## Graphing

 Course Support Lab Contents

### 3. Some Hints

Plotting

• graph in pencil
• a title and axis labels is required
• include units on each axis
• define all symbols on the graph itself
• use as full an area of the graph paper as will permit a reasonable scale
• choose a scale that is simple to use (multiples of 10, 20, 25, 40 or 50)
• for rough graphs speed of plotting is most important, so you may restrict the scale to multiples of 1, 2, or 5
• offset the axis to around the data plotted, include 0,0 only if it is part of you data
• do not break an axis to show an offset, simply begin the scale at the offset value. An offset shown as break in the axis is sometimes used in buisiness (eg. currency graph shown starting with $0 and then scaled$0.85 to $1.10). This is not done in scientific work (eg currency graph would be shown starting with$0.85 and scaled to \$1.10).

Graph Calculations

• In general, all slope calculations can be shown on the graph (provided there is room).
• Slope has units (in contrast to math where often one graphs functions without units)
• Slope is calculated using widely spaced locations on the drawn line (not from data points plotted)
• When a point is known to be an exact point (such as the origin sometimes is), then both the best and worst fit lines should pass through the exact point. Also the exact point is used as one point in the slope calculation

Benefits of Graphs

Pictorial models are very useful for analyzing and comparing data and for presenting information about the data to others. Summarizing a data set with a chart or graph often allows us to recognize special characteristics (such as the shape or distribution) of our data that may not be obvious from the numerical statistics. In addition, "pictures" are more easily understood than numerical summaries, even by someone with no formal training.

Graphical analysis has several advantages over numerical techniques for determining fits to data. By presenting data visually, one can make determinations as to the importance of points based on their uncertainties as well as their locations on the graph. Although there are numerical techniques for making these determinations, one finds that a visual analysis provides one of the best (and simplest) approaches.

Many calculators now provide simple regression tools (such as "least squares fit") for determining linear fits to data. These regression tools in general do not account for the certainty of a data point nor do they do point rejection of "bad points". The numerical tools work well if just a simple data fit is required with no detailed analysis or if the consistency of the data is well known and fits are need to many sets of data. In general though, for the first look at some data set, a graph is drawn and used in the analysis.