Statistics Made Clear: High School Statistics & Probability

Take a closer look at quantitative data by learning the difference between discrete and continuous variables. You’ll use real-world examples to determine whether values are counted or measured.

Learn four essential concepts used throughout statistics. You’ll distinguish between a population and a sample and learn how parameters and statistics are used to describe them.

Discover the two major ways statistics is used. You’ll learn how descriptive statistics summarizes collected data and how inferential statistics uses sample information to make conclusions about a larger population

Review data types, variables, discrete and continuous data, populations and samples, parameters and statistics, and descriptive versus inferential statistics. Then complete the Lesson 1 Mastery Quiz.

Learn the difference between a population and a sample and discover why statisticians often use samples to learn about larger populations. You’ll explore what makes a sample useful for concluding.

Put your sampling knowledge into practice by investigating real-world sampling situations. You’ll identify problems with sampling designs, evaluate potential sources of bias, and use your statistical reasoning to become a Statistics Detective

Review the major concepts from Lesson 2, including censuses, samples, representative sampling, sampling methods, bias, and sample quality, then complete the Lesson 2 Mastery Quiz to check your understanding.

Learn how raw data can be organized into a form that is easier to understand and analyze. Explore frequency tables and learn how they show how often different values or categories occur in a data set.

Explore bar charts and dot plots as tools for visualizing data. Learn how to construct, read, and interpret these displays and identify important patterns in the data.

Learn how histograms display the distribution of quantitative data and reveal patterns within a data set. You’ll also investigate misleading graphs and see how scales, intervals, and other design choices can influence how data is interpreted.

Learn how to select an appropriate graphical display for different types of data. Practice analyzing visualizations, identifying meaningful patterns, and using evidence from graphs to communicate conclusions.

Explore the three main measures of center: mean, median, and mode. Learn what each measure represents and how each can be used to describe a typical value within a data set.

Practice calculating the mean, median, and mode and learn how to determine which measure provides the most meaningful representation of a data set.

Investigate how outliers and extreme values affect measures of center. Compare their effects on the mean and median and learn why the median is considered a resistant measure.

Apply your knowledge to determine whether the mean, median, or mode is the most appropriate measure of center for different data sets. Practice justifying your choice and interpreting the result in context.

Review the mean, median, mode, outliers, resistant measures, and selecting the appropriate measure of center. Complete the mastery quiz and practice activities to check your understanding before moving on to measures of spread

Learn how to calculate and interpret the range of a data set and understand what the difference between the maximum and minimum values tells us about variability

Explore the interquartile range (IQR) and learn how it describes the spread of the middle 50% of the data. You’ll also use IQR to identify potential outliers.

Learn how variance measures the spread of data around the mean. You’ll work through the calculation process and understand why squared deviations are used to measure variability.

Discover how standard deviation describes the typical distance of values from the mean. You’ll calculate and interpret standard deviation and use it to compare variability between data sets.

Review range, IQR, outliers, variance, and standard deviation, then complete the Lesson 5 Mastery Quiz before moving on to distributions.

Learn what a distribution reveals about a data set and how to use SOCS—Shape, Outliers, Center, and Spread as a systematic framework for describing distributions.

Explore different distribution shapes and learn how to recognize symmetric, left-skewed, and right-skewed distributions. You’ll examine what the shape of a distribution can reveal about the data

Learn to recognize important features within distributions, including modality, gaps, clusters, and unusual observations. You’ll see how these features can reveal patterns that summary statistics alone may miss.

Use the center and spread, along with the distribution shape, to compare data sets. You’ll practice identifying meaningful similarities and differences and supporting your comparisons with statistical evidence.

Bring the concepts together to tell the complete story of a distribution. You’ll combine shape, unusual features, center, and spread to interpret data and communicate meaningful conclusions.

Review the major concepts from Section 6, including SOCS, symmetry, skewness, modality, gaps, clusters, center, spread, and comparing distributions, then complete the Mastery Quiz to check your understanding.

Learn what a z-score represents and how to calculate it using the mean and standard deviation. You’ll interpret positive, negative, and zero z-scores to determine where a value lies relative to the mean.

Explore the characteristics of the normal distribution and learn how the 68–95–99.7 Empirical Rule describes the percentage of data that falls within one, two, and three standard deviations of the mean.

Review z-score calculations, the normal distribution, the Empirical Rule, and how to compare performance using standardized scores, then complete the mastery quiz to check your understanding before moving on to probability.

Learn the foundations of probability, including outcomes, events, and sample spaces. You’ll identify possible outcomes and calculate the probability of simple events.

Discover how experimental probability is determined from actual trials and observations. Compare experimental results with theoretical probability and explore the Law of Large Numbers to understand why results tend to stabilize as the number of trials increases.

Review sample spaces, theoretical probability, complements, experimental probability, the Law of Large Numbers, simulations, and fair games, then complete the mastery quiz to check your understanding before moving on to compound probability.

Learn how to identify independent events and calculate the probability that multiple independent events occur together. You’ll apply the AND rule and interpret your answers in context.

Explore dependent events and learn how one event's outcome can affect the probability of another. You’ll develop an understanding of conditional probability and apply it to probability problems.

Learn how to calculate the probability that one event OR another event occurs. You’ll apply the Addition Rule and determine when probabilities can and cannot simply be added.

Use two-way tables to organize information and calculate joint, marginal, and conditional probabilities. You’ll use information from tables to analyze relationships between events.

Learn an efficient strategy for solving “at least one” probability problems using complements. You’ll also bring together different probability rules and determine which strategy is appropriate for a given problem.

Review independent and dependent events, AND and OR rules, conditional probability, two-way tables, and “at least one” strategies, then complete the mastery quiz to demonstrate your understanding of compound probability.