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85th Percentile Speed Question

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Please cite your reference in your statement above. I believe you're fabricating the definition of the 85th percentile in this example where the sample set of 100 values. Regardless of the number of values in a sample set, percentiles and actual values are not the same.

Here's one source of MANY definition references. Pick any one you'd like: http://www.psychasse.../pdf/barrat.pdf

And then there's FHWA-SA-10-001: "85th percentile speed – the speed at or below which 85 percent of vehicles travel"

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Here is a link to the FDOT standard for determining the 85th percentil speed. You'll note at the bottom of the worksheet that the 85th percentile speed is calculated based upon the cumulative totals in each speed range.

TXDOT provides a different explanation: http://onlinemanuals.txdot.gov/txdotmanuals/szn/determining_the_85th_percentile_speed.htm#i1002390. But neither TX of FL standards are included in the NCEES Transportation Design standards.

I suppose my response to this would be, what would you do when there isn't 100 values? What if there were, say, 99 or 101 values? I certainly don't agree with the concept of taking two completely different approaches to determining the speed when there's 100 values versus 99 values.

Also, as to people blindly following industry standard.... the use of the 85th percentile IS an industry standard so, by default, the industry standard for determining it should be employed.

When the percentile of interest doesn't align with actual samples, you should interpolate between ranks. I don't see this as using different approaches. The wikipedia entry for percentiles (http://en.wikipedia.org/wiki/Percentile) has some good explanation.

Maybe there's also one more interesting aspect of this: I think the 85th percentile refers to the population despite the fact that we're dealing with a sample.

I'm not arguing against the 85th percentile being an industry standard... clearly it is. I'm trying to get people to understand that the algorithm used produces an answer that defies reality. In my experience, exam questions that lead to such a contradiction aren't used.

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I was taught to use the formula I showed in my post #32 above.

SD = [ (PD - PMin) / (PMax - PMin) ] (SMax - SMin) + SMin

Where SD = Speed based on your chosen percentile; PD = Your selected percentile (85% in our case); PMin = The cumulative percentage below PD in your distribution table (84% in our case); PMax = The cumulative percentage above PD (97% in our case); SMin = The speed corresponding to PMin (42mph in our case) and SMax = The speed corresponding to PMax (47mph in our case).

You do not simply take the 85th fastest car.

OK... I think I understand where your confusion lies. The procedure you've given (linear interpolation) is used to establish the percentile when there is not enough data (i.e. observations) such that one of the speeds is not exactly equal to the percentile of interest. Take a look at http://en.wikipedia....wiki/Percentile for an explanation of other methods and note the exception for linear interpolation:

If there is some integer k for which , then we take .

By *definition*, when there are 100 values (as in this problem), the 85th percentile is the 85th largest value when put in rank order. So, yes, you *DO* simply take the 85th fastest car.

I don't think so. Even when there are 100 cars, you still don't simply take the 85th fastest car's speed unless the cumulative % total adds up to exactly 85. If not, then the 85% speed will need to be interpolated. For our problem, if there were just one more car in any of the lower speed intervals (and one less in the upper), then the 40-44 interval would have been at a cumulative % of 85 and the 85th percentile speed would have been the average of 40-44 (42mph).

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I don't think so. Even when there are 100 cars, you still don't simply take the 85th fastest car's speed unless the cumulative % total adds up to exactly 85. If not, then the 85% speed will need to be interpolated. For our problem, if there were just one more car in any of the lower speed intervals (and one less in the upper), then the 40-44 interval would have been at a cumulative % of 85 and the 85th percentile speed would have been the average of 40-44 (42mph).

If there are 100 cars, the 85th fastest car will have a cumulative total of 85%, no?

If we stay on just this question: "If 100 cars pass by, each with their speed recorded to the nearest mph, how do you determine the 85th percentile speed?" For me, the answer is simple and unequivocal: it's the speed of the 85th car when placed in order from slowest to fastest.

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I just became a member and this is my first post so I am not sure if I am doing this right. I will try to explain my point of view why I think C.43 is the more logical answer using the basic definitions. Below should be the table with the speed interval, frequency, and cumulative values:

Speed

Interval

(mph) Frequency Cumulative

20 to 24 2 2

25 to 29 11 13

30 to 34 18 31

35 to 39 29 60

40 to 44 24 84

45 to 49 13 97

50 to 54 3 100

“85th percentile speed – the speed at or below which 85 percent of vehicles travel” from the FHWA website.

