Line chart
Encyclopedia
A line chart or line graph is a type of graph
, 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 an extension of a scatter graph, and is created by connecting a series of points that represent individual measurements with 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.
For example, if one were to collect data on the speed of a body at certain points in time, one could visualize the data by a data table such as the following:
The table "visualization" is a great way of displaying exact values, but a very bad way of understanding the underlying patterns that those values represent. Because of these qualities, the table display is often erroneously conflated with the data itself; whereas it is just another visualization of the data.
Understanding the process described by the data in the table is aided by producing a graph or line chart of Speed versus Time. In this context, Versus (or the abbreviations vs and VS), separates the parameters appearing in an X-Y (two-dimensional) graph. The first argument indicates the dependent variable, usually appearing on the Y-axis, while the second argument indicates the independent variable
, usually appearing on the X-axis. So, the graph of Speed versus Time would plot time along the x-axis and speed up the y-axis. Mathematically, if we denote time by the variable
, and speed by 
, then the function plotted in the graph would be denoted 
indicating that 
(the dependent variable) is a function of 
.
It is simple to construct a "best-fit" layer consisting of a set of line segments connecting adjacent data points; however, such a "best-fit" is usually not an ideal representation of the trend of the underlying scatter data for the following reasons:
A true best-fit layer should depict a continuous mathematical function whose parameters are determined by using a suitable error-minimization scheme, which appropriately weights the error in the data values.
In either case, the best-fit 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.
Graph of a function
In mathematics, the graph of a function f is the collection of all ordered pairs . In particular, if x is a real number, graph means the graphical representation of this collection, in the form of a curve on a Cartesian plane, together with Cartesian axes, etc. Graphing on a Cartesian plane is...
, which displays information as a series of data points connected by straight line segments. It is a basic type of chart
Chart
A chart is a graphical representation of data, in which "the data is represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart"...
common in many fields. It is an extension of a scatter graph, and is created by connecting a series of points that represent individual measurements with line segments. A line chart is often used to visualize a trend in data over intervals of time – a time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
– thus the line is often drawn chronologically.
Example
In the experimental sciences, data collected from experiments are often visualized by a graph that includes an overlaid mathematical function depicting the best-fit trend of the scattered data. This layer is referred to as a best-fit layer and the graph containing this layer is often referred to as a line 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 by a data table such as the following:
| Elapsed Time (s) | "Speed" (ms−1) |
|---|---|
| 0 | 0 |
| 1 | 3 |
| 2 | 7 |
| 3 | 12 |
| 4 | 20 |
| 5 | 30 |
| 6 | 45 |
The table "visualization" is a great way of displaying exact values, but a very bad way of understanding the underlying patterns that those values represent. Because of these qualities, the table display is often erroneously conflated with the data itself; whereas it is just another visualization of the data.
Understanding the process described by the data in the table is aided by producing a graph or line chart of Speed versus Time. In this context, Versus (or the abbreviations vs and VS), separates the parameters appearing in an X-Y (two-dimensional) graph. The first argument indicates the dependent variable, usually appearing on the Y-axis, while the second argument indicates the independent variable
Independent variable
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...
, usually appearing on the X-axis. So, the graph of Speed versus Time would plot time along the x-axis and speed up the y-axis. Mathematically, if we denote time by the variable
, and speed by , then the function plotted in the graph would be denoted indicating that (the dependent variable) is a function of .It is simple to construct a "best-fit" layer consisting of a set of line segments connecting adjacent data points; however, such a "best-fit" is usually not an ideal representation of the trend of the underlying scatter data for the following reasons:
- It is highly improbable that the discontinuities in the slope of the best-fit would correspond exactly with the positions of the measurement values.
- It is highly unlikely that the experimental error in the data is negligible, yet the curve falls exactly through each of the data points.
A true best-fit layer should depict a continuous mathematical function whose parameters are determined by using a suitable error-minimization scheme, which appropriately weights the error in the data values.
In either case, the best-fit layer can reveal trends in the data. Further, measurements such as the gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....
or the area under the curve can be made visually, leading to more conclusions or results from the data.
See also
- Fan chart (time series)Fan chart (time series)In time series analysis, a fan chart is a chart that joins a simple line chart for observed past data, by showing ranges for possible values of future data together with a line showing a central estimate or most likely value for the future outcomes...
- List of information graphics software