Archive for October 27th, 2009

On Utilities Consumption I: Water

October 27th, 2009 2 comments

So more or less since I came back to Mexico I've been saving my water bills, just for fun.  "Eventually," I thought to myself, "I may be able to do something with them."   Of course by that I meant that sixty years later I would have enough data points to discern some fascinating trends, including those detailing draughts and relative water abundance, and I would absolutely be able to use Viterbi algortithms or some Markovian insight to predict next year's weather, oh, and the price of potable water.  I'm the impatient kind, and have accumulated only about four (sometimes five) year's worth of data.  Here it is; I have plotted my cubic-meter consumption on a month-to-month basis (the bills come in monthly).  I've assumed that I use the water that I need.  Also that the trends represent a fairly typical (there may be some argument here, I predict) three-person household consumption (I don't live alone).  And yes, admittedly, sometimes there are sisterly visits in December and there's that factor to take into account, but oh well!  Let's just hypothesize my water consumption is fairly typical for a 3 or 4 person household in this geographical region in Mexico, shall we?

I've plotted the average consumption, and the two-sigma 95% bounds I calculated using Bessel's correction of the standard deviation for samples, aka "sample standard deviation":  \sqrt{\frac{1}{N-1}\sum_{i=1}^{N}\left(x_i - \overline{x} \right)^2 } .  The correction gives an unbiased variance, even though the standard deviation is slightly underbiased... not that it matters much anyway.


An interesting detail is that September seems to me the more precise.  My friend Ben objects to my use of the word "precise" in such a way.  He's a physicist. He pointed out to me that what I meant was variance.  He kept going on about how precision applies to instrumentation, and how the readings would have a precision estimate that would be reported alongside.  I countered that it probably did have an implied precision, because the measure is (surely) to significant figures, and so, a reading of 34, really meant anywhere between 33 and 35, as per the usual rules. Also, I told him his interpretation of precision did not matter in this my particular case.  A not so interesting debate ensued, culminating in our agreeing that precision is dependent on context. My argument was that if my monthly data points represent estimates of an "actual" (fictitious) consumption for that month, then indeed my spread indicates precision (where accuracy would indicate how close I came to the "actual" consumption). Anyway.  The debate was illuminating in some ways, but banal in many others.

The wide fluctuation in March-April was probably due to a small leak I had in 2008 that I corrected immediately, although I did interpolate some values that were missing for 2007 and 2008 right around that time too. I'm estimating my consumption for October to be about 15 cubic meters, the (unbiased) sample (arithmetic) average for that month.