Poll: Indicated vs Actual MPG vs Date

I'm preparing a poll to look at date of manufacture versus the indicated and actual MPG error. You may see this note as I get it ready.

INSTRUCTIONS

We need two pieces of information:

• manufacture date - found on the door jam label
• % error of indicated vs actual MPG - another calculation

The best way to calculate your indicates versus actual MPG error is:

1. SUM_INDICATED - add "n" tanks, one or more, that you have indicated MPG values.
2. SUM_ACTUAL - add "n" tanks, one or more matching the "SUM_INDICATED" records to give a sum of actual MPG.
3. DIFF_MPG = SUM_INDICATED - SUM_ACTUAL
4. %ERROR = DIFF_MPG / SUM_INDICATED

The poll will run for 30 days so there is plenty of time to get a fresh tank if you've not been recording the data. It is perfectly OK to post your work before answering the poll and ask questions. This is not a 'race.' <grins> However, you only get one answer and we can't erase it.

F8L and I collaborated on what the poll needs to ask.

Thanks,
Bob Wilson

 

Example:

indicated - actual MPG
57.7 - 51.7
60.6 - 53.6
58.1 - 52.0
59.4 - 53.1
74.5 - 67.2
76.4 - 64.0
56.4 - 49.9
---- ----
443.1 - 391.0 = 52.1

52.1 / 443.1 = 11.75%

Now to go read the door jam value. I have to admit I'm surprised at this error.

Bob Wilson

 

Early morning algerbra, I need to double-check how ACTUAL_MPG and INDICATED_ MPG are used to determine the error. Sometimes I work fast and don't checked my work. I should have done this first:

1. ACTUAL_MPG = A_MPG; INDICATED_MPG = I_MPG; PERCENT_ERROR = N :: variables
2. A_MPG = N*I_MPG + I_MPG :: Calibration formula
3. A_MPG = (N+1) * I_MPG :: separate terms
4. A_MPG / I_MPG = N+1 :: put known on one side
5. (A_MPG / I_MPG) - 1 = N :: good enough to stop here
6. (A_MPG / I_MPG) - ( I_MPG / I_MPG) = N :: convert "1" to ratio
7. (A_MPG - I_MPG) / I_MPG = N :: the formula I should have posted

Looking at my earlier posting, I posted two steps:

but I failed to explain all of the parts involved. Now I did the formal proof using a different set of variables to make sure my earlier posting is not confused with the formal analysis. We can make a one-for-one conversion table:

N = %ERROR :: the calibration constant
I_MPG = SUM_INDICATED :: the indicated MPGs
A_MPG = SUM_ACTUAL :: the actual MPGs
​

Using the same formula terms, we get:

1. (I_MPG - A_MPG) / I_MPG = N :: inverts the sign of the error
2. (A_MPG - I_MPG) / I_MPG = N :: correct sign, ~ "-5%"

We speak of the error being the indicated MPG is high so the actual MPG is lower. Although negative numbers are perfectly OK, I wrote the poll to reflect the error as positive error percentages when in fact they are actually negatives. It is an English language trick to avoid using negatives even in numbers since too many negatives can make a sentence confusing. Not really needed here, I was being a little lazy.

I also wrote the methodology to 'average the averages' rather can calculate a true average. A true average would weight each MPG by the number of miles (or fuel consumed) to achieve that indicated MPG. For example, if one drove 500 miles (800 km) and got an error of 5% and then drove 50 miles (80 km) and got an error of 10%, the true average error would be:

1. ((10/11) * 5%) + ((1/11) * 10%) :: weighted sum

There are several other ways to calculate a true error including summing the distances, summing the fuel, and calculating the actual MPG. Then using the indicated MPG and distance, calculate the indicated fuel burn and sum them. But you can see this quickly becomes a lot of operations ... trivial with a spreadsheet but not so easy if like me, the indicated and actual MPG are what is readily available.

In engineering I sometimes to use 'good enough,' back of the envelope, to save time and reduce workload. However, the clever engineer also does a 'sanity check' to make sure the simplification did not induce an error. In my case, I did individual error calculations for each pair and quickly noted the errors were nicely grouped regardless of the miles covered. The unweighted error is likely to be pretty close ("close enough") to the true value. Furthermore, I knew the poll would require interpolation to the closest value ... exact accuracy and would not be of great use as long the accuracy was "close enough." Unfortunately, I didn't go far enough to explain the 'average of averages' short-cut and its implications.

Sad to say, I had a limited amount of time when I first posted the approach but today is a USA holiday, Thanksgiving Day. The spritual core of Thanksgiving Day is to give thanks for our blessings and life itself and share what we have with others. Happy Thanksgiving my friends. Often the best Thanksgiving meals are when everyone brings a dish. Perhaps someone else would like to bring one of of at least two methods to calculate a more accurate error? <GRINS>

Bob Wilson