Statistical Graphics
Statistical graphics allow results to be displayed in some sort of pictorial form and include scatter plots, histograms, and box plots.
Learning Objective

Recognize the techniques used in exploratory data analysis
Key Points
 Graphical statistical methods explore the content of a data set.
 Graphical statistical methods are used to find structure in data.
 Graphical statistical methods check assumptions in statistical models.
 Graphical statistical methods communicate the results of an analysis.
 Graphical statistical methods communicate the results of an analysis.
Terms

histogram
a representation of tabulated frequencies, shown as adjacent rectangles, erected over discrete intervals (bins), with an area equal to the frequency of the observations in the interval

scatter plot
A type of display using Cartesian coordinates to display values for two variables for a set of data.

box plot
A graphical summary of a numerical data sample through five statistics: median, lower quartile, upper quartile, and some indication of more extreme upper and lower values.
Full Text
Statistical graphics are used to visualize quantitative data. Whereas statistics and data analysis procedures generally yield their output in numeric or tabular form, graphical techniques allow such results to be displayed in some sort of pictorial form. They include plots such as scatter plots , histograms, probability plots, residual plots, box plots, block plots and biplots.
An example of a scatter plot
A scatter plot helps identify the type of relationship (if any) between two variables.
Exploratory data analysis (EDA) relies heavily on such techniques. They can also provide insight into a data set to help with testing assumptions, model selection and regression model validation, estimator selection, relationship identification, factor effect determination, and outlier detection. In addition, the choice of appropriate statistical graphics can provide a convincing means of communicating the underlying message that is present in the data to others.
Graphical statistical methods have four objectives:
• The exploration of the content of a data set
• The use to find structure in data
• Checking assumptions in statistical models
• Communicate the results of an analysis.
If one is not using statistical graphics, then one is forfeiting insight into one or more aspects of the underlying structure of the data.
Statistical graphics have been central to the development of science and date to the earliest attempts to analyse data. Many familiar forms, including bivariate plots, statistical maps, bar charts, and coordinate paper were used in the 18^{th} century. Statistical graphics developed through attention to four problems:
• Spatial organization in the 17^{th} and 18^{th} century
• Discrete comparison in the 18^{th} and early 19^{th} century
• Continuous distribution in the 19^{th} century and
• Multivariate distribution and correlation in the late 19^{th} and 20^{th} century.
Since the 1970s statistical graphics have been reemerging as an important analytic tool with the revitalisation of computer graphics and related technologies.
Key Term Reference
 bivariate
 Appears in these related concepts: Graphing Bivariate Relationships, Lab 2: Regression (Textbook Cost), and Summary
 block
 Appears in these related concepts: Random Sampling, Randomized Block Design, and Comparing Three or More Populations: Randomized Block Design
 correlation
 Appears in these related concepts: Benefits of Globalization, Controlling for a Variable, and Descriptive and Correlational Statistics
 datum
 Appears in these related concepts: Change of Scale, Lab 1: Confidence Interval (Home Costs), and Type I and II Errors
 distribution
 Appears in these related concepts: Application of Knowledge, Monte Carlo Simulation, and Selling to Consumers
 exploratory data analysis
 Appears in these related concepts: Exploratory Data Analysis (EDA), Elements of a Hypothesis Test, and References
 factor
 Appears in these related concepts: Rational Algebraic Expressions, Factors, and Finding Factors of Polynomials
 mean
 Appears in these related concepts: Mean, Variance, and Standard Deviation of the Binomial Distribution, Averages, and Understanding Statistics
 outlier
 Appears in these related concepts: Fitting a Curve, Median, and Outliers
 plot
 Appears in these related concepts: Graphs for Quantitative Data, Plotting Points on a Graph, and Introduction to Bivariate Data
 probability
 Appears in these related concepts: Theoretical Probability, Rules of Probability for Mendelian Inheritance, and The Addition Rule
 quantitative
 Appears in these related concepts: Preparing the Research Report, Overview of the IMRAD Model, and Math Review
 regression
 Appears in these related concepts: Making a Box Model, Standard Error, and Coefficient of Determination
 residual
 Appears in these related concepts: Plotting the Residuals, Models with Both Quantitative and Qualitative Variables, and Degrees of Freedom
 residuals
 Appears in these related concepts: Two Regression Lines, Inferences of Correlation and Regression, and Midterm elections and unemployment
 statistics
 Appears in these related concepts: Communicating Statistics, Population Demography, and Basic Inferential Statistics
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