# 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

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

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.