Mathematics
Tables and Graphs
Tables and graphs are visual representations of data used to organize and present information in a clear and concise manner. Tables display data in rows and columns, while graphs visually illustrate relationships and trends through various types such as bar graphs, line graphs, and pie charts. Both tables and graphs are essential tools for analyzing and interpreting mathematical data.
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6 Key excerpts on "Tables and Graphs"
eBook - PDF- Doug French(Author)
- 2004(Publication Date)
- Continuum(Publisher)
Chapter 6 Functions and Graphs Harnessing this new power [of computer technology] within mathematics and school mathematics is the challenge for the 21st century. (RS/JMC, 1997, p. 6) STRAIGHT-LINE GRAPHS Straight-line graphs were discussed in Chapter 3 as one of a number of ways of introducing algebraic ideas and symbols. They are particularly attractive in this respect because they provide a ready link between numbers, symbols and pictures. An equation provides a way of encapsulating the patterns in the co-ordinates of a set of points that lie on a straight line by acting as a unique label which highlights key properties. Although a graph is an abstract representation it has a visual appeal and looks interesting, particularly when a family of related graphs is depicted. Students need to understand the links between the equation, the table of values or set of co-ordinates and the graph, and to be able to move fluently between these different representa-tions. In Chapter 3 it was suggested that introductory work on straight-line graphs should be confined to positive whole numbers and should begin by looking at a set of points on a straight line, using the pattern in the numbers to determine the equation of the line. This builds on the idea of representing the terms of a linear sequence algebraically and makes clear from the start where the equation comes from and what it means. Text books often start with equations and show students how to produce a table of values and then plot the corresponding lines. Whilst this may seem simpler as it is a more routine task, it starts from something that is unfamiliar, namely the equation, which can set up an immediate barrier because it looks strange and new and seems to have appeared for no apparent reason. Co-ordinates and their graphical representation should already be familiar and therefore provide a more reassuring start to a new idea.
eBook - PDFMathematical Literacy NQF4 SB
TVET FIRST
- K van Niekerk O Roberts(Author)
- 2017(Publication Date)
- Macmillan(Publisher)
Topic 4: Patterns, relationships and representations 232 Module 12 Topic 4: Patterns, relationships and representations Tables, graphs and formulae in the workplace Module 12 Learning Outcomes In this module, you will: • Move between representations of relationships as follows: ¢ Complete a table of values by reading values from the graph. ¢ Complete a table of values from given formulae and/or descriptions of relationships. • Draw graphs of one or two relationships on a system of axes by: ¢ Plotting points from a given table of values. ¢ Plotting points from values calculated using given equations. ¢ Constructing axes with an appropriate scale chosen for both the vertical and horizontal axes. ¢ Labelling the vertical and horizontal axes and the graph appropriately. • Identify and distinguish between dependent and independent variables. • Identify and select the following information when working with relationships represented in tables, equations, graphs and formulae: ¢ Dependent variables for given independent variables. ¢ Independent variables for given dependent variables. • Describe relationships represented in tables and/or graphs for: ¢ Direct/linear relationships. ¢ Indirect/inverse relationships. • Use formulae supplied to determine: ¢ The value of the dependent variable for given value(s) of the independent variable using substitution. ¢ The value of the independent variable for given value(s) of the dependent variable using simple algebraic manipulation to solve only linear equations. Unit 12.1 Reading values off graphs A graph shows a number pattern by giving the input numbers on one axis and the output numbers on the other axis. The shape of the graph shows how the numbers change in relation to each other. We usually put the independent variable on the horizontal axis, and the dependent on the vertical axis.
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.
eBook - PDFPrecalculus
Functions and Graphs
- Earl Swokowski, Jeffery Cole(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
81 2.1 Rectangular Coordinate Systems 2.2 Graphs of Equations 2.3 Lines 2.4 Definition of Function 2.5 Graphs of Functions 2.6 Quadratic Functions 2.7 Operations on Functions THE MATHEMATICAL TERM function (or its Latin equivalent) dates back to the late seventeenth century, when calculus was in the early stages of development. This important concept is now the backbone of advanced courses in mathematics and is indispensable in every field of science. In this chapter we study properties of functions using algebraic and graphical methods that include plotting points, determining sym-metries, and making horizontal and vertical shifts. These techniques are adequate for obtaining rough sketches of graphs that help us understand properties of functions; modern-day methods, however, employ sophisticated computer software and advanced mathematics to generate extremely accurate graphical representations of functions. Functions and Graphs 2 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. In Section 1.1 we discussed how to assign a real number (coordinate) to each point on a line. We shall now show how to assign an ordered pair s a , b d of real numbers to each point in a plane. Although we have also used the notation s a , b d to denote an open interval, there is little chance for confusion, since it should always be clear from our discussion whether s a , b d represents a point or an interval.
