Data set in the context of Correlogram

Reproducibility, closely related to replicability and repeatability, is a major principle underpinning the scientific method. For the findings of a study to be reproducible means that results obtained by an experiment or an observational study or in a statistical analysis of a data set should be achieved again with a high degree of reliability when the study is replicated. There are different kinds of replication but typically replication studies involve different researchers using the same methodology. Only after one or several such successful replications should a result be recognized as scientific knowledge.

The median of a set of numbers is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as the “middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center. Median income, for example, may be a better way to describe the center of the income distribution because increases in the largest incomes alone have no effect on the median. For this reason, the median is of central importance in robust statistics.

Median is a 2-quantile; it is the value that partitions a set into two equal parts.

A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose.

The arithmetic mean, also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x₁, x₂, ..., x_n is typically denoted using an overhead bar, ${\displaystyle {\bar {x}}}$. If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the sample mean (${\displaystyle {\bar {x}}}$) to distinguish it from the group mean (or expected value) of the underlying distribution, denoted ${\displaystyle \mu }$ or ${\displaystyle \mu _{x}}$.

Cluster analysis, or clustering, is a data analysis technique aimed at partitioning a set of objects into groups such that objects within the same group (called a cluster) exhibit greater similarity to one another (in some specific sense defined by the analyst) than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistical data analysis, used in many fields, including pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning.

Cluster analysis refers to a family of algorithms and tasks rather than one specific algorithm. It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small distances between cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated as a multi-objective optimization problem. The appropriate clustering algorithm and parameter settings (including parameters such as the distance function to use, a density threshold or the number of expected clusters) depend on the individual data set and intended use of the results. Cluster analysis as such is not an automatic task, but an iterative process of knowledge discovery or interactive multi-objective optimization that involves trial and failure. It is often necessary to modify data preprocessing and model parameters until the result achieves the desired properties.

In statistics and econometrics, panel data and longitudinal data are both multi-dimensional data involving measurements over time. Panel data is a subset of longitudinal data where observations are for the same subjects each time.

Time series and cross-sectional data can be thought of as special cases of panel data that are in one dimension only (one panel member or individual for the former, one time point for the latter). A literature search often involves time series, cross-sectional, or panel data.

The Iris flower data set or Fisher's Iris data set is a multivariate data set used and made famous by the British statistician and biologist Ronald Fisher in his 1936 paper The use of multiple measurements in taxonomic problems as an example of linear discriminant analysis. It is sometimes called Anderson's Iris data set because Edgar Anderson collected the data to quantify the morphologic variation of Iris flowers of three related species. Two of the three species were collected in the Gaspé Peninsula "all from the same pasture, and picked on the same day and measured at the same time by the same person with the same apparatus".

The data set consists of 50 samples from each of three species of Iris (Iris setosa, Iris virginica and Iris versicolor). Four features were measured from each sample: the length and the width of the sepals and petals, in centimeters. Based on the combination of these four features, Fisher developed a linear discriminant model to distinguish each species. Fisher's paper was published in the Annals of Eugenics (today the Annals of Human Genetics).

In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, variance is the average of the squared deviations from the mean.) A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. Standard deviation can also be used to calculate standard error for a finite sample, and to determine statistical significance.

Linguistic typology (or language typology) is a field of linguistics that studies and classifies languages according to their structural features to allow their comparison. Its aim is to describe and explain the structural diversity and the common properties of the world's languages. Its subdisciplines include, but are not limited to phonological typology, which deals with sound features; syntactic typology, which deals with word order and form; lexical typology, which deals with language vocabulary; and theoretical typology, which aims to explain the universal tendencies.

Linguistic typology is contrasted with genealogical linguistics on the grounds that typology groups languages or their grammatical features based on formal similarities rather than historic descendence. The issue of genealogical relation is however relevant to typology because modern data sets aim to be representative and unbiased. Samples are collected evenly from different language families, emphasizing the importance of lesser-known languages in gaining insight into human language.

Computational statistics, or statistical computing, is the study which is the intersection of statistics and computer science, and refers to the statistical methods that are enabled by using computational methods. It is the area of computational science (or scientific computing) specific to the mathematical science of statistics. This area is fast developing. The view that the broader concept of computing must be taught as part of general statistical education is gaining momentum.

As in traditional statistics the goal is to transform raw data into knowledge, but the focus lies on computer intensive statistical methods, such as cases with very large sample size and non-homogeneous data sets.

In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set. An outlier can be an indication of exciting possibility, but can also cause serious problems in statistical analyses.

Outliers can occur by chance in any distribution, but they can indicate novel behaviour or structures in the data-set, measurement error, or that the population has a heavy-tailed distribution. In the case of measurement error, one wishes to discard them or use statistics that are robust to outliers, while in the case of heavy-tailed distributions, they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two distinct sub-populations, or may indicate 'correct trial' versus 'measurement error'; this is modeled by a mixture model.

The Polity data series is a data series in political science research. Along with the V-Dem Democracy Indices project and The Economist Democracy Index, Polity is among prominent datasets that measure democracy and autocracy.

The Polity study was initiated in the late 1960s by Ted Robert Gurr and is now continued by Monty G. Marshall, one of Gurr's students. It was sponsored by the Political Instability Task Force (PITF) until February 2020. The PITF is funded by the Central Intelligence Agency.

In statistics, cross-sectional data is a type of data collected by observing many subjects (such as individuals, firms, countries, or regions) at a single point or period of time. Analysis of cross-sectional data usually consists of comparing the differences among selected subjects, typically with no regard to differences in time.

For example, if we want to measure current obesity levels in a population, we could draw a sample of 1,000 people randomly from that population (also known as a cross section of that population), measure their weight and height, and calculate what percentage of that sample is categorized as obese. This cross-sectional sample provides us with a snapshot of that population, at that one point in time. Note that we do not know based on one cross-sectional sample if obesity is increasing or decreasing; we can only describe the current proportion.

In statistics, exploratory data analysis (EDA) or exploratory analytics is an approach of analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but primarily EDA is for seeing what the data can tell beyond the formal modeling and thereby contrasts with traditional hypothesis testing, in which a model is supposed to be selected before the data is seen. Exploratory data analysis has been promoted by John Tukey since 1970 to encourage statisticians to explore the data, and possibly formulate hypotheses that could lead to new data collection and experiments. EDA is different from initial data analysis (IDA), which focuses more narrowly on checking assumptions required for model fitting and hypothesis testing, and handling missing values and making transformations of variables as needed. EDA encompasses IDA.

A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were used. Graphs are a visual representation of the relationship between variables, which are very useful for humans who can then quickly derive an understanding which may not have come from lists of values. Given a scale or ruler, graphs can also be used to read off the value of an unknown variable plotted as a function of a known one, but this can also be done with data presented in tabular form. Graphs of functions are used in mathematics, sciences, engineering, technology, finance, and other areas.

In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points higher than the adjacent points (presumably because of noise) are reduced, and points that are lower than the adjacent points are increased, leading to a smoother signal.

Reducing noise by smoothing may aid in data analysis in two notable ways: