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:
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.
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.
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)
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.
Creating graphs and linearizing in Google Sheets.mp4These 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
Labels with units for each axis
Consistent scales that allow all data/analysis points to be seen
Trendlines (if data displays a trend)
Equation of trendline (if trendline is appropriate)
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.