Dealing with Error

I have had some questions about how younger students can take error into account as they analyze their data. There are three simple ways to address error that even elementary students would be able to use.

Take LOTS of measurements
The easiest way to address error, and help reduce it, is to take lots and lots and lots of measurements. A good number of minimum times to measure something is 6 but more is better. By averaging several measurements you can reduce random error and hopefully obtain a more precise measurement. However, you need to be careful while you take these measurements so that you don't introduce any systematic error, such as from misuse of your measuring instrument, which will affect your accuracy.

Outliers
Once you've taken all of these measurements, you need to look at them critically. Are any of your measurements way off from the others? These are called outliers and simply tossing out these measurements is one simple way to address error that any student can do. However, do not toss out outliers unless you have several other measurements to compare them to. If you only took 3 measurements, say you measured a distance to be 31 cm, 32 cm and 48 cm, and one of them is off (48 cm), it is worth the effort to redo the measurement to be sure that 48 cm is the outlier and not the other two. This is one reason it is important to take at least 6 measurements.

Average Deviation
This sounds complicated but is really quite simple! Anyone who can calculate an average can calculate an average deviation. This is best explained with an example. Suppose you took some measurements of temperature (in degrees Fahrenheit.):

45, 48, 43, 45, 47, 58

First we would throw out the last measurement, it appears to be an outlier and could have resulted from the substance we are measuring warming up while we took the measurements. The average of the remaining 5 temperatures would be 46 degrees Fahrenheit.

Now we can calculate the deviations by subtracting each measurement from the average and using its absolute value:

46-45 = 1
46-48 = 2
46-43 = 3
46-45 = 1
46-47 = 1

Then you simply average the deviations! In this case we get 1.6 which rounds to 2. So now we can say that our measurement is 46 +/- 2 degrees Fahrenheit. This means that the true temperature is most likely somewhere between 44 and 48 degrees Fahrenheit.

For more on error, check out page 22 of Crime Scene Science Fair Projects.