Grade 12 · printable course

Statistics and Data Science: An Introduction to Statistical Reasoning (Part 1)

Grade 12, Units 1-4 · 300 pages · 36 lessons · PDF, print at home

A full-year, non-calculus statistics course designed as the standard fourth-year alternative to Calculus. Students learn to summarize and visualize real data, design studies that can support causal claims, model relationships between variables, and use probability to quantify uncertainty in decisions. Every major technique is computed by hand on small data sets before being computed in a free spreadsheet on real, downloadable public data sets (U.S. Census/ACS, CDC BRFSS, FiveThirtyEight, World Bank, General Social Survey). The course treats "what does this result NOT license you to claim" as a first-class learning objective, not an afterthought, and ends with students designing, executing, analyzing, and reporting an original study. This volume holds units 1 to 4: Describing Data: One Variable at a Time; Relationships Between Two Variables; Study Design: What a Result Does and Does Not License You to Claim; Probability as a Model for Uncertainty.

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What is inside

Every unit and lesson in this book, in order. The same lessons are taught online at lettersanddevotion.com, so a family can move between paper and screen.

Statistics and Data Science: An Introduction to Statistical Reasoning

36 lessons · try a lesson online free

Unit 1: Describing Data: One Variable at a Time9 lessons
  1. 1.Mean, median, and mode of a small numeric dataset
  2. 2.Range, interquartile range, and standard deviation of a small numeric dataset
  3. 3.The relationship between distribution skew and the divergence of mean from median
  4. 4.Outlier identification and the decision to report versus remove an outlier
  5. 5.Z-scores as standardized measures of position within a distribution
  6. 6.The limits of any single pair of summary statistics to fully characterize a distribution
  7. 7.Description and statistical summary of an unfamiliar real-world univariate dataset
  8. 8.The shape category of a graphically displayed distribution
  9. 9.The boxplot as a graphical representation of the five-number summary
Unit 2: Relationships Between Two Variables9 lessons
  1. 10.Association between two quantitative variables shown in a scatterplot (direction, form, strength)
  2. 11.The correlation coefficient r, computed via sum of standardized cross-products
  3. 12.The limits of r as a sole summary of a bivariate relationship (Anscombe-style contrast)
  4. 13.The least-squares regression line, its slope and y-intercept in context
  5. 14.Extrapolation risk in regression predictions relative to the observed x-range
  6. 15.Residual plots as a diagnostic for linearity
  7. 16.Coefficient of determination r-squared and its proportion-of-variability interpretation
  8. 17.Appropriateness of a linear model as a prior judgment made from raw scatterplot shape, independent of computed statistics
  9. 18.Regression/correlation analysis of a genuine real-world dataset, including its concealed limitations
Unit 3: Study Design: What a Result Does and Does Not License You to Claim9 lessons
  1. 19.Population/sample and parameter/statistic distinction
  2. 20.The four sampling-method labels as a directly taught classification routine
  3. 21.Sampling methods and their associated biases
  4. 22.Random assignment as the mechanism that rules out confounding and licenses causal claims
  5. 23.Confounding variables in observational studies
  6. 24.Wording effects as a source of response bias
  7. 25.Actual study design underlying a news article's causal claim
  8. 26.The licensed claim of a specific real study, synthesized across sampling method, design type, and confounding
  9. 27.The independence of sampling-method validity and assignment-method validity as two separate axes of a study's design
Unit 4: Probability as a Model for Uncertainty9 lessons
  1. 28.Sample space and events as subsets of outcomes
  2. 29.The addition rule for P(A or B), including the mutually-exclusive case and the general case
  3. 30.Independence of two events, tested via P(A|B) = P(A)
  4. 31.Expected value of a discrete random variable, E(X) = Σx·P(x)
  5. 32.Standard deviation of a discrete random variable
  6. 33.Simulation as an empirical estimate of a theoretical probability
  7. 34.The logical structure required to test independence, generalized beyond the two-variable two-way-table case
  8. 35.The distinction between a probability as a long-run claim versus a prediction about a single trial
  9. 36.The formal definition of independent events

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