Statistics is the mathematical science of collecting, organizing, analyzing, and interpreting numerical data to make informed decisions under uncertainty. It bridges probability theory (which models randomness) and practical data analysis (which extracts patterns from observations), forming the foundation for fields ranging from machine learning to clinical trials. Statistics divides into descriptive statistics (summarizing data you have) and inferential statistics (generalizing from samples to populations), each serving distinct but complementary roles. The key insight: variation is everywhere—statistics gives us principled ways to measure it, understand it, and reason through it, transforming raw numbers into actionable knowledge.
What This Cheat Sheet Covers
This topic spans 27 focused tables and 196 indexed concepts. Below is a complete table-by-table outline of this topic, spanning foundational concepts through advanced details.
A jump-to index of every table row in this cheat sheet.
An interactive map of every table and concept in this topic.
Table 1: Population vs Sample
The whole point of inferential statistics is to learn about a group too large to measure by studying a small piece of it. The vocabulary here keeps that logic straight—population versus sample, parameter versus statistic—and explains why a sample mean is only an estimate, complete with the sampling error and bias that come with reasoning from a part to the whole.
| Concept | Example | Description |
|---|---|---|
all 10,000 employees | • Complete set of all individuals or observations of interest • typically too large to measure entirely. | |
random 100 employees | • Subset of population actually measured • must be representative to support valid inference. | |
μ = 65 (population mean)Greek letters | • Fixed value describing a population • usually unknown • denoted by Greek letters (μ, σ, ρ). | |
x̄ = 67 (sample mean)Roman letters | • Calculated value from sample data used to estimate a parameter • denoted by Roman letters (x̄, s, r). |