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Chapter 1 of 8

Foundations of Statistical Thinking

Statistics is the science of learning from data, and every statistical study begins by clarifying what is being measured and from whom. The entire collection of individuals, items, or measurements that share a common property is called the population, while a subset selected from that population for analysis is called a sample. Because measuring every member of a population is often impractical, costly, or even impossible, statisticians rely on samples to draw conclusions about larger groups. This practical necessity gives rise to a crucial distinction: a parameter is a numerical characteristic of a population (such as the population mean \(\mu\) or standard deviation \(\sigma\)), whereas a statistic is a numerical characteristic computed from a sample (such as the sample mean \(\bar{x}\) or sample standard deviation \(s\)).

Statistics is commonly divided into two broad branches. Descriptive statistics encompasses the tools used to summarize and present the main features of a dataset — its center, spread, and shape — without attempting to generalize beyond the data at hand. Inferential statistics, by contrast, provides the methods for moving from sample data to claims about a wider population, using probability theory to quantify uncertainty. Understanding this distinction is the foundation for everything that follows: descriptive tools help us see what our data look like, while inferential tools tell us what those data allow us to say about the world.

All chapters
  1. 1Foundations of Statistical Thinking
  2. 2Describing Data: Summaries and Visualization
  3. 3Probability Foundations and Random Variables
  4. 4Common Probability Distributions
  5. 5Sampling, Estimation, and Hypothesis Testing
  6. 6Statistical Tests in Practice
  7. 7Regression, Correlation, and Predictive Modeling
  8. 8Special Topics, Biases, and Modern Methods

Drill it

Reading is not remembering. These come from the Statistics Essentials deck:

Q

What is a population in statistics?

The entire set of individuals, items, or measurements that share a common property and are the subject of a statistical study.

Q

What is a sample?

A subset of a population selected to represent it for analysis.

Q

Why do we use samples instead of populations?

Because measuring the entire population is often impractical, costly, or impossible.

Q

What is a parameter?

A numerical value that describes a characteristic of a population (e.g., μ for mean, σ for standard deviation).