Adjusting claims and hypothesis

An example of a comparative line graph.

Line graphs are a good way to compare anything between two or more variables. These are one of the easier types of graphs to look at because you can clearly see the changes in the line as time goes on. A line graph should never be used to show statistics at a set moment in time. A disadvantage of line graphs is it can be difficult to see exactly what number is being specified at a data point. If it is important that the numbers be easily read, they may be inserted within the graph at their respective data points. Since most line graphs are used to convey a trend over time, however, specific numbers are not always necessary.

Main things to be included in a line graph are as follows:

• Title: The most important thing (what is a chart without a title). Must be to the point.
• X-axis (Horizontal) and Y-axis (Vertical): Both axes should be labeled and provide units of measurement. They should extend slightly past the highest graphed value.
• Tick Marks: Use tick marks on both axes to show units. Make sure they are not cluttering the graph.
• Line: The line shows the actual data being displayed. It can be displayed as a single data point, data points with a line connecting the points, or as a single smooth line with no data points. Different colors can also be used to designate various elements.
• Source: Should be included if the source will not be obvious to readers.

Tips for making line graphs:

• Use different colors to ensure that the reader can distinguish between the lines. If you cannot use different colors, use different types of lines, for example, dots or dashes.
• If possible, start axes at zero to avoid misleading readers. If this is not possible, use hash marks to inform your readers that your graph does not start at zero.

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	18
5	30
6	45.6

The table representation of data 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

A parody line graph (1919) by William Addison Dwiggins.

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 table.

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.

References

1. Spear, Mary Eleanor (1952). Charting Statistics. New York: McGraw-Hill. p. 41. OCLC 166502.
2. Burton G. Andreas (1965). Experimental psychology. p.186
3. Michael Friendly (2008). "Milestones in the history of thematic cartography, statistical graphics, and data visualization". pp 13–14. Retrieved 7 July 2008.
4. "Curve fitting". The Physics Hypertextbook.

Licensing

Content obtained and/or adapted from:

• Charts, Wikibooks under a CC BY-SA license
• Line chart, Wikipedia under a CC BY-SA license