A free, self-paced textbook in 8 chapters. Read a chapter, then drill it with the 214 companion flashcards using spaced repetition.
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,...
The most common numerical summaries describe a dataset's center. The mean is the arithmetic average — the sum of all values divided by the count — while the median is the middle va...
Probability provides the mathematical language for uncertainty. A probability is a number between 0 and 1 that quantifies how likely an event is to occur. Several rules govern how...
Several named probability distributions serve as building blocks for statistical models. The Bernoulli distribution models a single trial with two outcomes, success with probabilit...
Inferential statistics depends on how data are collected. In simple random sampling, every member of the population has an equal chance of selection; in stratified sampling, the po...
The choice of test depends on the data and the question. A z-test is appropriate when the population standard deviation is known or the sample is large, whereas a t-test is used wh...
Correlation quantifies the strength and direction of a linear relationship between two numerical variables. Pearson's correlation coefficient \(r\) ranges from \(-1\) to \(+1\); va...
Beyond the core toolkit, several specialized areas round out statistical practice. A time series is a sequence of observations recorded over time; such data exhibit autocorrelation...