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Measure of statistical dispersion
In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be
Interquartile_range
The interquartile mean (IQM), also called midmean, is a statistical measure of central tendency based on the truncated mean of the interquartile range. The
Interquartile_mean
Concept in statistics
The range provides an indication of statistical dispersion. Robust measures of range include the interdecile range and the interquartile range. For n
Range_(statistics)
Statistic which divides data into four same-sized parts for analysis
points evenly, the range is generally not the same between adjacent quartiles (i.e. usually (Q3 - Q2) ≠ (Q2 - Q1)). Interquartile range (IQR) is defined
Quartile
Data visualization
notably the interquartile range, midhinge, range, mid-range, and trimean. Box plots can be drawn either horizontally or vertically. The range-bar method
Box_plot
Method of plotting numeric data
marker for the median of the data; a box or marker indicating the interquartile range; and possibly all sample points, if the number of samples is not
Violin_plot
Statistical property quantifying how much a collection of data is spread out
statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data
Statistical_dispersion
Empirical law on the variance of species in a habitat
Hanski's model predicted that the power law exponent would be constrained to range closely about the value of 2, which seemed inconsistent with many reported
Taylor's_law
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
possibility is the quartile coefficient of dispersion, half the interquartile range ( Q 3 − Q 1 ) / 2 {\displaystyle {(Q_{3}-Q_{1})/2}} divided by the
Coefficient_of_variation
Graphical representation of the distribution of numerical data
{\operatorname {IQR} (x)}{\sqrt[{3}]{n}}},} which is based on the interquartile range, denoted by IQR. It replaces 3.5σ of Scott's rule with 2 IQR, which
Histogram
Statistical measure of variability
of the accuracy of numerical observations. Deviation (statistics) Interquartile range Probable error Robust measures of scale Relative mean absolute difference
Median_absolute_deviation
Probabilistic problem-solving algorithm
probability distributions shows that the Monte Carlo analysis has a narrower range than the "what if" analysis.[example needed] This is because the "what if"
Monte_Carlo_method
Middle quantile of a data set or probability distribution
there are several choices for a measure of variability: the range, the interquartile range, the mean absolute deviation, and the median absolute deviation
Median
dataset fall into each interval. independence independent variable interquartile range (IQR) A measure of the statistical dispersion or spread of a dataset
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Statistical modeling method
between the ( − ∞ , ∞ ) {\displaystyle (-\infty ,\infty )} range of the linear predictor and the range of the response variable. Some common examples of GLMs
Linear_regression
Statistical distribution for dependence between random variables
\times \operatorname {Ran} (F_{d})} which is the cartesian product of the ranges of the marginal cdf's. This implies that the copula is unique if the marginals
Copula_(statistics)
Method of data analysis
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Principal_component_analysis
Form of causal modeling that fit networks of constructs to data
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Structural_equation_modeling
Selection of data points in statistics
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Sampling_(statistics)
Study of collection and analysis of data
Mathematics Subject Classification. Mathematical statistics is covered in the range 276-280 of subclass QA (science > mathematics) in the Library of Congress
Statistics
Concepts from statistical hypothesis testing
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Type_I_and_type_II_errors
Normalized measure of statistical dispersion
dispersion is the ratio of half of the difference of quartiles (the interquartile range, IQR) to the average of the quartiles (the midhinge, MH): Q C D =
Quartile coefficient of dispersion
Quartile_coefficient_of_dispersion
Study of health and disease within a population
to define treatment effects. There is increasing recognition that a wide range of modern data sources, many not originating from healthcare or epidemiology
Epidemiology
Statistical method
developed to solve this problem, allowing users to determine an appropriate range of solutions to investigate. However these different methods often disagree
Factor_analysis
Statistical measure of how far values spread from their average
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Variance
Measure of the joint variability
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Covariance
Probability distribution
maximum (FWHM). γ {\displaystyle \gamma } is also equal to half the interquartile range and is sometimes called the probable error. This function is also
Cauchy_distribution
Branch of statistics
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Survival_analysis
Method of estimating the parameters of a statistical model, given observations
possible values {m, m + 1, ...}, rather than somewhere in the "middle" of the range of possible values, which would result in less bias.) The expected value
Maximum_likelihood_estimation
Measure of linear correlation
correlation coefficient is usually not a concern; for instance, if the range of the distribution is bounded, ρ is always defined. If the sample size
Pearson correlation coefficient
Pearson_correlation_coefficient
Set of statistical processes for estimating the relationships among variables
Prediction within the range of values in the dataset used for model-fitting is known informally as interpolation. Prediction outside this range of the data is
Regression_analysis
Estimator for quality of a statistical model
