Graphing

Sketching Graphs by hand:

You may be required to graph by hand.

Sketching a graph

Sketched graphs are meant to just show trends, so you do not put data points, units or scale values. You should still have axes labels, possibly a zero y axis shown for reference, and a trendline.

See the examples of sketched graphs (as opposed to complete graphs below):

Complete graphs drawn by hand

Complete graphs should have the following elements, whereas sketches of graphs can be simpler.

  • Axes titles (with units)
    • Most often we graph dependent variables on the y axis and independent on x, but on occasion we find it useful to plot variations on this.
  • Axes scales (numbers that tell how much each box is worth)
    • Your data points should span at least 1/2 of the graph space on each axis. If not, you should consider changing your scale. I have a method for determining scale below.
    • PLEASE do not just label your X values from your data set along the X axis. This will always make a linear graph, but it will always be meaningless.
  • Data points
    • each data point should be plotted as a dot. Be very careful in making sure that your read your scale correctly.
  • If applicable, scale should be chosen so you should be able see x and y intercepts
  • If linear draw a best fit line
  • If there are asymptotes, they should be identified

How to scale a graph by hand:

  1. Find the spread you need to show on your graph.
    • I often use zero and the maximum value. In the data set at shown by the good graph example I chose a spread of 27.5 on the Y axis and 7 on the X.
  2. Count the number of vertical and horizontal spaces on your graph.
    • On the grid used to graph in the example I counted 15 spaces each way.
  3. Divide the spread by the number of spaces on each axis and then round up to a convenient number to work with.
    • For the Y axis 27.5/15=1.8, I rounded up to 2 and made each box worth 2 s. I chose not to label every line because that would be too crowded.

Be careful: Do not take uneven intervals (like 0.15, 0.40, 0.65) and plot them evenly on an axis. (See y axis on bad example below)

https://sites.google.com/a/apps.wylieisd.net/physishipp/general-skills/graphing/Screen%20Shot%202016-08-08%20at%2011.43.39%20PM.png

Digitizing Hand Completed Work to include in an online lab notebook or online assignment

Using Google sheets to create graphs:

Before starting to graph you should have your data prepared - - this video shows how to calculate values needed and format them to make it easy to graph.

These steps will help you create a scatter plot with trend lines, labels, equations, and an R^2 value to compare precision.

Use the Insert menu and select Chart to start creating a graph. Follow the following steps to format the graph:

1. Select your data

Under the Data tab of the chart editor select the data by doing the following:

    • set the chart type to scatter chart
    • set the series to the Y axis values (click add series and then highlight data with header; remove any excess series shown)
    • set the X-axis to your X axis values (click Add X-axis and then highlight data with your header)
    • the only box needed to be checked below is Use column A as labels

2. Add labels

3. Under the Customize tab of the chart editor expand the chart & axis titles settings to add axis labels:

    • Add a chart title if desired
    • Change the type to Horizontal axis title and enter the measurement and unit for your x-axis values (example: time (s)) as the horizontal axis title.
    • Repeat with Vertical axis title

3. Add trendline

4. Still on the customize tab, expand the series settings.

  • Check the box for the trendline
  • Change the type between linear, polynomial, and power to find the best fit.
  • Change the label to Use Equation to show the equation on the chart.
  • Check the box for Show R^2 to display the how well the line matches your data (closer to 1.000 is good, 0.995 and up indicates that the line is a good model for the data set).

4. Check scales

4. Still on the Customize tab, expand the Horizontal Axis settings

  • Make sure the box Treat labels as text is not selected. This will cause a non-linear scale
  • If the default zoom over-emphasizes differences or fails to show an intercept, adjust min or max values to represent your data better.
  • Repeat with the Vertical axis if needed.

5. Double check all required elements

Graphs need

  1. Labels with units for each axis
  2. Consistent scales that allow all data/analysis points to be seen
  3. Trendlines (if data displays a trend)
  4. Equation of trendline (if trendline is appropriate)
  5. R^2 value (if trendline is appropriate)

Interpreting Graphs:

  • You should be able to describe graphs relationships by looking at them and matching them to the above trends
    • A dependent relationship just means that one changes the other. This can describe all relationships except constant (not shown above, but where the y value does not change the X or vice versa).
    • A positive correlation indicates that when one value increases the other does as well.
      • A linear relationship is represented by a linear function y=mx+b
        • A direct also known as proportional relationship is a special kind of linear relationship in that the b value is zero. so, y=mx. It must pass through the origin.
    • A negative correlation indicates that when one value increases the other decreases.
      • An inverse relationship (also called inversely proportional) follows the equation y=m/x or y=m(1/x).
        • There is debate about what indirect means and I would avoid it's use. Some people consider it the same as inverse while others use it for any negative correlation.
      • An inverse square relationship is tough to tell from a simple inverse relationship - you need to linearize it to tell the difference.

Analyzing graphs: Linearization