence intervals.

Compare mean load times using hypothesis testing in a real-world case, applying left-tail z-test and p-value methods at alpha 0.01 for a 99% confidence level.

Perform a test of proportion on a 400-sample survey showing 58% teenagers, testing p ≤ 0.5 against p > 0.5, and note how sample size influences the conclusion.

Understand type one and type two errors in hypothesis testing, including rejecting a null hypothesis (false positive) and failing to reject a false null hypothesis, illustrated by medical screening examples.

Explore the student's t distribution and t tests for unknown population standard deviation, compare with z tests, and cover degrees of freedom, significance level, and one-sample, two-sample, and paired tests.

Explore analysis of variance (anova) and the f distribution to assess whether multiple samples share the same variance, extending from one or two samples to three or more.

Investigate whether three discount plans (2 percent, 1 percent, and no discount) speed up invoice payments using ANOVA, the F distribution, and F critical values.

Explore two-way anova, or two-factor anova, which tests two independent variables—such as discount and amount due—simultaneously, while accounting for blocks and separating between-group and within-group variance.

Use a two-way ANOVA without replication to test how discounts (2%, 1%, or none) and invoice amounts affect days until payment; results show a statistically significant effect of discounts.

Explore two-way anova with replication, analyzing interactions between fertilizer types and temperature blocks using plant height data, sample means, and an f test in Excel.

Explore the fundamentals of linear regression, derive the line of best fit using two variables, minimize sum of squared errors, and interpret residuals, visualization, and pitfalls like Anscombe's quartet.

Apply linear regression to relate hours of operation to weekly production, deriving y = -46 + 4.5x, and predict required hours using the model; practice with Excel or Python.

Learn how multiple regression extends linear regression with several predictors, interpret coefficients, assess multicollinearity, and implement models in Excel and Python (scikit-learn) using real-world examples.

Explore chi-square tests and goodness-of-fit by comparing observed and expected frequencies using the (o-e)^2/e formula. Use degrees of freedom and p-values to test hypotheses with examples like coin flips.