Mathematics
Statistical Graphs
Statistical graphs are visual representations of data that allow for easy interpretation and analysis. They include various types such as bar graphs, line graphs, and pie charts, each suited for different data sets and purposes. These graphs are essential tools in mathematics for displaying and understanding numerical information.
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11 Key excerpts on "Statistical Graphs"
eBook - PDF- Barbara Illowsky, Susan Dean(Authors)
- 2020(Publication Date)
- Openstax(Publisher)
In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called descriptive statistics. You will learn how to calculate and, even more important, how to interpret these measurements and graphs. A statistical graph is a tool that helps you learn about the shape or distribution of a sample or a population. A graph can be a more effective way of presenting data than a mass of numbers because we can see where data values cluster and where there are only a few data values. Newspapers and the internet use graphs to show trends and to enable readers to compare facts and figures quickly. Statisticians often graph data first to get a picture of the data. Then more formal tools may be applied. Some of the types of graphs that are used to summarize and organize data are the dot plot, the bar graph, the histogram, the stem-and-leaf plot, the frequency polygon—a type of broken line graph—the pie chart, and the box plot. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs as well as frequency polygons, time series graphs, and dot plots. Our emphasis will be on histograms and box plots. NOTE This book contains instructions for constructing a histogram and a box plot for the TI-83+ and TI-84 calculators. The Texas Instruments (TI) website (http://education.ti.com/educationportal/sites/US/sectionHome/ support.html) provides additional instructions for using these calculators. 2.1 | Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs One simple graph, the stem-and-leaf graph or stemplot, comes from the field of exploratory data analysis. It is a good choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The stem consists of the leading digit(s), while the leaf consists of a final significant digit. For example, 23 has stem two and leaf three. The number 432 has stem 43 and leaf two.
eBook - PDF- John Peterson, Robert Smith(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
Statistical data are often time-consuming and difficult to interpret. Graphs present data in simple and concise picture form. Data, when graphed, often can be interpreted more quickly and are easier to understand. The Cartesian coordinate system was studied in Unit 16, The Cartesian Coordi-nate System and Graphs of Linear Equations . Now, three different types of graphs will be shown. Bar graphs, circle graphs or charts, and line graphs are three common ways of picturing statistical data. These three types of graphs can be seen on television, in magazines, books, and manuals, and, almost everyday, in newspapers. 31–1 TYPES AND STRUCTURE OF GRAPHS Many kinds of graphs are designed for special-purpose applications. An understanding of basic graphs, such as bar graphs, circle graphs and line graphs, provides a background for the reading and construction of other more specialized graphs. Circle graphs are constructed with the use of a protractor. Protractors were discussed in Unit 20, Angular Measure . UNIT 31 GRAPHS: BAR, CIRCLE, AND LINE Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Unit 31 GRAPHS: BAR, CIRCLE, AND LINE 751 Bar graphs are used to compare quantities. The bars can be either horizontal or ver-tical, with the length or height of the bar representing the quantity. The quantities do not have to add up to 100%. One variation of the bar graph is the stacked bar graph. In a stacked bar graph each bar is divided into sub-parts. 31–2 BAR GRAPHS Graph paper, which is also called coordinate and cross-section paper, is used for graphing data.
eBook - PDF- D.R. Helsel, R.M. Hirsch(Authors)
- 1993(Publication Date)
- Elsevier Science(Publisher)
Graphical Data Analvsis Perhaps it seems odd that a chapter on graphics appears at the front of a text on statistical methods. We believe this is very appropriate, as graphs provide crucial information to the data analyst which is difficult to obtain in any other way. For example, figure 2.1 shows eight scatterplots, all of which have exactly the same correlation coefficient. Computing statistical measures without looking at a plot is an invitation to misunderstanding data, as figure 2.1 illustrates. Graphs provide visual summaries of data which more quickly and completely describe essential information than do tables of numbers. Graphs are essential for two purposes: 1. to provide insight for the analyst into the data under scrutiny, and 2. to illustrate important concepts when presenting the results to others. The first of these tasks has been called exuloratorv data analvsis (EDA), and is the subject of this chapter. EDA procedures often are (or should be) the 'first look at data. Patterns and theories of how the system behaves are developed by observing the data through graphs. These are inductive procedures - the data are summarized rather than tested. Their results provide guidance for the selection of appropriate deductive hypothesis testing procedures. Once an analysis is complete, the findings must be reported to others. Whether a written report or oral presentation, the analyst must convince the audience that the conclusions reached are supported by the data. No better way exists to do this than through graphics. Many of the same graphical methods which have concisely summarized the information for the analyst will also provide insight into the data for the reader or audience. The chapter begins with a discussion of graphical methods for analysis of a single data set. Two methods are particularly useful: boxplots and probability plots. Their construction is presented in detail. Next, methods for comparison of two or more groups of data are discussed.
