Curriculum Map

Statistics

Learn to collect, analyze, and interpret data. Probability, distributions, confidence intervals, hypothesis testing, regression, and experimental design — with Desmos statistical visualizations. TEKS §111.43 aligned.

14 Units

Early Units (Foundation)

Building Skills

Advanced Concepts

Capstone/Synthesis

Exploring Data: Seeing the Story Numbers Tell

Learn to classify data by type, organize it into frequency tables, and visualize patterns using bar charts, histograms, dotplots, and stemplots — the essential first step in any statistical investigation.

3-4 days

Descriptive Statistics: Measuring Center, Spread, and Position

Master the numerical tools that summarize data — mean, median, standard deviation, IQR, z-scores, and boxplots — and learn when each measure is appropriate and what it reveals about a distribution.

4-5 days

Data Collection and Study Design: Where Good Data Comes From

Understand the critical difference between observational studies and experiments, master sampling methods that produce trustworthy data, and learn to identify the biases that can invalidate even the most sophisticated analysis.

3-4 days

Probability Foundations: The Mathematics of Uncertainty

Build the mathematical framework for reasoning about chance — from sample spaces and basic probability rules through the addition rule, multiplication rule, conditional probability, and independence.

4-5 days

Discrete Random Variables: Modeling Chance with Numbers

Learn to assign numerical values to random outcomes, compute expected values and variances of discrete random variables, and apply the binomial distribution to model real-world scenarios with fixed numbers of independent trials.

4-5 days

The Normal Distribution: The Bell Curve and Its Power

Explore the properties of the normal distribution, apply the empirical rule and z-scores to find probabilities, use the standard normal table for precise calculations, and understand why this single curve appears throughout statistics and nature.

4-5 days

Sampling Distributions and the Central Limit Theorem

Discover how sample statistics vary from sample to sample, why this variability is predictable, and how the Central Limit Theorem guarantees that sample means and proportions follow approximately normal distributions — the foundation of all statistical inference.

4-5 days

Confidence Intervals

Learn to construct and interpret confidence intervals for means and proportions, understanding how sample size and confidence level control the precision of our estimates about populations.

4-5 days

Hypothesis Testing

Master the logic of hypothesis testing — formulating null and alternative hypotheses, calculating p-values, making decisions about statistical significance, and understanding the errors that can occur when drawing conclusions from data.

5-6 days

Comparing Two Groups

Extend inference methods to compare two populations — testing whether two means or two proportions differ and constructing confidence intervals for the difference, the core of experimental and observational comparisons.

4-5 days

Regression Analysis

Explore the relationship between two quantitative variables using least squares regression, learning to fit lines to data, interpret slopes and intercepts, assess model quality through residuals and correlation, and recognize the limits of regression as a predictive tool.

5-6 days

Chi-Square Tests

Learn to analyze categorical data using chi-square tests — testing whether observed frequency distributions match expected ones, whether two categorical variables are independent, and whether different populations share the same distribution.

4-5 days

Experimental Design

Learn the principles that make experiments the gold standard for establishing causation — randomization, control, replication, and blinding — and explore the major experimental designs used in medicine, agriculture, psychology, and industry.

4-5 days

Statistics Capstone: Putting It All Together

Synthesize the entire course by conducting complete statistical investigations — from formulating questions and designing data collection to choosing appropriate analyses, drawing conclusions, and communicating results with clarity and intellectual honesty.

5-6 days

Learning Progression

This course is designed to be taken sequentially. Earlier units establish foundational concepts that later units build upon. While you can explore units in any order, following the numbered sequence provides the most coherent learning experience.