214 cards
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...
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 value of an ordered dataset (or the average of the two middle values when the count is even). The mode is the value or values that occur most...
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 probabilities combine. The complement rule states that \(P(\text{not } A) = 1 - P(A)\). The addition rule gives \(P(A \text{ or } B) = P(A)...
Several named probability distributions serve as building blocks for statistical models. The Bernoulli distribution models a single trial with two outcomes, success with probability \(p\) and failure with probability \(1 - p\). Repeating such trials independently yields the binomial distribution, which counts the numbe...
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 population is divided into strata and a random sample is drawn from each, which can improve precision when strata differ. Cluster sampling sel...
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 when the population standard deviation is unknown and must be estimated from the sample. An independent samples t-test compares the means of t...
Correlation quantifies the strength and direction of a linear relationship between two numerical variables. Pearson's correlation coefficient \(r\) ranges from \(-1\) to \(+1\); values near \(0\) indicate no linear association, although a non-linear relationship may still exist. Spearman's correlation captures monotoni...
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 (correlation with a lagged version of themselves) and may or may not be stationary (having constant mean and variance over time). A moving...