# Statistical dispersion

**dispersionvariabilityspreadmeasure of statistical dispersionstatistical variabilityvariationintra-individual variabilitydispersedintraindividual variabilityMeasures of scale**

In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed.wikipedia

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### Statistics

**statisticalstatistical analysisstatistician**

In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed.

Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other.

### Standard deviation

**standard deviationssample standard deviationsigma**

Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range.

In statistics, the standard deviation (SD, also represented by the lower case Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

### Interquartile range

**inter-quartile rangebelowinterquartile**

Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range.

In descriptive statistics, the interquartile range (IQR), also called the midspread or middle 50%, or technically H-spread, is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles, IQR = Q 3 − Q 1 . In other words, the IQR is the first quartile subtracted from the third quartile; these quartiles can be clearly seen on a box plot on the data.

### Probability distribution

**distributioncontinuous probability distributiondiscrete probability distribution**

In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed.

Variance: the second moment of the pmf or pdf about the mean; an important measure of the dispersion of the distribution.

### Central tendency

**Localitycentral locationcentral point**

Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.

The central tendency of a distribution is typically contrasted with its dispersion or variability; dispersion and central tendency are the often characterized properties of distributions.

### Robust measures of scale

**Qn estimatorrobust estimator of dispersionrobust measure of scale**

These are frequently used (together with scale factors) as estimators of scale parameters, in which capacity they are called estimates of scale. Robust measures of scale are those unaffected by a small number of outliers, and include the IQR and MAD.

In statistics, a robust measure of scale is a robust statistic that quantifies the statistical dispersion in a set of numerical data.

### Scale parameter

**scalerate parameterestimation**

These are frequently used (together with scale factors) as estimators of scale parameters, in which capacity they are called estimates of scale. Robust measures of scale are those unaffected by a small number of outliers, and include the IQR and MAD.

then s is called a scale parameter, since its value determines the "scale" or statistical dispersion of the probability distribution.

### Qualitative variation

**M2Margalef index**

For categorical variables, it is less common to measure dispersion by a single number; see qualitative variation.

An index of qualitative variation (IQV) is a measure of statistical dispersion in nominal distributions.

### Median absolute deviation

**MAD**

Median absolute deviation (MAD)

In statistics, the median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data.

### Range (statistics)

**rangerangingsample range**

Range

The range is the size of the smallest interval (statistics) which contains all the data and provides an indication of statistical dispersion.

### Coefficient of variation

**CVrelative standard deviationcoefficients of variation**

Coefficient of variation

In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution.

### Average absolute deviation

**mean absolute deviationmean deviationMAD**

Average absolute deviation (or simply called average deviation)

It is a summary statistic of statistical dispersion or variability.

### Mean absolute difference

**MDMean differenceaverage absolute difference**

Mean absolute difference (also known as Gini mean absolute difference) Relative mean difference, equal to twice the Gini coefficient

The mean absolute difference (univariate) is a measure of statistical dispersion equal to the average absolute difference of two independent values drawn from a probability distribution.

### Estimator

**estimatorsestimateestimates**

These are frequently used (together with scale factors) as estimators of scale parameters, in which capacity they are called estimates of scale. Robust measures of scale are those unaffected by a small number of outliers, and include the IQR and MAD.

This occurs frequently in estimation of scale parameters by measures of statistical dispersion.

### Gini coefficient

**Gini indexGiniequality**

Relative mean difference, equal to twice the Gini coefficient

In economics, the Gini coefficient, sometimes called Gini index, or Gini ratio, is a measure of statistical dispersion intended to represent the income or wealth distribution of a nation's residents, and is the most commonly used measurement of inequality.

### Dimensionless quantity

**dimensionlessdimensionless numberdimensionless quantities**

Other measures of dispersion are dimensionless. In other words, they have no units even if the variable itself has units. Variance-to-mean ratio – mostly used for count data when the term coefficient of dispersion is used and when this ratio is dimensionless, as count data are themselves dimensionless, not otherwise.

In statistics the coefficient of variation is the ratio of the standard deviation to the mean and is used to measure the dispersion in the data.

### Accuracy and precision

**accuracyprecisionaccurate**

In the physical sciences, such variability may result from random measurement errors: instrument measurements are often not perfectly precise, i.e., reproducible, and there is additional inter-rater variability in interpreting and reporting the measured results.

Precision is a description of random errors, a measure of statistical variability.

### Index of dispersion

**variance-to-mean ratiocoefficient of dispersionrelative variance**

Variance-to-mean ratio – mostly used for count data when the term coefficient of dispersion is used and when this ratio is dimensionless, as count data are themselves dimensionless, not otherwise.

In probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard statistical model.

### Quartile coefficient of dispersion

Quartile coefficient of dispersion

In statistics, the quartile coefficient of dispersion is a descriptive statistic which measures dispersion and which is used to make comparisons within and between data sets.

### Measurement uncertainty

**uncertaintyerroruncertainties**

Measurement uncertainty

In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity.

### Summary statistics

**summary statisticSummarizationdata summarization**

Summary statistics

a measure of statistical dispersion like the standard deviation

### Entropy (information theory)

**entropyinformation entropyShannon entropy**

Entropy: While the entropy of a discrete variable is location-invariant and scale-independent, and therefore not a measure of dispersion in the above sense, the entropy of a continuous variable is location invariant and additive in scale: If Hz is the entropy of continuous variable z and y=ax+b, then Hy=Hx+log(a).

Qualitative variation – other measures of statistical dispersion for nominal distributions

### Variance

**sample variancepopulation variancevariability**

Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range.

### Real number

**realrealsreal-valued**

A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse.

### Unit of measurement

**unitunits of measurementunits**

Most measures of dispersion have the same units as the quantity being measured.