eBook - PDF- Roxy Peck, Chris Olsen, , Tom Short, Roxy Peck, Chris Olsen, Tom Short(Authors)
- 2019(Publication Date)
- Cengage Learning EMEA(Publisher)
● ● How a graphical display of numerical data is described in terms of center, shape, and spread. ● ● How a scatterplot is used to investigate the relationship between two numerical variables. ● ● How a time series plot is used to investigate a trend over time. Students will be able to: ● ● Construct and interpret graphical displays of categorical data: pie charts and seg-mented bar charts. istock.com/florintt 9,179 6,880 9,884 7,577 9,070 9,128 11,106 11,670 4,438 7,011 9,263 6,915 13,387 8,745 7,879 8,011 9,490 8,162 9,186 8,942 11,670 11,708 10,701 7,175 8,178 6,443 7,446 5,298 14,986 13,021 6,262 7,647 6,944 7,208 9,757 6,680 9,406 13,516 11,321 11,791 8,273 8,932 8,091 6,140 15,062 11,669 7,782 6,900 8,504 4,179 Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. CHAPTER 3 Graphical Methods for Describing Data 78 ● ● Construct and interpret graphical displays of numerical data: stem-and-leaf displays, histograms, and relative frequency histograms. ● ● Construct and interpret graphical displays designed to compare groups: comparative bar charts and comparative stem-and-leaf displays. ● ● Construct and interpret a scatterplot of bivariate numerical data. ● ● Construct and interpret a time series plot. SECTION 3.1 Displaying Categorical Data: Comparative Bar Charts and Pie Charts Comparative Bar Charts In Chapter 1 we saw that categorical data could be summarized in a frequency distribu-tion and displayed graphically using a bar chart. Bar charts can also be used to give a visual comparison of two or more groups.
eBook - PDFStatistics
Learning from Data
- Roxy Peck, Tom Short(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
44 Graphical Methods for Describing Data Distributions S E C T I O N II DESCRIBING DATA DISTRIBUTIONS 2 Preview Chapter Learning Objectives 2.1 Selecting an Appropriate Graphical Display 2.2 Displaying Categorical Data: Bar Charts and Comparative Bar Charts 2.3 Displaying Numerical Data: Dotplots, Stem-and-Leaf Displays, and Histograms 2.4 Displaying Bivariate Numerical Data: Scatterplots and Time Series Plots 2.5 Graphical Displays in the Media 2.6 Avoid These Common Mistakes Chapter Activities Explorations in Statistical Thinking Are You Ready to Move On? Chapter 2 Review Exercises Technology Notes pollockg/Shutterstock.com PREVIEW When you carry out a statistical study, you hope to learn from the data you collect. But it is often difficult to “see” the information in data if it is presented as just a list of observations. An important step in the data analysis process involves summarizing data graphically and numerically. This makes it easier to see important characteristics of the data and is an effective way to communicate what you have learned. Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 45 Conceptual Understanding After completing this chapter, you should be able to C1 Distinguish between categorical and numerical data. C2 Distinguish between discrete and continuous numerical data. C3 Understand that selecting an appropriate graphical display depends on the number of variables in the data set, the data type, and the purpose of the graphical display.
