Frequency (statistics)

From Wikipedia, the free encyclopedia

Histogram of travel time (to work), US 2000 census. Histograms depict the frequencies of observations occurring in certain ranges of values

In statistics the frequency (or absolute frequency) of an event $i$ is the number $n_{i}$ of times the event occurred in an experiment or study.^[1]^:12-19 These frequencies are often graphically represented in histograms.

Cumulative frequency refers to the total of the absolute frequencies of all events at or below a certain point in an ordered list of events.^[1]^:17-19

The relative frequency (or empirical probability) of an event refers to the absolute frequency normalized by the total number of events:

$f_{i}={\frac {n_{i}}{N}}={\frac {n_{i}}{\sum _{i}n_{i}}}.$

The values of $f_{i}$ for all events $i$ can be plotted to produce a frequency distribution.

Under the frequency interpretation of probability, it is assumed that as the length of a series of trials increases without bound, the fraction of experiments in which a given event occurs will approach a fixed value, known as the limiting relative frequency. This interpretation is often contrasted with Bayesian probability.

References

↑ 1.0 1.1 Kenney, J. F.; Keeping, E. S. (1962). Mathematics of Statistics, Part 1 (3rd ed.). Princeton, NJ: Van Nostrand Reinhold.

Statistics

Descriptive statistics

Continuous data

Location	Mean (Arithmetic, Geometric, Harmonic) Median Mode

Dispersion	Range Standard deviation Coefficient of variation Percentile Interquartile range

Shape	Variance Skewness Kurtosis Moments L-moments

Count data

Index of dispersion

Summary tables

Dependence

Statistical graphics

Data collection

Designing studies	Effect size Standard error Statistical power Sample size determination

Survey methodology	Sampling Stratified sampling Cluster sampling Opinion poll Questionnaire

Controlled experiment	Design of experiments Randomized experiment Random assignment Replication Blocking Factorial experiment Optimal design

Uncontrolled studies	Natural experiment Quasi-experiment Observational study

Statistical inference

Statistical theory	Sampling distribution Order statistic Scan statistic Record value Sufficiency Completeness Exponential family Permutation test (Randomization test) Empirical distribution Bootstrap U statistic Efficiency Asymptotics Robustness

Frequentist inference	Unbiased estimator (Mean unbiased minimum variance, Median unbiased) Biased estimators (Maximum likelihood, Method of moments, Minimum distance, Density estimation) Confidence interval Testing hypotheses Power Parametric tests (Likelihood-ratio, Wald, Score)

Specific tests	Z (normal) Student's t-test F Goodness of fit (Chi-squared, G, Sample source, sample normality, Skewness & kurtosis Normality, Model comparison, Model quality) Signed-rank (1-sample, 2-sample, 1-way anova) Shapiro–Wilk Kolmogorov–Smirnov

Bayesian inference	Bayesian probability Prior Posterior Credible interval Bayes factor Bayesian estimator Maximum posterior estimator

Correlation and regression analysis

Correlation	Pearson product–moment correlation Partial correlation Confounding variable Coefficient of determination

Regression analysis	Errors and residuals Regression model validation Mixed effects models Simultaneous equations models MARS

Linear regression	Simple linear regression Ordinary least squares General linear model Bayesian regression

Non-standard predictors	Nonlinear regression Nonparametric Semiparametric Isotonic Robust Heteroscedasticity Homoscedasticity

Generalized linear model	Exponential families Logistic (Bernoulli) Binomial Poisson

Partition of variance	Analysis of variance (ANOVA) Analysis of covariance Multivariate ANOVA Degrees of freedom

Categorical, multivariate, time-series, or survival analysis

Categorical data

Multivariate statistics

Time series analysis

General	Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration

Specific tests	Granger causality Q-Statistic Durbin–Watson

Time domain	ACF PACF XCF ARMA model ARIMA model ARCH Vector autoregression

Frequency domain	Spectral density estimation Fourier analysis

Survival analysis

Applications

Biostatistics	Bioinformatics Clinical trials & studies Epidemiology Medical statistics

Engineering statistics	Chemometrics Methods engineering Probabilistic design Process & Quality control Reliability System identification

Social statistics	Actuarial science Census Crime statistics Demography Econometrics National accounts Official statistics Population Psychometrics

Spatial statistics	Cartography Environmental statistics Geographic information system Geostatistics Kriging

Category
Portal
Outline
Index

This article is issued from Wikipedia. The text is available under the Creative Commons Attribution/Share Alike; additional terms may apply for the media files.

Frequency (statistics)

See also

References