Odd Consumption "30 Mi Average" Behavior

[mxnym]

Or put, perhaps, more simply

(x1 + x2 + x3)/3 is the smoothed average of three 0.1 mile consumptions. Similar sliding window averages would be (x2 + x3 + x4)/3 and so on.

The average over the averages is

[(x1 + x2 + x3)/3 + (x2 + x3 + x4)/3 + (x3 + x4 + x5)/3]/5 =

(x1/3 + 2*x2/3 + x3 + 2*x4/3 + x5/3)/5 ≠ (x1 + x2 + x3 + x4 + x5)/5

Now notice that one pointy, x3, is the same in the average of averages and in the overall average. It is the end points that cause the average of the averages to be different from the average.

Are you stating that you now think the average on the chart is an average of the displayed points, or simply illustrating the difference between a real average and my expected behavior based on the points in the chart?

 

[ajdelange]

No. I was just thinking that stating that the average of averages is equal to the expected value of the average of averages which is equal to the expected value of the average is not likely to be meaningful to most readers.

OP looked at the data points, which are short term averages, and noted that when a big blob fell off the left end the overall average nonetheless went up which would not happen were the overall average equal to the sum of the averages on the plot.

 

[gnuarm]

I took another long trip... really long trip, I think it was around 1500 miles this time counting all three legs. I didn't dig into the filtering of the energy display, but I did give it enough attention to see that the filtering is very different between the three averaging distances. On the five mile range peaks appear that are averaged together to form a single plateau in the 15 and/or 30 mile displays. I also observed the same sort of behavior on the 5 mile display regarding the average mileage not changing the way expected from observing the energy graph. So it seems pretty clear the mileage average is being calculated using the raw data samples while the graph data is only updated every few seconds and is an average over several displayed points in all cases.

 

[ajdelange]

Do you mean the graph on the instrument panel or the touch screen? The touch screen is updated every 10th mile whatever range you have selected. Yes, the windows are longer for the higher range displays. Thus a group of high amplitude spikes clearly resolved on the 5 mile display will be smeared together into a lower amplitude blob on the 30 mi display. Perfectly consistent with the behavior of a boxcar or near boxcar sliding window smoother.