✏️ Exercises¶

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30 practice sets, one per notes file, each with 6–9 questions and a complete worked solution. Every set mixes:

By-hand computation — the formula written out, so you can follow it in an exam
Excel — worksheet functions and the Analysis ToolPak dialog
R — the function you would actually use, plus the assumption checks
Python — scipy.stats, pandas, and statsmodels
Interpretation — what the number means, and what it does not mean

Tip

Attempt each question before reading the solution. The solutions are deliberately detailed — they show the arithmetic, the decision, the effect size, and the common traps — so they are worth reading even after you get the answer.

01 — Foundations of Data¶

File	Focus
01-01-…-exe.md	Population/sample, parameter/statistic, variable types, the four levels of measurement, declaring levels in software
01-02-…-exe.md	Fixing a messy sheet, wide vs. long, quality checks, cleaning categories, banding, dummy coding, reshaping

02 — Frequency Distributions¶

File	Focus
02-01-…-exe.md	Categorical tables, Sturges' rule, class limits/boundaries/midpoints, grouped distributions, overlapping and empty classes
02-02-…-exe.md	Choosing the graph, bar vs. histogram, stem-and-leaf, reading a boxplot, polygons and ogives, misleading axes

03 — Central Tendency¶

File	Focus
03-01-…-exe.md	The four measures, resistance to outliers, choosing a centre, Pearson skewness, bimodality, trimmed means, the averaging trap
03-02-…-exe.md	GPA, combining group means, mean/SD/median/mode from a frequency table, geometric and harmonic means

04 — Variation & Position¶

File	Focus
04-01-…-exe.md	Both variance formulas, population vs. sample, CV, the empirical rule, Chebyshev, grouped SD, choosing a spread measure
04-02-…-exe.md	Comparing across scales with z, percentiles by hand, five-number summary, IQR vs. z outlier rules, masking, standardizing

05 — Probability¶

File	Focus
05-01-…-exe.md	Sample spaces, classical and empirical probability, the complement shortcut, odds, the birthday problem, simulation, the gambler's fallacy
05-02-…-exe.md	Addition and multiplication rules, with/without replacement, contingency tables, tree diagrams, independence vs. mutual exclusivity
05-03-…-exe.md	Medical screening, base rates, multi-source Bayes, counting principle, permutations vs. combinations, lottery odds, Bayesian updating

06 — Discrete Distributions¶

File	Focus
06-01-…-exe.md	Validity checks, `μ`/`σ²`/`σ` of a distribution, carnival games, insurance pricing, rules for `E` and `Var`, simulation
06-02-…-exe.md	Binomial conditions, full tables, Poisson and interval rescaling, geometric and hypergeometric, airline overbooking

07 — Continuous & Normal¶

File	Focus
07-01-…-exe.md	Why `P(X = x) = 0`, uniform probabilities, exponential waits, the Poisson–exponential link, memorylessness, density vs. probability
07-02-…-exe.md	Standard normal areas, inverse normal, both directions, solving for a parameter, normal approximation with continuity correction, normality checks

08 — Sampling Theory¶

File	Focus
08-01-…-exe.md	Identifying designs, stratified vs. cluster, error vs. bias, diagnosing specific biases, experimental design, drawing samples in code
08-02-…-exe.md	Standard error, one value vs. a mean, when the CLT applies, proportions, solving for `n`, simulating the CLT

09 — Confidence Intervals¶

File	Focus
09-01-…-exe.md	z- and t-intervals, choosing between them, correct interpretation, sample size, what changes the width, CI for a variance
09-02-…-exe.md	Proportion intervals, three confidence levels, sample size, why polls use ~1,000, small-sample failures, two proportions, coverage simulation

10 — Hypothesis Testing¶

File	Focus
10-01-…-exe.md	Writing hypotheses, spotting bad ones, Type I/II errors in context, power, p-values from statistics, what a p-value is not, the five steps
10-02-…-exe.md	One-, two-tailed z-tests for a mean and a proportion, the `p₀` vs. `p̂` trap, two proportions, choosing the tail honestly

11 — t-Tests¶

File	Focus
11-01-…-exe.md	Critical values, tests from summary stats and raw data, t vs. z, reading output, assumption checks, what to do when they fail
11-02-…-exe.md	Independent vs. paired, pooled vs. Welch, raw-data tests, the F-test for variances, reading ToolPak output, power and sample size
11-03-…-exe.md	Full paired test, the cost of ignoring pairing, subtraction direction, checking the differences, choosing a paired design, McNemar's test

12 — Chi-Square & ANOVA¶

File	Focus
12-01-…-exe.md	Uniform and specified distributions, reading cell contributions, small expected counts, fitting a Poisson, test for a variance, counts vs. percentages
12-02-…-exe.md	Expected counts, full tests, homogeneity, small 2×2 tables and Fisher's exact test, building tables from raw data, effect size vs. sample size
12-03-…-exe.md	Why not repeated t-tests, the ANOVA table by hand, Tukey HSD, reading ToolPak output, assumptions, unequal `n`, `F = t²`

13 — Correlation & Regression¶

File	Focus
13-01-…-exe.md	`r` by hand, testing `ρ = 0`, interpreting `r` and `r²`, Anscombe's quartet, outlier sensitivity, Pearson vs. Spearman, causation, correlation matrices
13-02-…-exe.md	Fitting by hand, prediction and residuals, `SST`/`SSR`/`SSE`, reading `LINEST`, residual plots, CI vs. PI, log transformation
13-03-…-exe.md	Testing the slope, three equivalent tests, reading full output, multiple regression, adjusted `R²`, multicollinearity, dummies and interactions

Study Sequence¶

For each topic:

  1.  Read the NOTES file            01-notes/NN-MM-topic.md
  2.  Attempt every exercise         02-exercises/NN-MM-topic-exe.md
  3.  Check the worked solution      — read it even when you were right
  4.  Reproduce the answer in EXCEL  — this is where most exams live
  5.  Reproduce it in R              — one line, with the assumption checks
  6.  Take the chapter QUIZ          03-quiz/
  7.  After each chapter block, build the matching PROJECT   04-projects/

Tool Cheat Sheet Across All Sets¶

Task	Excel	R	Python
Descriptive stats	Data Analysis ▸ Descriptive Statistics	`summary()`, `psych::describe()`	`df.describe()`
Frequency table	`FREQUENCY` / PivotTable	`table(cut(x, breaks))`	`pd.cut().value_counts()`
Normal probability	`NORM.DIST` / `NORM.INV`	`pnorm` / `qnorm`	`norm.cdf` / `norm.ppf`
Binomial / Poisson	`BINOM.DIST` / `POISSON.DIST`	`dbinom` / `dpois`	`binom.pmf` / `poisson.pmf`
Confidence interval	`CONFIDENCE.T`	`t.test(x)$conf.int`	`stats.t.interval`
One-sample t	`T.TEST(x, const, 2, 1)`	`t.test(x, mu =)`	`ttest_1samp`
Two-sample t	Data Analysis ▸ t-Test	`t.test(x, y)`	`ttest_ind`
Paired t	Data Analysis ▸ Paired	`t.test(x, y, paired = TRUE)`	`ttest_rel`
Chi-square	`CHISQ.TEST`	`chisq.test()`	`chi2_contingency`
ANOVA	Data Analysis ▸ Anova: Single Factor	`aov(y ~ g)`	`f_oneway` / `anova_lm`
Correlation	`CORREL`	`cor.test(x, y)`	`stats.pearsonr`
Regression	Data Analysis ▸ Regression	`lm(y ~ x)`	`sm.OLS(y, X).fit()`