On May 13, I wrote a blog post about a new way I was introducing MAD, Mean Absolute Deviation. Post is here.
I taught the lesson yesterday and today. It took a lot longer than I anticipated, but I do think it was worth it. I showed the kids the 20 famous people, including our principal. I asked them not to discuss the ages at all, just write down their guess. There was a lot of other fun discussion about the people.
Then, I read their real ages and there was a lot of "yeah, I got it" or "oh my gosh, I was off by 10!" Next, we plotted x for the actual ages versus y for the estimated ages. I asked them to enter their points into their calculator and do a linear regression to come up with the equation of their line of best fit. Some kids had slopes slightly less than 1 and some closer to 2. The y-intercepts varied from less than one to about 14. I asked the two students with 14 if they were quite off on their guesses and they agreed. Then, I asked, "if I got all the guesses correct, what would the equation of my line be?" The first class got it, the second class, not quite. It was be y = x. I had them graph that and then draw vertical lines from their estimated age to the line and write next to it how many points it was away. This took a LONG time. I did want them to get the visual though. Some had points very close to the line (good guessers). Some all over the place (not so great of guessers). Some had most of their points above the line - I asked - what did that mean. They got it - they guessed to old.
Finally, we went back to my table with x as the actual ages, y as the estimated ages and we did x-y for a new column. This was positive and negative numbers. And, the last column was the positive difference aka the absolute value. We found the average of the last column and had our MAD. Lots of work, but I think they got it. Their MADs were mostly between 1 and 4, not too bad.