Intro Statistics — Study Wiki Overview

The raw material is one set of personal lecture and textbook notes, indexed at Lecture notes.md, covering four lectures. From that source, each topic was compiled into a Cornell note page — a format that separates the explanatory notes from active-recall cue questions and closes with a one-line Feynman summary. The idea is simple: you read the notes once to understand, then cover them and try to answer the cue questions from memory, forcing retrieval rather than passive re-reading. Finally, Review & Spaced Repetition pools all cue questions from every topic into one place and provides a scheduled review calendar so knowledge moves into long-term memory before the exam. [Lecture notes.md]

The Intro Statistics — Study Wiki Home page serves as the navigator: it lists all topic pages, tracks progress (topics compiled, cue questions written, review sessions scheduled, and topics mastered), and explains the Cornell workflow step by step. [Lecture notes.md]

The first question you ask about any dataset is *where does it sit?* Central Tendency (Mean / Median / Mode) introduces the three standard answers to that question. The mean is the arithmetic average — sum all values, divide by the count. It is intuitive and mathematically convenient, but it is acutely sensitive to extreme values: a single billionaire added to a salary dataset can drag the mean far above what any typical person earns. The median, the middle value after sorting, is immune to that distortion, which is why it is preferred whenever data is skewed — income, house prices, and exam scores with a few very high marks all call for the median. The mode, the most frequently occurring value, is most meaningful for categorical or discrete data and can be used when neither averaging nor sorting makes conceptual sense. [Lecture notes.md]

Knowing which measure to use is a judgment call, not a formula. The guiding principle is: ask whether your data is roughly symmetric and free of extreme outliers (use the mean) or whether it is skewed or contaminated by outliers (use the median). The mode is a supplementary descriptor rather than a replacement for the other two in most numeric contexts. Understanding this trade-off is also the gateway to understanding Spread (Variance & Standard Deviation), because spread is always measured *around* a centre — and choosing the wrong centre gives you a meaningless measure of spread. [Lecture notes.md]

Knowing the centre of a dataset tells you only half the story. Two classes of students might both average 70 on an exam, yet one class has scores bunched between 65 and 75 while the other ranges from 20 to 100. Spread (Variance & Standard Deviation) captures that difference. [Lecture notes.md]

The foundational measure is variance: for each data point, compute how far it sits from the mean, square that distance, then average all the squared distances. Squaring is not arbitrary — plain (unsigned) deviations always sum to exactly zero because the positive and negative deviations cancel perfectly, making the average useless as a measure of scatter. Squaring forces every deviation to be positive before averaging. The result, variance, is expressed in *squared units* (dollars squared, centimetres squared), which is mathematically tractable but hard to interpret intuitively. Standard deviation (σ) solves that by taking the square root of the variance, returning the measure to the original units of the data. [Lecture notes.md]

Interpreting σ is straightforward: σ = 0 means every value in the dataset is identical; a larger σ means values are widely scattered from the mean; a smaller σ means they cluster tightly around it. Standard deviation is not just a summary statistic — it is the unit of distance used throughout the rest of statistics, most visibly in the Normal Distribution where the entire 68-95-99.7 rule is expressed in multiples of σ. [Lecture notes.md]

The Normal Distribution is arguably the single most important concept in introductory statistics, appearing everywhere from natural measurements (height, blood pressure) to manufacturing tolerances to standardised test scores. Its defining feature is a bell-shaped, perfectly symmetric curve centred on the mean. Because of that symmetry, the mean, median, and mode all coincide at the peak — a fact that ties directly back to Central Tendency (Mean / Median / Mode). [Lecture notes.md]

The shape of the bell is controlled entirely by standard deviation σ. A larger σ stretches the bell wider and flatter; a smaller σ squeezes it narrower and taller. This makes Spread (Variance & Standard Deviation) the geometric language of the normal distribution: you cannot draw or reason about a normal curve without specifying σ. [Lecture notes.md]

The 68-95-99.7 rule (also called the Empirical Rule) is the key practical tool the normal distribution provides:

The immediate corollary is that only about 5% of values in a normal distribution fall outside the mean ± 2σ band — a threshold used constantly in hypothesis testing and quality control. [Lecture notes.md]

Once you can describe a single variable — its centre, its spread, its shape — the natural next step is asking whether two variables move together. Correlation vs Causation addresses exactly that, and draws a critical boundary between *measuring* a relationship and *explaining* it. [Lecture notes.md]

The correlation coefficient r quantifies the strength and direction of a *linear* relationship between two variables on a scale from −1 to +1. A value of +1 means a perfect positive linear relationship (as one variable rises, the other rises proportionally); −1 means a perfect negative linear relationship; 0 means no detectable *linear* relationship — though a strong nonlinear pattern could still exist. This last nuance is important: r = 0 does not mean the variables are unrelated, only that their relationship is not captured by a straight line. [Lecture notes.md]

The deeper lesson of this topic is the warning against confusing correlation with causation — the claim that one variable directly produces a change in another. Two mechanisms can produce a correlation without any causal link between the variables:

• Confounding variables (lurking variables): A hidden third variable drives both observed variables. The textbook example is ice-cream sales and drowning rates, which are both elevated in summer not because ice cream causes drowning but because warm weather drives both — *warm weather* is the confounder. [Lecture notes.md]
• Reverse causation: The direction of any genuine causal arrow cannot be read from r alone.
• Coincidence: Random patterns in finite data can produce spurious correlations with no underlying mechanism whatsoever.

Establishing causation requires controlled experiments, not just high r values. This is one of the most practically important ideas in the entire course — misreading correlational data as causal is a pervasive error in journalism, policy, and everyday reasoning. [Lecture notes.md]

Correlation also connects back to earlier topics: variability in both variables (captured by Spread (Variance & Standard Deviation)) affects the magnitude of r, and many correlation-based methods assume the underlying data follows a Normal Distribution. Outliers — the same values that distort the Central Tendency (Mean / Median / Mode) mean — can also inflate or deflate r dramatically. [Lecture notes.md]

The four topics are not independent modules — they form a logical chain of ideas:

• Central Tendency (Mean / Median / Mode) establishes the language of location.
• Spread (Variance & Standard Deviation) extends that to the language of variability, building directly on the mean.
• Normal Distribution synthesises both: its centre is the mean and its width is σ, and it is the canonical shape that makes the 68-95-99.7 rule possible.
• Correlation vs Causation applies everything to two-variable relationships, with outliers and distributional assumptions tying it back to all three earlier topics.

1. 1.Read a topic Cornell note — Central Tendency (Mean / Median / Mode), Spread (Variance & Standard Deviation), Normal Distribution, or Correlation vs Causation — and absorb the notes and summary.
2. 2.Test yourself on the cue questions on each page *before* revealing the answers.
3. 3.Review on schedule — open Review & Spaced Repetition and follow the spaced-review calendar to space out sessions and consolidate knowledge into long-term memory.
4. 4.Track mastery — update the stats block on the Intro Statistics — Study Wiki Home as topics click into place.

All raw source material is at Lecture notes.md. [Lecture notes.md]