Line chart

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This simple graph shows data over intervals with connected points

A line chart or line graph is a type of chart which displays information as a series of data points called 'markers' connected by straight line segments.[1] 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 x-axis value) and joined with straight line segments. Line Charts show how a particular data changes at equal intervals of time. 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. [2]

Structure

A line chart is typically drawn bordered by two perpendicular lines, called axes. The horizontal axis is called the x-axis and the vertical axis is called the y-axis. To aid visual measurement, there may be additional lines drawn parallel to 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 y-axis represents the dependent variable and the x-axis (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 y-axis and quantity two along the x-axis.

The individual axes represent number lines and so may contain small marks, called ticks, indicating significant values on the line. The ticks may be annotated with the value they represent. A short description of the axis is often used to annotate each axis, usually in the pattern ``Physical Quantity (physical unit). These annotations are called labels.

The chart may contain an overall description called a title, and if the chart contains more than one line, it may also contain a list describing each line, called a key or a legend.

Finally, the data to be presented is plotted at the intersection of the (imaginary) perpendicular lines extending from the axes, and straight line segments are drawn between those intersection points.

Example

In the experimental sciences, 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 by a data table such as the following:

Graph of Speed Vs Time
Elapsed Time (s) Speed (m s−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 can be a poor way to understand 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. Such a visualisation appears in the figure to the right.

Mathematically, if we denote time by the variable t, and speed by v, then the function plotted in the graph would be denoted v(t) indicating that v (the dependent variable) is a function of t.

Best-fit

Charts often include 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.

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:

  1. It is highly improbable that the discontinuities in the slope of the best-fit 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 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.

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. Such curve fitting functionality is often found in graphing software or spreadsheets. Best-fit curves may vary from simple linear equations to more complex quadratic, polynomial, exponential, and periodic curves.[3]

See also

Wikimedia Commons has media related to Line charts.

References

  1. ↑ Burton G. Andreas (1965). Experimental psychology. p.186
  2. ↑ Neil J. Salkind (2006). Statistics for People who (think They) Hate Statistics: The Excel Edition. page 106.
  3. ↑ "Curve fitting". The Physics Hypertextbook. 
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