A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of

information Information is an Abstraction, abstract concept that refers to something which has the power Communication, to inform. At the most fundamental level, it pertains to the Interpretation (philosophy), interpretation (perhaps Interpretation (log ...

, while descriptive statistics (in the

mass noun In linguistics, a mass noun, uncountable noun, non-count noun, uncount noun, or just uncountable, is a noun with the syntactic property that any quantity of it is treated as an undifferentiated unit, rather than as something with discrete eleme ...

sense) is the process of using and analysing those statistics. Descriptive statistics is distinguished from inferential statistics (or inductive statistics) by its aim to summarize a sample, rather than use the data to learn about the

population Population is a set of humans or other organisms in a given region or area. Governments conduct a census to quantify the resident population size within a given jurisdiction. The term is also applied to non-human animals, microorganisms, and pl ...

that the sample of data is thought to represent. This generally means that descriptive statistics, unlike inferential statistics, is not developed on the basis of

probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...

, and are frequently

nonparametric statistics Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric s ...

. Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented. For example, in papers reporting on human subjects, typically a table is included giving the overall sample size, sample sizes in important subgroups (e.g., for each treatment or exposure group), and

demographic Demography () is the statistics, statistical study of human populations: their size, composition (e.g., ethnic group, age), and how they change through the interplay of fertility (births), mortality (deaths), and migration. Demographic analy ...

or clinical characteristics such as the

average In colloquial, ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean the sum of the numbers divided by ...

age, the proportion of subjects of each sex, the proportion of subjects with related co-morbidities, etc. Some measures that are commonly used to describe a data set are measures of central tendency and measures of variability or dispersion. Measures of central tendency include the

mean 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 statist ...

median The median of a set of numbers is the value separating the higher half from the lower half of a Sample (statistics), data sample, a statistical population, population, or a probability distribution. For a data set, it may be thought of as the “ ...

and mode, while measures of variability include the

standard deviation In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...

(or

variance In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion ...

), the minimum and maximum values of the variables, kurtosis and skewness.Investopedia
Descriptive Statistics Terms
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Use in statistical analysis

Descriptive statistics provide simple summaries about the sample and about the observations that have been made. Such summaries may be either quantitative, i.e. summary statistics, or visual, i.e. simple-to-understand graphs. These summaries may either form the basis of the initial description of the data as part of a more extensive statistical analysis, or they may be sufficient in and of themselves for a particular investigation. For example, the shooting

percentage In mathematics, a percentage () is a number or ratio expressed as a fraction (mathematics), fraction of 100. It is often Denotation, denoted using the ''percent sign'' (%), although the abbreviations ''pct.'', ''pct'', and sometimes ''pc'' are ...

basketball Basketball is a team sport in which two teams, most commonly of five players each, opposing one another on a rectangular Basketball court, court, compete with the primary objective of #Shooting, shooting a basketball (ball), basketball (appro ...

is a descriptive statistic that summarizes the performance of a player or a team. This number is the number of shots made divided by the number of shots taken. For example, a player who shoots 33% is making approximately one shot in every three. The percentage summarizes or describes multiple discrete events. Consider also the

grade point average Grading in education is the application of standardized Measurement, measurements to evaluate different levels of student achievement in a course. Grades can be expressed as letters (usually A to F), as a range (for example, 1 to 6), percentage ...

. This single number describes the general performance of a student across the range of their course experiences. The use of descriptive and summary statistics has an extensive history and, indeed, the simple tabulation of populations and of economic data was the first way the topic of

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

appeared. More recently, a collection of summarisation techniques has been formulated under the heading of

exploratory data analysis In statistics, exploratory data analysis (EDA) is an approach of data analysis, analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or ...

: an example of such a technique is the

box plot In descriptive statistics, a box plot or boxplot is a method for demonstrating graphically the locality, spread and skewness groups of numerical data through their quartiles. In addition to the box on a box plot, there can be lines (which are ca ...

. In the business world, descriptive statistics provides a useful summary of many types of data. For example, investors and brokers may use a historical account of return behaviour by performing empirical and analytical analyses on their investments in order to make better investing decisions in the future.

Univariate analysis

Univariate analysis involves describing the distribution of a single variable, including its central tendency (including the

, and mode) and dispersion (including the range and quartiles of the data-set, and measures of spread such as the

and

). The shape of the distribution may also be described via indices such as skewness and kurtosis. Characteristics of a variable's distribution may also be depicted in graphical or tabular format, including

histograms A histogram is a visual representation of the distribution of quantitative data. To construct a histogram, the first step is to "bin" (or "bucket") the range of values— divide the entire range of values into a series of intervals—and then ...

and stem-and-leaf display.

Bivariate and multivariate analysis

When a sample consists of more than one variable, descriptive statistics may be used to describe the relationship between pairs of variables. In this case, descriptive statistics include: * Cross-tabulations and contingency tables * Graphical representation via scatterplots * Quantitative measures of dependence * Descriptions of conditional distributions The main reason for differentiating univariate and bivariate analysis is that bivariate analysis is not only a simple descriptive analysis, but also it describes the relationship between two different variables. Quantitative measures of dependence include correlation (such as Pearson's r when both variables are continuous, or Spearman's rho if one or both are not) and covariance (which reflects the scale variables are measured on). The slope, in regression analysis, also reflects the relationship between variables. The unstandardised slope indicates the unit change in the criterion variable for a one unit change in the predictor. The standardised slope indicates this change in standardised ( z-score) units. Highly skewed data are often transformed by taking logarithms. The use of logarithms makes graphs more symmetrical and look more similar to the

normal distribution In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac ...

, making them easier to interpret intuitively.

References

External links

* Descriptive Statistics Lecture: University of Pittsburgh Supercourse: http://www.pitt.edu/~super1/lecture/lec0421/index.htm {{Authority control