Calculations from the previous posts show different answers, C.43 and D.45; both have shown different ways of calculating the 85th percentile speed. The problem I see with the D.45 answer is that there is a probability that it will not meet the 85th percentile definition. What if you have at least 2 cars traveling at 45mph? Won’t you have 86 cars traveling at 45mph or less making it 86% which is more than 85%? C.43 will always meet the definition of the 85th percentile speed because it will always stay below the 85% mark.

In addition, if you have 100 cars with speeds arranged in ascending order, the 85th car will not always give you the 85th percentile speed. Just as I mentioned earlier, what if the 85th and 86th car have the same speed? You will have 86% of the vehicles traveling at that speed which will not meet the definiton.

My explanation is just based on how I understand the definition and not based on experience. I hope my explanation will help. J

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Kram,

Good response... it brings up some things that are helpful.

1) Yes, the response chosen should always be on the conservative side of an exact answer rather than the liberal side. That is, err on the side of caution.

2) "What if you have at least 2 cars traveling at 45mph? Won’t you have 86 cars traveling at 45mph or less making it 86% which is more than 85%?" If the definition was "below" instead of "at or below", I'd agree with this concern. If all 100 hypothetical vehicles were traveling at 45 mph, what would you call the 85th percentile speed? Surely 45 mph, no?

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Kram,

2) "What if you have at least 2 cars traveling at 45mph? Won’t you have 86 cars traveling at 45mph or less making it 86% which is more than 85%?" If the definition was "below" instead of "at or below", I'd agree with this concern. If all 100 hypothetical vehicles were traveling at 45 mph, what would you call the 85th percentile speed? Surely 45 mph, no?

Yes, statistically the 85th percentile speed will be 45mph; however, is it a good 85th percentile speed? What if the sample size of 100 vehicles is observed traveling at 100mph at a school zone? Will 100mph be considered as the new safe speed at that location?

Another hypothetical question: What if there are 100 cars traveling, the first 84 cars are traveling at 30mph then the remaining 16 cars traveling at 100mph? Would it then be safe to assume that the speed of the 85th car which is traveling at 100mph be the 85th percentile speed and be considered as the new safe speed? Does that mean that 85% of the cars are traveling at 100mph or less? Or, would it be safer to assume that the 84th car’s speed which is 30mph be a better representation of the 85th percentile speed?

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I don't think so. Even when there are 100 cars, you still don't simply take the 85th fastest car's speed unless the cumulative % total adds up to exactly 85. If not, then the 85% speed will need to be interpolated. For our problem, if there were just one more car in any of the lower speed intervals (and one less in the upper), then the 40-44 interval would have been at a cumulative % of 85 and the 85th percentile speed would have been the average of 40-44 (42mph).

If there are 100 cars, the 85th fastest car will have a cumulative total of 85%, no? (1)

If we stay on just this question: "If 100 cars pass by, each with their speed recorded to the nearest mph, how do you determine the 85th percentile speed?" For me, the answer is simple and unequivocal: it's the speed of the 85th car when placed in order from slowest to fastest. (2)

(1) No sir. Please see my post #32 (and jaa's #17). Look at the cumulative column. The cumulative frequency %'s for this problem's speed intervals is 2, 13, 31, 60, 84, 97 and 100%. Since 85% falls between the cumulative 84% and the 97%, interpolation is required to determine the 85th percentile speed.

(2) This would be true of there were no recorded speed intervals (bins). If 100 unique speeds were recorded and placed in order then, yes, the 85th fastest speed would be the 85th percentile speed. But per this problem and per many agency's method, the cars passing are counted in a speed interval range (20-24, 25-29 ....... 50-54) . Once speed intervals are used (such as in this problem) and the 85th fastest car falls in one of these intervals, then interpolation is required to solve for the 85th percentile speed. Does that make sense?

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(1) No sir. Please see my post #32 (and jaa's #17). Look at the cumulative column. The cumulative frequency %'s for this problem's speed intervals is 2, 13, 31, 60, 84, 97 and 100%. Since 85% falls between the cumulative 84% and the 97%, interpolation is required to determine the 85th percentile speed.

I wasn't clear... I was talking about the measured speeds, not the binned speeds. So this difference leads us to:

(2) This would be true of there were no recorded speed intervals (bins). If 100 unique speeds were recorded and placed in order then, yes, the 85th fastest speed would be the 85th percentile speed. But per this problem and per many agency's method, the cars passing are counted in a speed interval range (20-24, 25-29 ....... 50-54) . Once speed intervals are used (such as in this problem) and the 85th fastest car falls in one of these intervals, then interpolation is required to solve for the 85th percentile speed. Does that make sense?

