Data Management (Grade 12)

31 of 31 topics written so far. Greyed-out topics are coming soon.

Unit 1: Probability

1. Probability and Sample SpacesDraft — Outcomes, sample spaces, and events; theoretical probability for equally likely outcomes; and probability distributions.
2. Experimental Probability and SimulationsDraft — Estimating probabilities from trials, the law of large numbers, and designing simulations.
3. Complements and Mutually Exclusive EventsDraft — The complement rule, mutually exclusive events, the additive principle for P(A or B), and Venn diagrams.
4. Independent and Dependent EventsDraft — When one event affects another, multiplying probabilities for "and", drawing with and without replacement, and tree diagrams.
5. Conditional ProbabilityDraft — The probability of B given A, from formulas, two-way tables, and tree diagrams — and why the order matters.

Unit 2: Counting

1. Counting PrinciplesDraft — The additive and multiplicative counting principles, when to use a list or tree diagram instead, and factorial notation.
2. PermutationsDraft — Counting arrangements where order matters, the formula P(n, r) = n!/(n − r)!, and how to handle restrictions like fixed positions, items kept together, and items kept apart.
3. CombinationsDraft — Counting selections where order doesn't matter, the formula for n choose r, deciding between permutations and combinations, and committees with conditions.
4. Pascal's TriangleDraft — How Pascal's triangle is built, the patterns hiding in it, and how it counts paths and combinations.
5. Probability with CountingDraft — Using permutations and combinations to find probabilities for committees, card hands, and arrangements — including "at least one" with the complement.

Unit 3: Discrete Probability Distributions

1. Discrete Random VariablesDraft — Random variables, probability distributions in tables, probability histograms, and the uniform distribution.
2. Expected ValueDraft — The long-run average of a random variable — computing E(X), fair games, raffles, and the link to the weighted mean.
3. Binomial DistributionDraft — Counting successes in independent trials — the binomial conditions and formula, tables and histograms, E(X) = np, and how the shape changes with n.
4. Hypergeometric DistributionDraft — Counting successes when sampling without replacement — the hypergeometric formula, tables and histograms, E(X) = na/N, and how it compares with the binomial.

Unit 4: Continuous Probability Distributions

1. Continuous Random VariablesDraft — Discrete vs continuous data, grouping measurements into intervals, histograms and frequency polygons, and probability as area.
2. Standard DeviationDraft — Measuring spread with the range, variance, and standard deviation — population vs sample formulas, by hand and with technology.
3. The Normal DistributionDraft — The bell-shaped normal model, its properties, the notation X ~ N(μ, σ²), and estimating probabilities with the 68–95–99.7 rule.
4. Z-Scores and the Standard Normal DistributionDraft — Standardizing values with z-scores, finding normal probabilities and percentiles with a table or technology, and working backwards with the inverse normal.
5. Normal Approximation to the BinomialDraft — Why binomial and hypergeometric distributions look normal for many trials, when to approximate, and how to use the continuity correction.

Unit 5: Organizing Data

1. Types of DataDraft — Why statistical studies collect data, why data varies, and how to classify variables and data sets.
2. Sampling MethodsDraft — Populations and samples, random and non-random sampling methods, and organizing data in a spreadsheet.
3. Bias in SamplingDraft — How sampling bias, non-response bias, response bias, and measurement bias distort results, and how to reduce them.
4. Survey and Experiment DesignDraft — Randomization, replication, and control in experiments; and writing fair, ethical surveys with clear questions.

Unit 6: One-Variable Data Analysis

1. Measures of Central TendencyDraft — Mean, median, and mode; weighted means; estimating the mean from grouped data; the effect of outliers; and choosing the best measure.
2. Quartiles and PercentilesDraft — Quartiles, the interquartile range, the five-number summary, the 1.5 × IQR rule for outliers, boxplots, and percentiles.
3. Displaying One-Variable DataDraft — Choosing the right graph for the data — bar and circle graphs, histograms, stem-and-leaf plots, and boxplots — and spotting graphs that mislead.
4. Margin of ErrorDraft — Interpreting poll results reported with a margin of error and confidence level, and how sample size, margin of error, and confidence level are related.

Unit 7: Two-Variable Data Analysis

1. Scatter Plots and CorrelationDraft — Independent and dependent variables, scatter plots, describing a relationship, the correlation coefficient r, and side-by-side boxplots.
2. Linear RegressionDraft — The line of best fit by least squares, interpreting slope and intercept, interpolation and extrapolation, residuals, and the effect of outliers.
3. Correlation and CausationDraft — Why correlation doesn't prove cause and effect, the types of relationships between two variables, and how two-variable statistics get misused.
4. Contingency TablesDraft — Two-way tables for two categorical variables — totals, relative frequencies, row and column percentages, and judging whether the variables are related.