Nearly all science projects require at least one graph to display their results in a clear and convincing way. Once you have plotted your data you will need to connect the dots in a way that displays the underlying connection, if any, between your independent variable (whatever you change in your experiment) and your dependent variable (whatever changes in response). Here are a few tips about how to do that.
Suppose you plot your data with the errors bars and it looks something like this.
(Click on the picture to enlarge it.) You can see that the yield of whatever this graph refers to increases with temperature. How do you connect the dots?
First, NEVER simply connect the dots with a ruler like this.
(Click on the picture to enlarge it.) Every measurement you make is subject to experimental errors and so each datum you take will have error associated with it, meaning that it is unlikely to lie exactly where it should. A few of your data points might be pretty close to where then should be, but you'll measure some to be a little above or below their their true position simply because the no measurement process is perfect. The curve you want to draw needs to be the best estimate you can make of the underling trend that produced the data. It needs to a smooth continuous line or curve that the data is centered around.
OK, so what line or curve should you try first? Answer: The first function you should try to fit the data on any graph is ALWAYS A STAIGHT LINE.
Here's the same data with the best straight line I could plot by eye, without the use of complex mathematics or a computer.
(Click on the picture to enlarge it.) This is actually a pretty good fit. Note that although this line actually touches all the vertical error bars, this need not have been the case. Your error bars are not absolute bounds on your data.
Let me repeat that since no many students do are completely confused about this.
YOUR ERROR BARS ARE NOT ABSOLUTE BOUNDS ON YOUR DATA. In fact, about 1/3 of your data an be expected to be located more than one error bar away from the best fitting curve.
If you can find a line that fits your data then you are done. Never try complex curves or functions when a straight line will do. Why not? Ockham's Razor again... a simple straight line is about the most boring relationship you can imagine. So if a straight line fits the data, then you must take that as the best explanation of your data.
Dr. Shawn
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