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.

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.

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.

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 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.

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.

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.

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.

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.

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.