Plotting Lines
A line graph is a type of chart which displays information as a series of data points connected by straight line segments.
Learning Objective

Explain the principles of plotting a line graph
Key Points
 A line chart is often used to visualize a trend in data over intervals of time – a time series – thus the line is often drawn chronologically.
 A line chart is typically drawn bordered by two perpendicular lines, called axes. The horizontal axis is called the xaxis and the vertical axis is called the yaxis.
 Typically the yaxis represents the dependent variable and the xaxis (sometimes called the abscissa) represents the independent variable.
 In statistics, charts often include an overlaid mathematical function depicting the bestfit trend of the scattered data.
Terms

bell curve
In mathematics, the bellshaped curve that is typical of the normal distribution.

line
a path through two or more points (compare ‘segment'); a continuous mark, including as made by a pen; any path, curved or straight

gradient
of a function y = f(x) or the graph of such a function, the rate of change of y with respect to x, that is, the amount by which y changes for a certain (often unit) change in x
Full Text
A line graph is a type of chart which displays information as a series of data points connected by straight line segments. It is a basic type of chart common in many fields. It is similar to a scatter plot except that the measurement points are ordered (typically by their xaxis value) and joined with straight line segments. A line chart is often used to visualize a trend in data over intervals of time – a time series – thus the line is often drawn chronologically.
Plotting
A line chart is typically drawn bordered by two perpendicular lines, called axes. The horizontal axis is called the xaxis and the vertical axis is called the yaxis. To aid visual measurement, there may be additional lines drawn parallel either axis. If lines are drawn parallel to both axes, the resulting lattice is called a grid.
Each axis represents one of the data quantities to be plotted. Typically the yaxis represents the dependent variable and the xaxis (sometimes called the abscissa) represents the independent variable. The chart can then be referred to as a graph of quantity one versus quantity two, plotting quantity one up the yaxis and quantity two along the xaxis.
Example
In the experimental sciences, such as statistics, data collected from experiments are often visualized by a graph. For example, if one were to collect data on the speed of a body at certain points in time, one could visualize the data to look like the graph in :
Data Table
A data table showing elapsed time and measured speed.
The table "visualization" is a great way of displaying exact values, but can be a poor way to understand the underlying patterns that those values represent. Understanding the process described by the data in the table is aided by producing a graph or line chart of Speed versus Time:
Line chart
A graph of speed versus time
BestFit
In statistics, charts often include an overlaid mathematical function depicting the bestfit trend of the scattered data. This layer is referred to as a bestfit layer and the graph containing this layer is often referred to as a line graph.
It is simple to construct a "bestfit" layer consisting of a set of line segments connecting adjacent data points; however, such a "bestfit" is usually not an ideal representation of the trend of the underlying scatter data for the following reasons:
1. It is highly improbable that the discontinuities in the slope of the bestfit would correspond exactly with the positions of the measurement values.
2. It is highly unlikely that the experimental error in the data is negligible, yet the curve falls exactly through each of the data points.
In either case, the bestfit layer can reveal trends in the data. Further, measurements such as the gradient or the area under the curve can be made visually, leading to more conclusions or results from the data.
A true bestfit layer should depict a continuous mathematical function whose parameters are determined by using a suitable errorminimization scheme, which appropriately weights the error in the data values. Such curve fitting functionality is often found in graphing software or spreadsheets. Bestfit curves may vary from simple linear equations to more complex quadratic, polynomial, exponential, and periodic curves. The socalled "bell curve", or normal distribution often used in statistics, is a Gaussian function.
Key Term Reference
 datum
 Appears in these related concepts: Change of Scale, Controlling for a Variable, and Type I and II Errors
 dependent variable
 Appears in these related concepts: The Cartesian System, Converting between Exponential and Logarithmic Equations, and What is a Quadratic Function?
 distribution
 Appears in these related concepts: Application of Knowledge, Monte Carlo Simulation, and Selling to Consumers
 error
 Appears in these related concepts: Estimation, Precise Definition of a Limit, and Basic properties of point estimates
 experiment
 Appears in these related concepts: Experiments, Descriptive and Correlational Statistics, and Primary Market Research
 graph
 Appears in these related concepts: Graphical Representations of Functions, Graphing Equations, and Graphs of Equations as Graphs of Solutions
 independent
 Appears in these related concepts: Fundamentals of Probability, Unions and Intersections, and Party Identification
 independent variable
 Appears in these related concepts: Experimental Design, Formulating the Hypothesis, and Experimental Research
 normal distribution
 Appears in these related concepts: Shapes of Sampling Distributions, The Average and the Histogram, and Standard Deviation: Definition and Calculation
 plot
 Appears in these related concepts: Plotting Points on a Graph, Using a Statistical Calculator, and Introduction to Bivariate Data
 polynomial
 Appears in these related concepts: Domains of Rational and Radical Functions, Simplifying, Multiplying, and Dividing, and Partial Fractions
 scatter plot
 Appears in these related concepts: Graphs for Quantitative Data, Plotting the Residuals, and Statistical Graphics
 slope
 Appears in these related concepts: SlopeIntercept Equations, Rates of Change, and Slope
 statistics
 Appears in these related concepts: Communicating Statistics, Basic Inferential Statistics, and Understanding Statistics
 trend
 Appears in these related concepts: Interpreting Ratios and Other Sources of Company Information, Line of Best Fit, and Scanning and Analysis
 variable
 Appears in these related concepts: What is a Linear Function?, Math Review, and Introduction to Variables
Sources
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