eBook - PDF- Barbara Illowsky, Susan Dean(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
CHAPTER REVIEW 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs A stem-and-leaf plot is a way to plot data and look at the distribution. In a stem-and-leaf plot, all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends. That is, finding a general pattern in data sets including temperature, sales, employment, company profit or cost over a period of time. A bar graph is a chart that uses 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 (grouped bar graphs), and others show the bars divided into subparts to show cumulative effect (stacked bar graphs). Bar graphs are especially useful when categorical data is being used. 2.2 Histograms, Frequency Polygons, and Time Series Graphs A histogram is a graphic version of a frequency distribution. The graph consists of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Histograms are typically used for large, continuous, quantitative data sets. A frequency polygon can also be used when graphing large data sets with data points that repeat. The data usually goes on y-axis with the frequency being graphed on the x-axis. Time series graphs can be helpful when looking at large amounts of data for one variable over a period of time. 2.3 Measures of the Location of the Data The values that divide a rank-ordered set of data into 100 equal parts are called percentiles.
eBook - PDF- Dawn A. Willoughby(Author)
- 2016(Publication Date)
- Wiley(Publisher)
C H A P T E R • 4 Graphical Representation OBJECTIVES This chapter explains how to: • construct charts to display qualitative data - bar chart - pie chart • draw graphs to display quantitative data - scatter diagram - histogram - time series plot - stem and leaf diagram • visually compare multiple data sets using a single graph or chart • understand some of the ways that diagrams can be misinterpreted • choose the appropriate diagram for your data KEY TERMS bar chart histogram pie chart scatter diagram stem and leaf diagram time series plot Introduction Graphs and charts provide a useful method for showing what your data mean in a visual way. When you are working with a small amount of data, a simple table may be sufficient for presenting the data and results. However, if you have collected large sets of data using a questionnaire or through interviewing then a diagram will help you to summarise your results in a concise way, highlight important facts and patterns in the data and describe comparisons between different data sets. When information is presented in a visual form, it is more likely that people will be able to understand and remember the results you are trying to show about the data you have collected. Whether you need to describe your results by writing a report, displaying details on a website or giving a verbal presentation to an audience, the use of graphs and charts is not always straightforward. You should aim to choose a diagram that is appropriate for the data you have collected, the audience you are writing for, and the type of results to be shown. It is also important that diagrams are drawn carefully and accurately so that the audience does not misinterpret their meaning because of the way in which the data are presented. Bar Charts Qualitative data are often displayed using a bar chart. This is a diagram drawn with rectangular bars where each bar represents a different category in the data set.
- Ken Black, Tiffany Bayley, Ignacio Castillo(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
instamatics/Getty Images 22 CHAPTER 2 Visualizing Data with Charts and Graphs Introduction In this era of seemingly boundless big data, the application of business analytics has great potential to unearth business knowledge and intelligence that can substantially improve busi- ness decision-making. A key objective of business analytics is to convert data into deeper and broader actionable insights and understandings for all aspects of business. One of the first steps is to visualize the data through graphs and charts, thereby providing business analysts with an overview of the data and a glimpse into any underlying relationships. In this chapter, we will study how to visually represent data in order to convey infor- mation that can unlock potentialities for making better business decisions. Using visuals to convey information hidden in the data allows a broader audience with a wide range of back- grounds to understand its meaning. Data visualization tools can reveal surprising patterns and connections, making data-driven insights accessible to people at all levels of an organiza- tion. In business decision-making, graphical depictions of data are often much more effective communication tools than tables of numbers. In addition, key characteristics of graphs often suggest appropriate choices among potential numerical methods (discussed in later chapters) for analyzing data. A first step in exploring and analyzing data is to reduce important and sometimes expan- sive data to a graphic picture that is clear, concise, and consistent with the message of the original data. Converting data to graphics can be creative and artful. This chapter focuses on graphical tools for summarizing and presenting data.
