Subdivision Plat - rounded sum error 1

[kc27315]

At my Civil Firm, sometimes measurements shown on a plat don't appear to be correct due to the fact that sometimes a ROUNDED SUM of two numbers does not equal the SUM OF THE ROUNDED numbers. For example, in the attached image, there are three rounded distances that don't appear to add up: 340.83 + 38.82 does not equal 379.66. Since all three of these numbers are rounded to the second decimal place, it becomes clear why they don't appear to add correctly when we show more decimal places: i.e. 340.834 + 38.825 = 379.659

My question is: what should be done on a subdivision plat in this case? Should the numbers be left as is in the image (and if so, is it possible that the review agency will find exception when we submit the plat for review)? Or should I just "fudge" one of the numbers, such as changing the text to say 38.83 so that 340.83 + 38.83 = 379.66 appears to be correct on the plat?

Any Thoughts?

 

[Denial]

This might not be of much help in your context, where wars have been fought over minor apparent discrepancies.[ ] But in several other contexts where this sort of thing has arisen I have ensured that the individual components add up to the expected total by (if necessary) adjusting the component that has the largest absolute magnitude.

In a completely different context again, many years ago I investigated the statistics of how roundoff errors might accumulate.[ ] If we are rounding a set of M random large numbers to the nearest integer value our maximum error per rounding is 0.5, and our average error per rounding is 0.25.[ ] Call this average error E, and assume that that the error associated with any individual rounding is either +E or -E.

So we have a set of M values, each of which is (randomly) either +E or -E.[ ] Since I cannot readily access the Greek alphabet I will use S instead of "Sigma", and thus represent "Sigma(E)" as S(E).[ ] The trivial question is what is the distribution of S(E), and if we assume that M is reasonably large then the Binomial distribution tends to the Normal distribution and so
S(E) ~ N(0,Sqrt(M/4))

But we are interested in the magnitude of the accumulated error, so the interesting question is:[ ] What is the distribution of S(Abs(E))?[ ] I was able to convince myself that:
The mean of S(Abs(E)) is Sqrt(2M/Pi)
The standard deviation of S(Abs(E)) is Sqrt[(Pi-2)M/Pi]

The distribution of S(Abs(E)) is HIGHLY skewed, and so you cannot use the usual approach to calculating confidence intervals.[ ] (I did establish an approach for CIs, but won't bore you with it.)

 

[Denial]

Oops.[ ] Woke up screaming!
My above results for the mean and the standard deviation of S(Abs(E)) both need to be multiplied[ ]by[ ]E.
Apologies.

 

[kc27315]

Thanks for the responses Denial, you are quite the statistics expert. I realize there are certain probabilities that situations like this occur. I guess my question is: Do I need to do anything special when labeling the plat from a surveyor / County reviewer standpoint? Might be a question for a Surveyor, but I just don't know what the standard protocol is in this situation.

 

[kc27315]

In a bit simpler of a context, it's kind of like knowing that 1.4 + 1.4 = 2.8
Now round the numbers in this equation to the nearest whole number: 1 + 1 = 3
Of course 1+1 does not equal three, but why should we have to "fudge" the equation just to make the County reviewer happy (i.e. just erase one of the "1"s and write "2" in it's place --- something like 2 + 1 = 3). My preference would be just to leave the "rounded" equation as 1 + 1 = 3. After all, we are allowed to have a closure error in a traverse due to the fact that bearings and distances are often rounded. So why not allow for a summation error, since lengths are also often rounded?

 

[jgailla]

I don't do surveys, but anytime I have a tabular number set in a report I put a statement that numbers may not add up due to rounding.

 

[kc27315]

That's a great idea! I think it should be made into the standard for these situations. Thanks for sharing!

 

[BUGGAR]

I agree with jgailla. I did surveying in the Oakland hills where the ground was always moving. All you could do was survey what you found and write up your discrepancies when you filed. It is o.k. when things don't add up if there is a reason and if you adequately explain it.

 

[wannabeSE]

Have you asked a licensed land surveyor? They should know the proper method to correct the plat (or if it is OK as is). Also, do you need redundant dimensions on the plat? It seems like you could remove one of the dimensions and eliminate something that an attorney might contest.

 

[Denial]

wannabeSE.

My first reaction to your suggestion of leaving one of the dimensions off was that it is a neat solution.[ ] But on reflection, if you do that you are implicitly deciding that the dimension you are going to "fudge" (to use the OP's term) is the one you leave off.[ ] You are just making that decision a lot less obvious.

Adjustment suggestions above (including my suggestion on 20May15@23:48) are assuming that the "discrepancy" is only one unit (ie 0.01 in the OP's example).[ ] What happens if it is two units (0.02)?[ ] Or more? There is no guarantee this will not happen.[ ] In fact it is a statistical certainty to happen sooner or later, with as few as four component numbers.[ ]
1.004+2.004+3.004+4.004 = 10.016
Rounding:
1.00+2.00+3.00 = 10.02

I cannot think of any suitable one-size-fits-all answer here.[ ] But fudging ONE number is NOT the answer, because if you do that you are changing that number by more than the round-off error.[ ] It seems to me that the only hard & fast rule is that you must not change any individual number by more then one unit.

Jgailla's suggestion is looking more attractive by the minute.

 

[kc27315]

All, thanks for your input. Sorry it has taken a while for me to be able to respond again.

wannabeSE, I have spoken with a few PLS's. They don't seem to be able to come to any sort of general consensus. I have seriously considered your redundant dimension idea, but I'm hesitant to use it due to Denial's ideas.

Denial, I totally agree that it's not the answer to just fudge one number. I think jgailla's suggestion about the note is the best way to go.

Thanks again for all the responses on this thread!

 

[civilman72]

Considering surveyors with standard survey equipment can't measure to the nearest 0.01', I would hope the reviewer ignores the rounding "error." And if the reviewer does comment, it will be a good opportunity for you to educate the reviewer on the importance of significant digits.

 

[kc27315]

civilman72, I agree 100%. The problem is that some people are "yes sir/ma'am" people that would rather just take the reviewer's comments about the "error" and make a change to the plat (just to keep the reviewer happy) instead of sticking to their guns and helping to educate the reviewer about the principles of rounding.

 

[jgailla]

"Educating" reviewers tends not to go well if your goal is to actually get a permit.