No longer available |Learn moreSingle Case Research Methodology
Applications in Special Education and Behavioral Sciences
- Jennifer R. Ledford, David L. Gast, Jennifer R. Ledford, David L. Gast(Authors)
- 2018(Publication Date)
- Taylor & Francis(Publisher)
Graphic Displays of Data Types of Graphic Displays Line Graphs Bar Graphs Cumulative Graphs Semi-logarithmic Charts Guidelines for Selecting and Constructing Graphic Displays Figure Selection Graph Construction Data Presentation Using Computer Software to Construct Graphs Tables Summary Important Terms graphic display, abscissa, ordinate, origin, tic marks, axis labels, condition, phase, condition labels, figure caption, line graph, bar graph, cumulative graph, semi-logarithmic chart, scale break, blocking 7 Visual Representation of Data Amy D. Spriggs, Justin D. Lane, and David L. Gast Graphs should represent complex information without distortion, and should serve a clear pur- pose (Tufte, 2001). They should “induce the reader to think about the substance rather than about methodology, graphic design, the technology of graphic production, or something else” (Tufte, 2001, p. 1). Maximizing the impact of your data while minimizing consumer focus on “something else” can be done by following guidelines for graphing data that come from pro- fessional organizations (e.g., American Psychological Association [APA]), historical precedent, and empirical knowledge (i.e., research). In single case design (SCD) research, graphic displays are not only a way to share your outcomes with consumers of your research (as is also common in between-groups studies), but also to enable you to make formative decisions throughout the process of the study. Thus, well-designed graphics are essential in good SCD research. 158 • Amy D. Spriggs et al. Graphic displays (e.g., line graphs, bar graphs, cumulative graphs) and tables serve two basic purposes. First, they assist in organizing data during the data collection process, which facilitates formative evaluation. Second, they provide a detailed summary and description of behavior over time, which allows readers to analyze the relation between independent and dependent variables.
eBook - PDFMathematics NQF2 SB
TVET FIRST
- M Van Rensburg, I Mapaling A Thorne(Authors)
- 2017(Publication Date)
- Macmillan(Publisher)
58 Module 3 Topic 2: Functions and algebra Graphs of functions Module 3 Learning Outcomes This module will show you how to do the following: • Unit 3.1: Generate graphs by means of point-by-point plotting using, or supported by, available technology. • Unit 3.2: Define functions. • Unit 3.2: Identify characteristics of functions. • Units 3.3 to 3.7: Generalise the effects of the parameters a and q on the generated graphs of functions. • Units 3.3 to 3.7: Use the generated graphs to make and test conjectures. • Units 3.3 to 3.7: Sketch graphs and find equations of graphs for certain functions. Unit 3.1: Introduction to graphs A graph is a useful way to represent data visually and it enables us to easily see the relationship between the variables we are considering. A graph is drawn on the Cartesian plane , which is also known as a coordinate plane. –5 –4 –3 –2 –1 1 2 3 4 5 5 4 3 2 1 –1 –2 –3 –4 –5 Quadrant I Quadrant II Quadrant IV Quadrant III y x 0 – y – x Figure 3.1: The Cartesian plane This plane consists of a horizontal and vertical number line, with a positive and negative section that cross each other at zero. This point of intersection is called the origin . When the two axes cross each other, they form four quadrants , as shown in Figure 3.1. These are numbered I, II, III and IV in an anti-clockwise direction. The independent variable (usually x ) is plotted on the horizontal axis and the dependent variable (usually y ) is plotted on the vertical axis. It is important that the units of each axis are spaced at equal distances and marked off according to a scale when plotting graphs to ensure accuracy.
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