Graphing Techniques

What’s a graph?  Why do we need to make graphs?

1. Assign Variables To The Proper Axis A graph relates two variables from an experiment. One of the variables is changed in order to study how it affects the other variable. The variable that is manipulated by the experimenter is called the independent variable and it’s values are plotted on the ‘x’ or horizontal axis. The variable whose values are determined by the results of the experiment is called the dependent variable and is plotted on the ‘y’ or vertical axis.

UNITS!!! Units should always be drawn on both axes of the graph.  If you don’t know what units are being used, the graph isn’t very useful.

Independent vs. Dependent The x-axis of the graph is the independent variable and the y-axis is the dependent variable.  In other words, y changes when x changes and not the other way around. A good example would be a graph of age versus weight. Will your age change when your weight changes or will your weight change when you age? Since the second is true, age goes on the x-axis and weight goes on the y-axis.

2. Set-up the scales Each axis must have a numbered scale to show the values of each variable. The scale should begin with a number slightly less than the lowest value and extend to a number slightly more than the greatest value and designed to occupy the majority of the paper. The scale must be uniform. That is each block on the graph must represent the same amount as any other block of that scale. Scales do not necessarily need to begin at zero. The two scales do not necessarily need to match.

3. Label Each Axis Each axis must have a label which states the variable which is plotted on the axis. Each axis must indicate the unit used to measure the variable.

4. Plot And Circle The Points Use a small uniform dot to plot each point in it’s proper position. You may want do draw a small circle is drawn around each dot. The purpose of the circle is to represent the uncertainty in the measurements of that set of data. In more advanced classes you may be asked to calculate the uncertainty of the measurements and to draw a circle that precisely represents that uncertainty.

5. Connect The Points The points on the graph should be neatly connected to show the trend in the data. How the points are connected depends upon what kind of data was collected. Discrete data (counted items) are connected point-to- point by straight lines. Continuous data (measured quantities) are connected by a smooth line which may be straight or curved. The line does not need to touch each circle as it only shows the trend in the data.

Connect the dots Graphs should always be shown as smooth lines or curves. Never connect the dots with straight lines to form a sawtooth pattern.  The reason we can’t connect the dots with simple straight lines is that we recognize the data we take isn’t perfect. Besides that, the actual values in the 14 regions between the dots almost never lie on a straight line. If we use our data points as a guide for drawing smooth lines or curves rather than as absolute truth, they are more useful for helping us identify the underlying trend that we are really interested in.

Line Graph!  Always draw a line graph in chemistry class! (OK, so there may be a FEW times, but 99.9% of the time, chemist use line graphs)  Students invariably believe that bar graphs work better than line graphs. Explain to them that bar graphs are useful when graphing a number of unrelated things on the same chart. For example, if you want to show the sales of Brussels sprouts, machine tools, and Gucci handbags on the same chart you’d use a bar graph. However, since we’re graphing how one variable is changed by another one, a line graph is more appropriate.

6. Title The Graph Each graph should have a title placed in some clear area, usually near the top of the paper. The title should be informative. That means that it should relate to the reader information about the experiment that is not part of the graph without the title.

What is the title? The title of a graph should always be “The dependence of [dependent variable] on [independent variable].”  Another way this is commonly written is “The effect of [independent variable] on [dependent variable].”

Conclusions Abrupt changes in a graph tell you that something significant has happened.  We usually see straight lines or smooth curves on a graph. Obvious discontinuities suggest a significant change has taken place.

The Experiment Various amounts of table salt are added to water and the boiling point of the solution is measured with a thermometer.

The Data Grams of NaClBoiling Point 0g o C 2g o C 4g o C 6g o C 8g o C 10g o C

The Graph 1.Assign variables to the proper axis.

2.Set-up the scales. The Graph

Label each axis. Mass of NaCl in grams Temperature in o C The Graph

4.Plot and circle the points. The Graph Mass of NaCl in grams Temperature in o C

The Graph 5.Connect the points. Mass of NaCl in grams Temperature in o C

The Graph 6.Title the graph. Mass of NaCl in grams Temperature in o C The Boiling Point of Salt Solutions