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Akaike_information_criterion
Probability distribution
table lists values for t distributions with ν degrees of freedom for a range of one-sided or two-sided critical regions. The first column is ν, the percentages
Student's_t-distribution
Statistical hypothesis test
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Wilcoxon_signed-rank_test
Grouping a set of objects by similarity
these objects' range. Another interesting property of DBSCAN is that its complexity is fairly low – it requires a linear number of range queries on the
Cluster_analysis
Generalization of the one-dimensional normal distribution to higher dimensions
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Multivariate normal distribution
Multivariate_normal_distribution
Linear regression model with a single explanatory variable
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Simple_linear_regression
Collection of statistical models
have statistically different means include the Tukey's range test, and Duncan's new multiple range test. In turn, these tests are often followed with a
Analysis_of_variance
Measure of distance between two proportions
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Cohen's_h
Class of statistical survival models
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Proportional_hazards_model
Design of tasks
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Design_of_experiments
Diagnostic plot of binary classifier ability
precision and negative predictive value, such as 0.2 and 0.1 in the [0, 1] range. If one performed a binary classification, obtained an ROC AUC of 0.9 and
Receiver operating characteristic
Receiver_operating_characteristic
Method of logical reasoning
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Inductive_reasoning
Statistical indicators of the deviation of a sample
influenced by outliers. The most common such robust statistics are the interquartile range (IQR) and the median absolute deviation (MAD). Alternatives robust
Robust_measures_of_scale
Statistical measure of association
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Cramér's_V
Set of descriptive statistics
upper half of the data. These quartiles are used to calculate the interquartile range, which helps to describe the spread of the data, and determine whether
Five-number_summary
Statistical method that summarizes and/or integrates data from multiple sources
should be specific enough for a reader to reproduce the search. The date range of studies, along with the date (or date period) the search was conducted
Meta-analysis
Measure of the asymmetry of random variables
(another measure of location), while the denominator is the semi-interquartile range Q ( 3 / 4 ) − Q ( 1 / 4 ) 2 {\displaystyle {\frac {Q(3/4)-Q(1/4)}{2}}}
Skewness
Fundamental theorem in probability theory and statistics
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Central_limit_theorem
Nonparametric measure of rank correlation
statistics, Spearman's rank correlation coefficient or Spearman's ρ is a number ranging from -1 to 1 that indicates how strongly two sets of ranks are correlated
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Statistical property
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Standard_error
Statistical hypothesis test
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Student's_t-test
Term in statistical hypothesis testing
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Power_(statistics)
Statistical measure of the magnitude of a phenomenon
are statistically significant are almost always in the small to medium range. It is rare for large SMDs to be obtained. Robert E. McGrath; Gregory J
Effect_size
Form of scientific experiment
the use of sham controls, which are only considered possible for a narrow range of surgical interventions. RCTs may also be considered infeasible or unethical
Randomized_controlled_trial
N-th root of the product of n numbers
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Geometric_mean
Statistical test comparing two probability distributions
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Kolmogorov–Smirnov_test
Concept in machine learning
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Double_descent
Statistical measure
range and the interquartile range, and can be computed from the (non-parametric) seven-number summary. Despite its simplicity, the interdecile range of
Interdecile_range
Statistical relationship
is not bigger than 1. Therefore, the value of a correlation coefficient ranges between −1 and +1. The correlation coefficient is +1 in the case of a perfect
Correlation
Number taken as representative of a list of numbers
of the remaining data. A specific example of a truncated mean is the interquartile mean. In some circumstances, mathematicians may calculate a mean of
Average
Experiment methodology
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
A/B_testing
Human research survey of public opinion
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Opinion_poll
Phase of clinical research in medicine
validity and reproducibility of the results. Costs for clinical trials can range into the billions of dollars per approved drug, and the complete trial process
Clinical_trial
Statistical property
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Statistic measuring inter-rater agreement for categorical items
simpler to evaluate disagreement between items. Cohen's kappa coefficient ranges from -1 (complete disagreement) to 1 (complete agreement). The first mention
Cohen's_kappa
Statistical phenomenon
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Regression_toward_the_mean
Private university in Bethlehem, Pennsylvania, US
scores, the interquartile range was 1370–1480; of the 10% of incoming students in 2023 who submitted ACT scores, the interquartile range was 31–33. In
Lehigh_University
Statistical interpretation with many tests
