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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

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

bell curve
In mathematics, the bellshaped curve that is typical of the normal distribution.
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 :
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:
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 this related concepts: Change of Scale, Comparing Nested Models, and Controlling for a Variable
 dependent variable
 Appears in this related concepts: Evaluating Model Utility, Formulating the Hypothesis, and Experimental Research
 distribution
 Appears in this related concepts: Application of Knowledge, Interpreting Distributions Constructed by Others, and Selling to Consumers
 error
 Appears in this related concepts: Estimating the Accuracy of an Average, Estimation, and Precise Definition of a Limit
 experiment
 Appears in this related concepts: Experiments, Primary Market Research, and Descriptive and Correlational Statistics
 graph
 Appears in this related concepts: Graphing on Computers and Calculators, Reading Points on a Graph, and Graphing Equations
 independent
 Appears in this related concepts: Regression Analysis for Forecast Improvement, The Rise of Independents, and Unions and Intersections
 independent variable
 Appears in this related concepts: Experimental Design, Graphing Functions, and Converting between Exponential and Logarithmic Equations
 normal distribution
 Appears in this related concepts: Shapes of Sampling Distributions, The Average and the Histogram, and Standard Deviation: Definition and Calculation
 plot
 Appears in this related concepts: Plotting Points on a Graph, Guidelines for Plotting Frequency Distributions, and Using a Statistical Calculator
 polynomial
 Appears in this related concepts: Linear and Quadratic Functions, The Remainder Theorem and Synthetic Division, and Polynomials: Introduction, Addition, and Subtraction
 scatter plot
 Appears in this related concepts: Graphs for Quantitative Data, Plotting the Residuals, and Statistical Graphics
 slope
 Appears in this related concepts: Equations of Lines and Planes, Tangent Planes and Linear Approximations, and Derivatives and Rates of Change
 statistics
 Appears in this related concepts: What Is Statistics?, Understanding Statistics, and Population Demography
 trend
 Appears in this related concepts: Interpreting Ratios and Other Sources of Company Information, Line of Best Fit, and Selected Financial Ratios and Analyses
 variable
 Appears in this related concepts: Related Rates, Calculating the NPV, and Fundamentals of Statistics
Sources
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Cite This Source
Source: Boundless. “Plotting Lines.” Boundless Statistics. Boundless, 03 Jul. 2014. Retrieved 27 May. 2015 from https://www.boundless.com/statistics/textbooks/boundlessstatisticstextbook/visualizingdata3/graphingdata19/plottinglines954414/