# Graphical Representation of Data

## Discussion

Somebody else wrote this.

Graphs began to appear around 1770 and became common only around 1820. They appeared in three different places, probably independently. These three places were the statistical atlases of William Playfair, the indicator diagrams of James Watt, and the writings of Johann Heinrich Lambert. We should note as well the descriptive geometry of Gaspard Monge, which had an important indirect influence on the way that graphs developed.

William Playfair's statistical graphs of the British economy were the best known of these early efforts. (See Figure 4.) He first presented them in his Commercial and Political Atlas of 1785.

James Watt's indicator was another important early source of graphs, because it was one of the very first self-recording instruments. It drew a pressure-volume graph of the steam in the cylinder of an engine while it was in action. Recording instruments in the 19th century could not easily record numbers directly, and so they had to inscribe data by drawing a trace on paper or smoked glass. Thus recording instruments produced graphs by necessity, not by choice.

Johann Heinrich Lambert was the only scientist in the eighteenth century to use graphs extensively. He drew many beautiful graphs in the 1760s and 1770s and used them not only to present data but also to average random errors by drawing the best curve through experimental data points. Lambert insisted that natural philosophy could be pursued successfully only by careful mathematical analysis of quantitative measurements taken with precision instruments. The natural arrangement for such measurements was a table of quantities relating the values. In his Pyrometrie Lambert gave tables showing the number of days in each month that the temperature reached a certain value. The numbers in these tables snaked back and forth in a most graphlike manner, and Lambert followed them up with actual graphs of temperature data.

Thus by the 1790s graphs of several different forms were available for those who might want to use them, but for the most part they were ignored until the 1830s, when statistical and experimental graphs became much more common. (Hankins)

Another history lesson from The Canadian Museum of Making

Watt & Southern, c. 1796 The indicator was soon adapted to provide a written record of each individual application instead of merely a transient observation. This was a tremendous analytical breakthrough, allowing, as it did, an accurate picture to be formed of the pressure of steam at any time during the movement of the piston. The inspiration was due to John Southern (1758-1815), Watt's draughtsman, who recorded in a letter dated 14th March 1796 that he had 'contrived an instrument that shall tell accurately what power any engine exerts'.

Graphs of data serve the following purposes…

- to show what has happened
- to show the relationship between quantities
- to show distribution

There are then the following general types of graphs

- time series
- scatter plot
- histogram (a type of bar graph)

What about the axes?

- Independent Variable — usually plotted on the horizontal axis
- Dependent Variable — usually plotted on the vertical axis
- Explanatory Variable — usually plotted on the horizontal axis
- Response Variable — usually plotted on the vertical axis
- Categorical Variables — represented by different symbols on the same coordinate system
- Lurking Variables (Hidden Variables)

What's interesting?

- slope of tangent: rate of change of
*y*with*x*- in calculus the result is called the derivative and the process is known as differentiation
- interesting features
- maximum and minimum
- cusps
- inflection points
- asymptotes

- area under curve: cumulative product of
*x*and*y*- in calculus the result is called the integral and the process is known as integration