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Exploring sampling error


Tags: teaching, science

I’ve been teaching for nearly a full year now, and to say it’s been a massive learning curve would be just a bit of an understatement. As is probably pretty normal for a graduate, some of my ideas have worked well, some have been ok and others have fallen completely flat. I figured I might share one of the ideas that worked well, particularly since it took two attempts to get it working.

Since my Year 11 class is into the last section of Unit 2 of the new curriculum, we’ve been studying mechanical waves. A simple experiment is to measure the speed of sound in air, since it doesn’t need much equipment or space. In years past the standard was to use a starting pistol as they produce a nice puff of smoke to use as the cue to start timing. Since we didn’t have a starting pistol (they’ve been banned for a few years for safety reasons), my first attempt involved exaggerated clapping motions. Coupled with rain, student enthusiasm for this experiment hit a new low and we abandoned the attempt with pretty much nothing gained.

A couple of weeks later, I gave the experiment another shot, this time with the school’s starting pistol replacement - two pieces of wood, hinged at one end to make a clapper. Combining this with the lab technician’s trick of using talcum powder on one of the pieces of wood to give a visual cue to replace the smoke gave us a much better starting point for the experiment. I had five students take stopwatches to the end of the 100 m track, and they all attempted to record the time between seeing the powder and hearing the sound. After a few trials, students suggested we try a larger distance to improve accuracy; unfortunately we only managed 111 m thanks to the school’s small oval. Once all was said and done we had 42 measurements.

We ended up getting an average of 348 ms-1, which is very close to the theoretical value of 343 ms-1 (based on the day’s temperature from the Bureau of Meteorology). The best part of the experiment for me though, was showing the students just how close we got to the calculated value using stopwatches and human reflexes. Despite the big range in speeds (from 119 ms-1 to 667 ms-1), the number of measurements we took overcame the significant sampling error.

The main reason I liked this end result is because it shows the students something they’ve learned by rote since primary school: repeating experiments makes them more reliable. Although most students know this enough to repeat it - frequently - in assessments, it’s actually pretty rare to have an experiment that shows this in action. Most motion experiments, for example, vary from predicted values simply because high school physics doesn’t take into account significant factors such as friction and air resistance. Compared to these issues, measurement error is usually pretty small. Having a simple experiment where students can compare their results with a theoretical value and not have to account for a significant difference between them is, I think, a great teaching tool.

In case you’re interested in taking a look at the actual results and/or using them for your own class, they can be downloaded as a CSV file. It’s only the time and distance data, but could perhaps work well as an investigation where students need to process and interpret secondhand data.