Introduction to Statistics

Explore how statistics quantify uncertainty and reveal whether numbers reflect reality or bias. Learn to read basic charts, understand data sets, and question numbers to make informed decisions.

Organize data from observations and measurements into charts and visuals to extract useful facts, assess data quality and collection methods, and tell data-driven stories in statistics.

Learn how means and medians describe the center of a dataset, using exam scores to show how the mean and median reveal different stories and handle even data points.

Explore how the range measures variability beyond mean and median, illustrated with small and large datasets. Learn to interpret range, its pitfalls, and how histograms reveal data makeup.

Explore the standard deviation as a measure of spread, compute it from the mean, compare datasets, and identify outliers within a distribution.

Learn to use mean and standard deviation to compute z-scores and identify outliers, then apply the empirical (three sigma) rule for a normal distribution to interpret data spread.

Explore probability by defining the sample space and outcomes, and calculate odds from coin flips, dice rolls, and real-world scenarios like rain and life expectancy.

Explore classical, empirical, and subjective probability by comparing fair coin and die outcomes with real-world data and opinion-based forecasts, and learn when each type is appropriate.

Learn how to compute the probability of two events using addition and subtraction for overlaps, then apply conditional probability and independence concepts with coins, dice, and data.

Explore how Bayes' theorem uses prior and conditional probabilities to interpret true and false positives in disease testing, illustrated with probability trees and millionaire wealth data.

Explore permutations and combinations to compute probability using factorials. See how top-three rankings and team selections illustrate the difference between permutations and combinations.

Compare discrete and continuous random variables by examining outcomes like drinks ordered, rainfall, and wait times, and understand why this distinction matters for calculating probabilities and distributions.

Explore discrete probability distributions with real-world data, compute mean weighted and standard deviation, and interpret relative frequencies from drink orders; apply expected monetary value and binomial normal approximations.

Explain how probability densities represent continuous outcomes, using area under the curve to show probability between points, and introduce the bell shaped curve with calculus for area.

Explore how the bell-shaped normal curve centers at the mean, is symmetrical, and assigns 100 percent of outcomes under the curve, illustrating standard deviations and distribution shapes.

Compute probabilities using z scores and the standard normal distribution by consulting z-table, with means and standard deviations. For example, find the probability weights lie between 140 and 170 pounds.