📊 Applied statistics using real

What you’ll learn

1. A Statistic Is a CompressionEstablish the through-line: a statistic is a compression of reality, so the key question is always what it left out.A statistic squeezes many facts into a few, which is useful but always discards detail. Statistics is really the study of variation — describing it honestly and separating signal from noise — and most famous blunders come from forgetting what a number left out.
2. The Center Can Lie: Mean vs. MedianDistinguish mean from median and show how skew makes them diverge, so 'average' can mislead.The mean is dragged by extreme values; the median is not. On skewed data like income they diverge sharply, and the mean can name a value nobody has. Always ask which center is used and whether the data is lopsided.
3. A Center With No Spread Is Half a TruthExplain spread and standard deviation, and why a center must always come with a measure of spread.Two data sets can share a center yet differ entirely in spread — how tightly values cluster. Standard deviation is roughly the typical distance from the mean. A center without a spread is half a truth, because spread is the variation statistics exists to measure.
4. Always Look at the ShapeUse Anscombe's quartet to show identical summaries can hide different data, so raw data must be plotted.Anscombe's four eleven-point data sets share nearly identical means, spreads, correlation and best-fit line but look completely different when plotted — a line, a curve, an outlier, a false trend. The habit: plot and look before trusting any summary.
5. From a Sample to the Whole WorldExplain inference and representativeness via the 1936 Literary Digest vs Gallup case: bias beats size.Inference uses a sample to speak for a population, which works only if the sample is representative — best achieved by random sampling. The 1936 Literary Digest poll had 2.4 million responses but a biased sample and was badly wrong; Gallup's ~50,000 representative sample was right. Ask 'who, and how chosen?' before 'how many?'
6. Correlation Is Not CausationTeach that correlation is not causation, introduce confounders, and give the experiment as the fix.Two things can move together without one causing the other; a confounding variable (like summer heat behind ice cream and drownings) often explains it. Only a randomized controlled experiment, which scatters confounders across groups, can establish causation. 'Linked to' means correlation.
7. Significant Doesn't Mean ImportantClarify what a p-value and statistical significance do and don't mean, and separate significance from effect size.A p-value is the probability of data this extreme if there were no real effect; below 0.05 is called significant. It is not the probability the hypothesis is true, nor a measure of importance. A big sample can make trivial effects significant, so always ask about effect size.
8. When the Aggregate Lies: Simpson's ParadoxPresent Simpson's paradox via Berkeley 1973 and close with a practical checklist for reading statistics.In Berkeley's 1973 admissions an overall gap favoring men reversed within departments because women applied more to the most competitive ones — Simpson's paradox, driven by a lurking variable. A true aggregate can mislead; disaggregate to check. The course closes with a six-question checklist rooted in 'what did the number leave out?'.

Questions this course answers

Grounded in trusted sources

• Emory Math Center — 'Famous Statistical Blunders in History' (Literary Digest 1936: 10M mailed, 2.4M returned; predicted Landon 57–43; FDR won ~61–37; Gallup ~50,000 sample correct)
• Bickel, Hammel & O'Connell (1975), 'Sex Bias in Graduate Admissions: Data from Berkeley,' Science 187 (overall ≈44% men vs ≈35% women admitted; reversed within departments)
• Anscombe, F.J. (1973), 'Graphs in Statistical Analysis'; r-causal 'quartets' data — Anscombe's quartet summary statistics (mean x=9, mean y=7.5, correlation ≈0.82, line y=3+0.5x)
• Wikipedia — 'The Literary Digest' and 'Simpson's paradox' (case framing and details)

Every Wunder lesson is built from real, reputable sources — never invented.

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