Inspired by Dan Meyer‘s 2012 Annual Report, I decided to start tracking data on myself in February. Thanks to the Keep Track Pro android app on my phone, I have been tallying each and every coffee I drank since February 18. I’ve had a lot of fun self-analyzing through this activity and am trying to figure out a way to get students doing something similar in AP Statistics this year.
On to some graphs!
First, I decided to do a bar chart on the counts of coffees I drank in a day. I’d never gone above three cups in a day, but somehow survived the 18 days I had no coffee.
With this preliminary information in mind, I decided to think about the Law of Large Numbers and a moving average. The basics of the theorem suggest that over time, the average of some experimental outcome will approach the “true” value. I wanted to infer what my “true” average coffee intake per day was. Using some Microsoft Excel formula wizardry, I calculated an average after each day of the tracker, and decided to plot this cumulative average over time.
I noticed an interesting pattern here. As the Law of Large Numbers suggested, the cumulative average began to settle by May at around 1 coffee per day. Thinking about my routine during the school year, I would normally have a coffee at home before work, and every once in a while, maybe one or two times a week I would have another after work at home. Then I noticed that the graph became unsettled again after school ended and revealed an upward trend. At this point, I wanted to examine in a little more detail the reasons for the instability. Instead of looking at the cumulative average, more Excel wizardry enabled me to look at a running average, only looking at the prior 14 day period. This displayed a higher resolution of my caffeination habits.
I noticed a few regions of interest in this graph. First, around late March to early April, the running average reveals a drop in my drinking habits. I roast my own coffee, and I bet this period corresponds to a time when I had forgotten to re-order beans to roast and had to wait for them to come in. Secondly, I notice that about 2 weeks after school ends, my moving average starts to increase drastically. The red trendline begins to settle around 2 cups per day. This corresponds to what happens when I am at home without much structure. I either make several cups of coffee during the day or hang out at the coffee shop. The instability in the cumulative average (blue) is understandable based on understanding the running average (red).