I wasn’t scheduled to teach anything on day 4 of the institute, but anyone that knows me understands that I can’t sit there and not be involved. I somehow managed to talk one of the facilitators into letting me teach the lesson on the meaning of the mean and standard deviation…although, I’m betting he let me think I talked him into it.
To introduce the mean, I asked the participants define it in their groups. Most of the participants defined the mean as a process (sum the data and divide by the number of data points). Our goal was to get to a definition of the mean that wasn’t exclusively a process. I had some volunteers come to the front of the room and gave each of them different amounts of blocks. Next, the volunteers had to create a “fair” allocation of those blocks. With two volunteers, they just shared blocks from one person to the next. Even when there were three people, the volunteers just shared blocks until they all had the same amount. Once there were six volunteers, it got a little harder. Eventually someone simplified the situation by putting all of the blocks into one group and dividing them evenly amongst the volunteers. There was the a-ha moment of what the mean really is.
Next came a conversation about the standard deviation. Most of the participants have some knowledge of the standard deviation calculation, but not really of its meaning/use. We started here:
I asked them to rank the allocations from most fair to least fair. The entire group didn’t have a problem with allocation A being the most fair, allocation D being the second most fair and allocation B being the least fair. However, there was a relatively heated argument about whether C or E was fairer. This created a need for the standard deviation. The participants walked me through a way to measure fairness (spread) and we did some calculations:
The task is made easier with the values for the standard deviation.
I still had to completely change the prescribed lesson given to me. I think I’ve just decided I’m going to take liberties wherever I feel the need. The participants haven’t complained that what we’re doing doesn’t match their binder; at least they haven’t complained yet.