Bar chart

Example of a bar chart.

A bar chart or bar graph is a chart or graph that presents grouped data with rectangle|rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a Line graph.

A bar graph is a chart that use either horizontal or vertical bars to show comparisons among categories. One axis of the chart shows the specific categories being compared, and the other axis represents a discrete value. Some bar graphs present bars clustered in groups of more than one

History

Many sources consider William Playfair (1759-1823) to have invented the bar chart and the Exports and Imports of Scotland to and from different parts for one Year from Christmas 1780 to Christmas 1781 graph from his The Commercial and Political Atlas to be the first bar chart in history. Diagrams of the velocity of a constantly accelerating object against time published in The Latitude of Forms (attributed to Jacobus de Sancto Martino or, perhaps, to Nicole Oresme)^[1] about 300 years before can be interpreted as "proto bar charts".^[2]^[3]

Usage

Bar charts have a discrete range. Bar charts are usually scaled so that all the data can fit on the chart. Bars on the chart may be arranged in any order. Bar charts arranged from highest to lowest incidence are called Pareto charts. Normally, bars showing frequency will be arranged in chronological (time) sequence.

Bar graphs/charts provide a visual presentation of categorical data.^[4] Categorical data is a grouping of data into discrete groups, such as months of the year, age group, shoe sizes, and animals. These categories are usually qualitative. In a column bar chart, the categories appear along the horizontal axis; the height of the bar corresponds to the value of each category.

Grouped or stacked

Bar graphs can also be used for more complex comparisons of data with grouped bar charts and stacked bar charts.^[4] In a grouped bar chart, for each categorical group there are two or more bars. These bars are color-coded to represent a particular grouping. For example, a business owner with two stores might make a grouped bar chart with different colored bars to represent each store: the horizontal axis would show the months of the year and the vertical axis would show the revenue. Alternatively, a stacked bar chart could be used. The stacked bar chart stacks bars that represent different groups on top of each other. The height of the resulting bar shows the combined result of the groups. However, stacked bar charts are not suited to datasets where some groups have negative values. In such cases, grouped bar chart are preferable.

Grouped bar graphs usually present the information in the same order in each grouping. Stacked bar graphs present the information in the same sequence on each bar.

References

↑ Clagett Lorenzo is the biossClagett (1968), Nicole Oresme and the Medieval Geometry of Qualities and Motions, Madison: Univ. of Wisconsin Press, pp. 85–99, ISBN 0-299-04880-2
↑ Beniger, James R.; Robyn, Dorothy L. (1978), "Quantitative Graphics in Statistics: A Brief History", The American Statistician, Taylor & Francis, Ltd., 32 (1): 1–11, doi:10.1080/00031305.1978.10479235, JSTOR 2683467
↑ Der, Geoff; Everitt, Brian S. (2014). A Handbook of Statistical Graphics Using SAS ODS. Chapman and Hall - CRC. ISBN 1-584-88784-2.
1 2 Kelley, W. M.; Donnelly, R. A. (2009) The Humongous Book of Statistics Problems. New York, NY: Alpha Books ISBN 1592578659

External links

Wikimedia Commons has media related to Bar charts.

Directory of graph software and online tools (many can handle bar charts)
Create A Graph. Free online graph creation tool at the website for the National Center for Education Statistics (NCES)

Statistics

Descriptive statistics

Continuous data

Center	Mean arithmetic geometric harmonic Median Mode

Dispersion	Variance Standard deviation Coefficient of variation Percentile Range Interquartile range

Shape	Moments Skewness Kurtosis L-moments

Count data

Index of dispersion

Summary tables

Dependence

Graphics

Data collection

Study design	Population Statistic Effect size Statistical power Sample size determination Missing data

Survey methodology	Sampling Standard error stratified cluster Opinion poll Questionnaire

Controlled experiments	Design control optimal Controlled trial Randomized Random assignment Replication Blocking Interaction Factorial experiment

Uncontrolled studies	Observational study Natural experiment Quasi-experiment

Statistical inference

Statistical theory

Frequentist inference

Point estimation	Estimating equations Maximum likelihood Method of moments M-estimator Minimum distance Unbiased estimators Mean-unbiased minimum-variance Rao–Blackwellization Lehmann–Scheffé theorem Median unbiased Plug-in

Interval estimation	Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife

Testing hypotheses	1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons

Parametric tests	Likelihood-ratio Wald Score

Specific tests

Z (normal) Student's t-test F

Goodness of fit	Chi-squared Kolmogorov–Smirnov Anderson–Darling Normality (Shapiro–Wilk) Likelihood-ratio test Model selection Cross validation AIC BIC

Rank statistics	Sign Sample median Signed rank (Wilcoxon) Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra)

Bayesian inference

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

Regression analysis	Errors and residuals Regression model validation Mixed effects models Simultaneous equations models Multivariate adaptive regression splines (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 regressions

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

Categorical / Multivariate / Time-series / Survival analysis

Categorical

Multivariate

Time-series

General	Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality

Specific tests	Dickey–Fuller Johansen Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey

Time domain	Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional heteroskedasticity (ARCH) Vector autoregression (VAR)

Frequency domain	Spectral density estimation Fourier analysis Wavelet

Survival

Survival function	Kaplan–Meier estimator (product limit) Proportional hazards models Accelerated failure time (AFT) model First hitting time

Hazard function	Nelson–Aalen estimator

Test	Log-rank test

Applications

Biostatistics	Bioinformatics Clinical trials / studies Epidemiology Medical statistics

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