correction Tukey's HSD Two-stage "protected" procedures Duncan's new multiple range test Fisher's least significant difference Fisher-Hayter procedure Student-Newman-Keuls
Multiple_comparisons_problem
Type of numerical analysis
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Isotonic_regression
Statistical model validation technique
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Cross-validation_(statistics)
Distribution of an uncertain quantity
deviation 40 degrees, which very loosely constrains the temperature to the range (10 degrees, 90 degrees) with a small chance of being below -30 degrees
Prior_probability
Inverse of the average of the inverses of a set of numbers
volume per distance) when taking the mean value of the fuel economy of a range of cars one measure will produce the harmonic mean of the other – i.e.,
Harmonic_mean
Nonparametric test of the null hypothesis
measure. Like other correlational measures, the rank-biserial correlation can range from minus one to plus one, with a value of zero indicating no relationship
Mann–Whitney_U_test
Statistic for rank correlation
the total number of pair combinations, so the coefficient must be in the range −1 ≤ τ ≤ 1. If the agreement between the two rankings is perfect (i.e.,
Kendall rank correlation coefficient
Kendall_rank_correlation_coefficient
Measure of covariance of components of a random vector
( t ) {\displaystyle \mathbf {Y} _{j}(t)} are the same, except that the range of the time-of-flight t {\displaystyle t} differs. Panel a shows ⟨ X Y T
Covariance_matrix
Test of normality in frequentist statistics
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Shapiro–Wilk_test
Bias in causal inference
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Confounding
Theory and technique of psychological measurement
focus in psychometrics has been on personality testing. There has been a range of theoretical approaches to conceptualizing and measuring personality,
Psychometrics
Series of questions for gathering information
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Questionnaire
Correlation of a signal with a time-shifted copy of itself, as a function of shift
X {\displaystyle \rho _{XX}} is well defined, its value must lie in the range [ − 1 , 1 ] {\displaystyle [-1,1]} , with 1 indicating perfect correlation
Autocorrelation
Mathematical function for the probability a given outcome occurs in an experiment
scenarios where the set of possible outcomes can take on values in a continuous range (e.g. real numbers), such as the temperature on a given day. In the absolutely
Probability_distribution
Unit of information
be used as a basis for calculation, reasoning, or discussion. Data can range from abstract ideas to concrete measurements, including, but not limited
Data
Statistic which divides a data set into 100 parts and analyzes it as a percentage
proportion of individuals in a population will fall outside the −3σ to +3σ range. For example, with human heights very few people are above the +3σ height
Percentile
Class of statistical models
response variable is expected to be always positive and varying over a wide range, constant input changes lead to geometrically (i.e. exponentially) varying
Generalized_linear_model
Type of statistics
absolute deviation and interquartile range are robust measures of statistical dispersion, while the standard deviation and range are not. Trimmed estimators
Robust_statistics
Number of values in the final calculation of a statistic that are free to vary
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Statistical measure
RMSD a more useful comparison measure is to divide the RMSD by the interquartile range (IQR). When dividing the RMSD with the IQR the normalized value gets
Root_mean_square_deviation
University in Evanston, Illinois, US
2026, the interquartile range (middle 50%) on the post-2016 SAT was a combined (verbal and math) 1500–1560 out of 1600; the interquartile range on the evidence-based
Northwestern_University
Non-parametric statistic used to estimate the survival function
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Kaplan–Meier_estimator
Process of using data analysis for predicting population data from sample data
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Statistical_inference
Gathering information for analysis
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Data_collection
Statistical method for handling multiple comparisons
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
False_discovery_rate
Statistical test
Dispersion Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance Shape Central limit theorem Moments
Wald_test
Type of statistical measure over subsets of a dataset
{SMA}}_{k,{\text{next}}}} with the same sampling width k {\displaystyle k} the range from n − k + 2 {\displaystyle n-k+2} to n + 1 {\displaystyle n+1} is considered
Moving_average
Kth smallest value in a statistical sample
analysis that is simply related to the order statistics is the sample interquartile range. The sample median may or may not be an order statistic, since there
Order_statistic
Topics referred to by the same term
Work! the movie. "50% & 50%", a 1993 song by Hide Middle 50% or interquartile range, a measure of statistical dispersion Fifty Percent, a Taiwanese affordable
50%
Statistical method
least observed with more control than the response variable. Also, the range of the explanatory variables defines the information available from them
Bootstrapping_(statistics)
Variable representing a random phenomenon
result from tossing a coin); and the range is a measurable space (e.g. corresponding to the domain above, the range might be the set { − 1 , 1 } {\displaystyle
Random_variable
Scientific procedure performed to validate a hypothesis
can vary from personal and informal natural comparisons (e.g. tasting a range of chocolates to find a favorite), to highly controlled (e.g. tests requiring
Experiment
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