Graphing Tutorial for IAs

  • Graphing Tutorial for IAs

    Creating the Graph


    Time (±.0001 s)

    Time (±.02 s)

    Distance±.05 m

    Trial 1

    Trial 2

    Trial 3

    Average

     0.20

    0.2169

    0.2218

    0.2148

    0.22

    0.40

    0.4488

    0.4518

    0.4421

    0.45

    0.60

    0.6919

    0.6850

    0.6910

    0.69

    0.80

    0.9519

    0.9529

    0.9561

    0.95

    1.00

    1.2000

    1.2120

    1.1700

    1.19

    Above is a sample set of data.  Uncertainty for distance has been set at .05 meters, and uncertainty for average time is .02 seconds.  We will use this data to create a graph including the minimum and maximum gradients.

    Firstly, the data must be placed into a chart.  To do this, go to insert on the toolbar in the top left-hand corner.  Select "Scatter" in the charts tab, and choose the first picture labeled: "Scatter With Only Markers." 

     

    An empty graph should pop up in your Excel Worksheet.  Right click the graph, and select "Select Data." 

    On the left of the box you will see “Add”, click it and a small box will prompt you to enter sets of data. The X-values for this tutorial will be the distances, and the Y-values will be average time.



     

    Next click the little icon next to “Select Range” to add you x-values. Select your x-values. They should be shown in the new box that popped up.






     
      

    Then click in the icon circled in red to return to the previous window. Do the same procedure for your y-values (Time). In the first box, you can simply enter a name for your series.

    Exit the “Edit Series” window by clicking “ok.”

    Exit the “Select Data Source” window by clicking “ok.”

    Your graph should now be created

     

    Select Design on the tool bar, and this graph layout as shown below. 

     

    Best Fit Line and Equation

    The next thing to do is to add in your best fit line. This graph will be linear. To do this, right click any data point and select “Add Trendline.” A new window will pop up.  At the bottom select, “Display Equation on chart.”

     

    Your graph should now be created and will look similar to the graph shown below.

     

    Add appropriate titles for the x-axis, the y-axis and the Chart Title.


    Error Bars

    Now we have to format the uncertainty/error bars.  Select your points, look at the toolbar and select layout.  You should find error bars and select bars with standard arrows, as shown below:

     

    Right click the vertical or horizontal bars and select “Format Error Bars…” to format them. Select “Fixed value” and input the values established of your uncertainty in the data table. In this tutorial the Horizontal error bar value will be .05 and the vertical error bar value will be .02. These numbers are your uncertainty in distance and time.

    Max/Min Slopes

    Next we have to add the maximum and minimum slopes, and their corresponding equations.

    Firstly, we have to create the maximum and minimum points which we will use to draw gradient lines.

    We need two points to create a line. We can calculate the points for the maximum and minimum slopes using the uncertainties. This will be done by creating a new table in this worksheet. Your new table should look like the one below when you’re done. The instructions to calculate these values are below the table.

    Maximum Slope

    0.25

    0.20


    0.95

    1.21




    Minimum Slope

    0.15

    0.24


    1.05

    1.17





    In the first cell in this new table, we arrive at the number .25 by adding the uncertainty in distance (which is .05) to the first distance value in the data table (which is .2).  The time value that accompanies it is calculated by subtracting the uncertainty of time (which is .02) from the first average time (which is .22). Our next X-value point in the maximum slope, we see the value to be .95.  This answer was calculated by subtracting uncertainty in distance from the last distance used, or 1.00.  The corresponding time value was calculated by adding the uncertainty of time to the last average time value. This gives us a value of 1.21.

    For the minimum slope, simply reverse the operations you performed for the maximum slope.  Where you subtracted, add, and vice versa.

    Now to graph these points. Right click your graph and select “Select Data.”

     


    Add two new series, label them Maximum and Minimum slopes. Select the corresponding data using the techniques described earlier in this guide, if you do not remember scroll up and review them.  (Just to be clear, the x-values for your max slope are .25 and .95. The y-values for the max slope are .20 and 1.21.) Remember to add the trendline and show the equations. Also be sure to indicate what line equations go with what best fit lines. This was done via color coding.

    The finished product should look like the following: