Mathematics
Charts and Diagrams
Charts and diagrams are visual representations of data or mathematical concepts. They are used to organize and present information in a clear and concise manner, making it easier to understand complex relationships and patterns. In mathematics, charts and diagrams are commonly used to illustrate mathematical functions, relationships, and statistical data.
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9 Key excerpts on "Charts and Diagrams"
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.
eBook - ePubStatistics for Psychologists
An Intermediate Course
- Brian S. Everitt(Author)
- 2001(Publication Date)
- Taylor & Francis(Publisher)
According to Chambers, Cleveland, Kleiner, and Tukey (1983), “there is no statistical tool that is as powerful as a well chosen graph,” and although this may be a trifle exaggerated, there is considerable evidence that there are patterns in data, and relationships between variables, that are easier to identify and understand from graphical displays than from possible alternatives such as tables. For this reason researchers who collect data are constantly encouraged by their statistical colleagues to make both a preliminary graphical examination of their data and to use a variety of plots and diagrams to aid in the interpretation of the results from more formal analyses. The prime objective of this approach is to communicate both to ourselves and to others.But just what is a graphical display? A concise description is given by Tufte (1983).Data graphics visually display measured quantities by means of the combined use of points, lines, a coordinate system, numbers, symbols, words, shading and colour.Tufte estimates that between 900 billion (9 × 1011 ) and 2 trillion (2 × 1012 ) images of statistical graphics are printed each year.Some of the advantages of graphical methods have been listed by Schmid (1954).- In comparison with other types of presentation, well-designed charts are more effective in creating interest and in appealing to the attention of the reader.
- Visual relationships as portrayed by charts and graphs are more easily grasped and more easily remembered.
- The use of charts and graphs saves time, because the essential meaning of large measures of statistical data can be visualized at a glance (like Chambers and his colleagues, Schmid may perhaps be accused of being prone to a little exaggeration here).
- Charts and graphs provide a comprehensive picture of a problem that makes for a more complete and better balanced understanding than could be derived from tabular or textual forms of presentation.
- Charts and graphs can bring out hidden facts and relationships and can stimulate, as well as aid, analytical thinking and investigation.
eBook - PDF- Daniel Callison, Annette Lamb(Authors)
- 2012(Publication Date)
- Libraries Unlimited(Publisher)
Types of Graphics 27 Diagrams Diagrams often show the relationships among parts and wholes such as the anatomy of the human body or the operation of a machine. Technology has made the creation of diagrams much easier. A simplified visual representation of an object, concept, or idea is often called a diagram. Usually a line drawing, diagrams provide a quick reference to information that would otherwise be complex and difficult to understand. I II III 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 28 27 26 25 24 23 22 18 17 16 21 20 19 29 From the technical drawings of Leonardo DaVinci to the schematic etched in the Pioneer spacecraft, diagrams are classic tools to visualize concepts. The ability to show complex concepts using simple lines and shapes is the key to effective diagrams. 28 Graphic Inquiry There are many different types of diagrams.
eBook - PDF- UNESCO Office Bangkok and Regional Bureau for Education in Asia and the Pacific, UNICEF. East Asia and the Pacific Regional Office (Thailand)(Authors)
- 2019(Publication Date)
- UNESCO(Publisher)
Charts are especially useful for: ● Faster understanding of numbers; ● Recognizing distributions in data, showing patterns and comparing trends; ● Easing comparing numerical information; ● Allowing information to be presented in various ways. There are numerous ways of visually presenting statistical information. In short, the main purpose of charts is to visually impart information that cannot be easily read and interpreted from a table of data. In other words, the advantage of charts is that they are visually more attractive than tables, and can ease presentations. With the help of computer software packages, graphical visualization of data can be made in a variety of ways. As mentioned, charts are not suitable for communicating detailed and precise information, and can be time-consuming and expensive to design. The following section will explain a few charts and provide a structured overview (Figures 19 and 20) to help decide on which chart is appropriate to pick for which purpose. 4.3.1 Explaining when to use certain charts LINE CHART: These are used to track changes over short and long periods of time. When smaller changes exist, line graphs are better to use than bar graphs. Line graphs can also be used to compare changes over the same period of time for more than one group. BAR CHART: These are used for categorical data or metric data that are transformed into categorical data and are used to compare things between different groups, or to track changes over time Categories are shown on the horizontal axis. Frequency, percentage, or proportion is shown on the vertical axis. Bars are separated from each other to emphasize the distinctness of the categories. The bars must be of the same width. The length of each bar is proportional to the frequency, percentage, or proportion in the category. Levels ought to be provided on both axes. However, when trying to measure change over time, bar graphs are best when the changes are larger.
- 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 - 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.
- Mary M. Hatfield, Nancy Tanner Edwards, Gary G. Bitter, Jean Morrow(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
Source: NCTM Principles and Standards for School Mathematics (2000, pages 400–401). 416 CHAPTER 15 Data Analysis, Statistics, and Probability children learn to refine their questions, collect data, and organize and display their data in ways that will help them to answer the question they posed (Friel, 2003). By the time students reach middle school, their questions will expand from seeking informa- tion about a single population to asking about relationships among several populations or rela- tionships between two variables in a given popula- tion. Their data collection methods expand to include experiments that require controlling vari- ables or choosing samples. Their methods for representing data will also increase to include stem and leaf graphs, box and whisker plots, and relative frequency bar graphs (Friel, 2003). Let’s take time now to look at ways to repre- sent data. Data AnalysisöGraphing Graphing presents data in a concise and visual way that allows relationships in the data to be seen more easily. Students need to learn how to tally information, arrange data in a table, and display the information visually using a graph. Students can be introduced to graphing as a means of repre- senting or organizing data early in the elementary years. Young children can make their own graphs and will benefit from collecting and organizing the information. A suggested developmental sequence for presenting graphs is generally followed in text- books for young children. 1. Real graphs: actual objects to compare two or three groups. 2. Picture graphs: pictures or models to represent real things to compare two or three groups. 3. Real graphs: actual objects to compare up to four groups. 4. Picture graphs: pictures or models to compare up to four groups. 5. Symbolic graphs: most abstract using only symbols.
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 - ePub- Heather Cooke(Author)
- 2003(Publication Date)
- Routledge(Publisher)
5Mathematical communication
This chapter is about mathematical communication in speech and text, using words and symbols, and is also about various forms of visual representations, including diagrams and graphs. It includes discussion of both speaking and writing about mathematical activity, and considers the purposes and audiences for which mathematical work is produced, as well as the conventions used. It will help you to make sense of other people's mathematical communication and to make your own more effective.REPRESENTING MATHEMATICS
Mathematics is abstract in that it is about ideas and relationships, but in order to be communicated these have to be expressed and represented in various ways. Part of learning mathematics is becoming fluent at understanding and using these representations, both for your own use and for communicating with other people (tutors, fellow students, examiners, text authors).Mathematical communication has three main ingredients: symbols, words and images (see Figure 5.1 ).Figure 5.1 Ways of communicating mathematics.Each of these three contributes to effective understanding and communication, although for any particular topic, purpose or audience one may convey greater meaning than the others. These different ways of communicating mathematics all have their uses, but it is important to be aware of their strengths and limitations. In an important sense, mathematics is a language with a formal grammar, so in mathematical communication involving verbal or symbolic text there are generally accepted conventions (for example, the use of logical connectives like ‘and’, ‘or’, ‘since’ or ‘therefore’ in correct mathematical sentences), which must be used to ensure successful and accurate communication. The combination of symbols is governed by accepted notational rules.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
