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Guide 1-1b. Drawing and Analyzing Graphs

1. Label your axes with variable names and units. Note that you will never write x and y as axis labels! Always use the actual names of the variables. Place the independent variable on the horizontal axis.

2. Design a decimal-based scale for each axis such that your data will stretch across as much as the available grid space as possible. By decimal-based scale, we mean a scale such as that used by a ruler. Take a look at your ruler to see what we mean. There are 10 divisions between major units of centimeters. This makes it easy to read measurements in decimals. Imagine how much more difficult it would be if there were, say, 7 divisions per centimeter. On your graph paper, notice that there are 5 minor divisions per major division. Thus, each minor division is two-tenths of a major division. Once you've determined a scale for your graph, place equally-spaced numbers along the scale. You need only number every couple of major divisions. Also, indicate the position of the origin.

3. Title your graph at the top with the names of the variables and a descriptive phrase in this form: Vertical Axis Variable vs. Horizontal Axis Variable for Such-and-Such. This is standard scientific form. The descriptive phrase identifies the object of measurement. Units of measurement aren't required in the title.

4. As you plot points on your graph, first locate their coordinates as accurately as you can. Read to fractions of a minor division. Think of the graph as an instrument of analysis and use it as such. At each data point, place a large marker. We recommend a large X. You could also use a point, but be sure to surround it with a circle so that it will be easy to locate.

5. If your data is linear, draw the best straight line through the points. Do this by placing a ruler or straightedge on the graph in such a way as to split the difference between the data points. That is, you'll have some above the ruler and some below so that the differences average out to about 0, to the best of your judgment. When you carry out this process, don't force the line to pass through the origin unless the origin is one of your data points. In this lab, the origin is not a data point.

6. Select two points to calculate slope. Don't select actual data points for this purpose. Instead, pick two points that are actually on the line that you drew. In addition, pick points that are far apart. This will give your result greater accuracy. In general, greater accuracy is obtained in measuring greater amounts.

7. Once you've selected the two points, read their coordinates from the axes. As always, read to a fraction of a minor unit. Write the coordinates in the usual mathematical form beside each point.

8. Show your calculation of the slope. Start by writing the equation for slope in terms of the actual physical variables (not x and y). Then substitute the coordinates of the points with units and reduce.

If you are using Logger Pro 3...

1. Rename the variables in your data table with appropriate physics names. Enter the correct units and numbers of significant figures or decimal places. In order to do this, double click on the column heading in the data table. Enter the full name of the variable, the short-hand symbol, and the units of measurement. Then click on the Options tab.  Under Displayed Precision, select the appropriate number of decimal places.

2. LP3 may connect the data points by default. If so, remove these connecting lines and add point symbols. In order to do so, double click on the graph. Under Graph Options, make sure Point Symbols is checked and Connect Points is unchecked.

3. LP3 generally doesn't start the axes at 0, but it's frequently a good idea to be able to see the origin. In order to change the scaling, double click on the axis on the graph and select the Axis Options tab. Then make the changes in scaling that you wish.

4. Be sure that the fit results are displayed on the graph and that they have the appropriate Displayed Precision.

5. For all curve fits, whether done by hand or with software, a matching table and equation of fit are required.

1. The matching table has the following form for a linear fit. For other kinds of fits, the coefficients may be different.

 Math maps to Physics Value (fit) Value (expected) Units y --> m --> x --> b -->
1. The equation of fit is written using the physics variables. The math symbols x and y are not used except in the case that they represent horizontal and vertical position. Numerical values of the fit coefficients, rounded to the proper number of significant figures, are expressed together with units.