How to "Connect the Dots" on a Graph

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

For more FREE help, visit my Super Science Project Support Site. Check out my collection of killer science fair project downloads. Are you running out of time? Check out my Desperation Science Projects for complete science project instructions that can be carried out in just one day! Or, better, have a complete science experiment sent directly to your home for professional results fast! And, of course, you'll find plenty of science project ideas at my science project idea bank, or my student-driven science project idea exchange.

Comments

[Generic Viagra]

I really like this blog, you are very good making them. I say that the issue discussed in this blog is quite interesting and of high quality.

[childhood obesity statistics]

The curve you want to draw needs to be the best estimate you can make of the underling trend that produced the data.

[jordan 1 flight low]

But if the while I think on thee, dear friend, all losses are restored, and sorrows end.Do you like it?

[Generic Viagra]

I would love to participate in this. But I think the date has passed, if this comes around again I would like to be notified ~ Thanks

[soft cialis]

Simple and useful, but if a person don't know how to connect dots on a graph he haves issues for sure.

[Cheap viagra]

Articles like this are returned by the desire to read to the readers, I think it's important that today there are still people who are responsible for disseminating messages and information as interesting as this, I am very grateful to have had the delicacy to share with me I served too! thanks ...