eBook - PDFBeginning R
The Statistical Programming Language
- Mark Gardener(Author)
- 2012(Publication Date)
- Wrox(Publisher)
Introduction to Graphical Analysis WHAT YOU WILL LEARN IN THIS CHAPTER: ➤ How to create a range of graphs to summarize your data and results ➤ How to create box-whisker plots ➤ How to create scatter plots, including multiple correlation plots ➤ How to create line graphs ➤ How to create pie charts ➤ How to create bar charts ➤ How to move graphs from R to other programs and save graphs as files on disk Graphs are a powerful way to present your data and results in a concise manner. Whatever kind of data you have, there is a way to illustrate it graphically. A graph is more readily understandable than words and numbers, and producing good graphs is a vital skill. Some graphs are also useful in examining data so that you can gain some idea of patterns that may exist; this can direct you toward the correct statistical analysis. R has powerful and flexible graphical capabilities. In general terms, R has two kinds of graphical commands: some commands generate a basic plot of some sort, and other commands are used to tweak the output and to produce a more customized finish. You have already encountered some graphical commands in previous chapters. This chapter focuses on some of the basic graph types that you may typically need to create. In Chapter 11, you will revisit the graphical commands and add a variety of extras to lift your graphs from the merely adequate, to fully polished publication quality material. BOX-WHISKER PLOTS The box-whisker plot (often abbreviated to boxplot) is a useful way to visualize complex data where you have multiple samples. In general, you are looking to display differences 7 216 x CHAPTER 7 INTRODUCTION TO GRAPHICAL ANALYSIS between samples. The basic form of the box-whisker plot shows the median value, the quartiles (or hinges), and the max/min values. This means that you get a lot of information in a compact manner. The box-whisker plot is also useful to visualize a single sample because you can show outliers if you choose.
eBook - PDFExperimental Methods for Science and Engineering Students
An Introduction to the Analysis and Presentation of Data
- Les Kirkup(Author)
- 2019(Publication Date)
- Cambridge University Press(Publisher)
3 Graphical Presentation of Data 3.1 Overview: The Importance of Graphs Our ability to absorb and process information when it is presented in the form of a picture is so good that it is natural to exploit this talent when analysing data obtained from an experiment. When data are presented pictorially, trends or fea- tures in the data can be detected that we would be unlikely to recognise if the data were given only in tabular form. This is especially true in situations where a set of data consists of hundreds or thousands of values, which is a common occurrence when a computer is used to assist in data gathering. Additionally, a pictorial representation of data in the form of a graph is an excellent way to summarise many of the important features of an experiment. A graph can indicate: (i) the quantities being studied (ii) the range of values obtained through measurement (iii) the uncertainty in each value (iv) the existence or absence of a trend in the data gathered (for example, plotted points may lie in a straight line or a curve, or may appear to be scattered randomly across the graph) (v) which plotted points do not follow the general trend exhibited by most of the data. x–y graphs (also known as scatter plots or Cartesian coordinate graphs) are used extensively in science and engineering to present experimental data, and it is those that we will concentrate on in this chapter. 3.2 Plotting Graphs An x–y graph possesses horizontal and vertical axes, referred to as the x and y axes, respectively. Each point plotted on the graph is specified by a pair of numbers termed the coordinates of the point. For example, point A in Figure 3.1 has the coordinates x = 20, y = 50. The coordinates of the point may be written in shorthand as (x,y), which in the case of point A on Figure 3.1 would be (20,50). To assist in the accurate plotting of data, graph paper may be used on which are drawn evenly spaced vertical and horizontal gridlines as shown in Figure 3.1.
- David Anderson, Dennis Sweeney, Thomas Williams, Jeffrey Camm(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 40 Chapter 2 Descriptive Statistics: Tabular and Graphical Displays Bar Charts and Pie Charts A bar chart is a graphical display for depicting categorical data summarized in a frequency, relative frequency, or percent frequency distribution. On one axis of the graph we specify the labels that are used for the classes (categories). A frequency, relative frequency, or percent frequency scale can be used for the other axis of the chart. Then, using a bar of fixed width drawn above or next to each class label, we extend the length of the bar until we reach the frequency, relative frequency, or percent frequency of the class. For categorical data, the bars should be separated to emphasize the fact that each class is separate. Figure 2.3 shows a bar chart of the frequency distribution for the 50 soft FIGURE 2.2 Relative Frequency and Percent Frequency Distributions of Soft Drink Purchases Constructed Using Excel’s Recommended PivotTables Tool FIGURE 2.3 Bar Chart of Soft Drink Purchases Frequency Soft Drink Coca-Cola Diet Coke Dr. Pepper Pepsi Sprite 20 0 2 4 6 8 10 12 14 16 18 Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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