Statistical Foundations

What statistics is, where data come from, and how to summarize a dataset.

In suggested reading order:

1. Introduction to Statistics. What statistics is for, the difference between describing data and drawing conclusions from it, and how this encyclopedia is organized.
2. Populations and Samples. The population is the whole group we want to learn about; a sample is the part we actually observe, and how it is chosen decides what it can tell us.
3. Types of Data and Variables. Categorical and numerical variables, their subtypes, and why the type of a variable decides which summaries and plots make sense.
4. Descriptive Statistics. Numbers and pictures that summarize a dataset's centre, spread, and shape, without making claims beyond the data.
5. Mean, Median, and Mode. Three ways to describe the typical value of a dataset, how they differ, and when to use which.
6. Variance and Standard Deviation. Measures of how far data values typically lie from their mean, including why the sample variance divides by n − 1.
7. Quantiles, Percentiles, and Outliers. Values that cut ordered data into given proportions, the interquartile range, and how to find and handle unusual observations.