Estimating average daily consumption with samples randomly scattered in time

Question

I want to estimate my daily water consumption. I have taken pictures of the water meters (total m3 used since last reset) every now and then, but without any regularity. There can be a difference of a few days to several weeks between samples.

What would be the best way to estimate this? I have thought of the following approaches:

• Create a double-entry table with the sample dates in the column and in the row headers. Each cell is the average consumption per day between the corresponding two dates. Finally, average all the cells in the table.
• Calculate the daily consumption between every two consecutive samples. Finally, average all of them.

It seems to me that the first one would give a better estimation given the higher number of samples compared, but I am not sure if this is valid.

Answer 1

If you only want the average daily consumption over the whole period of time, you can simply calculate the difference between the last and first reading and divide by the total number of days.

As far as I understand your explanation:

• your method 1 would not give you the true average over the period, unless you multiply each individual average by a weight corresponding to the number of days in the period.
• your method 2 gives the true average, since it would represent every day individually (if I understand correctly)

However if you want to be able to observe the variations across time while smoothing some of the irregularities, you could:

1. calculate the daily average for every day like in method 2.
2. calculate a rolling average over a fixed number of days for every day. This is not perfect if there are long periods with no reading, but it should show the general trend better.
3. Plot a graph based on rolling average.