I think we're getting somewhere!

Regardless of how speeds are recorded (as measured or binned), they are surely measured in mph. Putting the speeds in bins (whatever their size) only has the effect of losing some (important!) information but the underlying measurement remains unchanged. In this problem of ours, the 85th fastest vehicle is very clearly in the 45-49 bin. So why should any decision on how to create bins (the bigger, the worse for losing information) affect this absolute truth: the 85th fastest vehicle is, without question, traveling between 45 and 49 mph.

To specifically address your last sentence, it makes perfect sense to me: once you know which bin the 85th fastest car falls in, you need to interpolate to solve for the 85th percentile speed. Because there are enough data points, I think it's even fine to linearly interpolate even though the distribution of speeds is best assumed to be normal.

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Yes, statistically the 85th percentile speed will be 45mph; however, is it a good 85th percentile speed? What if the sample size of 100 vehicles is observed traveling at 100mph at a school zone? Will 100mph be considered as the new safe speed at that location?

"Statistically" is all the 85th percentile is about. Yes, if all 100 vehicles are observed traveling at 100mph in a school zone, 100mph can be considered a safe speed. However, it is also assumed that the large majority of drivers are reasonable and prudent, do not want to have a crash, and desire to reach their destination in the shortest possible time. If these assumptions aren't true, the 85th percentile speed makes no sense. And remember, speeds are distributed normally unless something odd is happening. So you'll never see all of them going the same speed like your scenario unless they're in a convoy!

Another hypothetical question: What if there are 100 cars traveling, the first 84 cars are traveling at 30mph then the remaining 16 cars traveling at 100mph? Would it then be safe to assume that the speed of the 85th car which is traveling at 100mph be the 85th percentile speed and be considered as the new safe speed? Does that mean that 85% of the cars are traveling at 100mph or less? Or, would it be safer to assume that the 84th car’s speed which is 30mph be a better representation of the 85th percentile speed?

An interesting question (what's the "safest" way to answer) but, again, the example doesn't happen in the real world because speeds are normally distributed. The "proper" answer is the 85th percentile is still 100mph, even though just one more vehicle observed at 30mph would drastically change the answer.

85th percentile speeds don't make much sense if the traffic isn't normally distributed. For explanation why traffic studies use the 85th percentile speed, you can read http://onlinemanuals...ntile_speed.htm which includes:

Statistical Rationale

The results of numerous and extensive “before-and-after” studies substantiates the general propriety and value of the 85th percentile criterion.

Statistical techniques show that a normal probability distribution will occur when a random sample of traffic is measured. From the resulting frequency distribution curves, one finds that a certain percentage of drivers drive too fast for the existing conditions and a certain percentage of drivers travel at an unreasonably slow speed compared to the trend of traffic.

Most cumulative speed distribution curves “break” at approximately 15 percent and 85 percent of the total number of observations (see Figure 3-1). Consequently, the motorists observed in the lower 15 percent are considered to be traveling unreasonably slow and those observed above the 85th percentile value are assumed to be exceeding a safe and reasonable speed. Because of the steep slope of the distribution curve below the 85th percentile value, it can readily be seen that posting a speed below the critical value would penalize a large percentage of reasonable drivers.

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Percentile definition: http://en.wikipedia.org/wiki/Percentile

The 25th percentile is also known as the first quartile (Q1), the 50th percentile as the median or second quartile (Q2)…

Median definition: http://en.wikipedia.org/wiki/Median

In statistics and probability theory, median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values.[1][2]

This is one reason why I do not believe that the 85th percentile speed is always the 85th car’s speed if there is a sample of 100 cars unless I interpreted this incorrectly. If it is true that the 85th car’s speed is the 85th percentile speed then by that definition the 50th car’s speed would then be considered as the 50th percentile speed which is also called the median. However, by the definition of median if there is an even number of observations then the median is then usually defined to be the mean of the two middle values. If you have 100 cars and the speed of the 50th is 45mph and the 51st car is 47mph then the median would be 46mph which would not equal the 50th which is 45mph.

In my understanding the percentile ranges from 0.00 to 1.00 which is 101 values. If 1 to 100 (100 total values) is entered in Excel and the percentile(range:0.50) and percentile(range:0.85) is used the results would be 50.50 and 85.15 respectively. 50.50 will easily make sense because it’s the average of the 50th and 51st values which is also the median. However, if 0 to 100 (101 values representing each percentile) is entered in Excel and the percentile(range:0.50) and percentile(range:0.85) is used then the results would be 50 and 85 respectively. The 85th percentile speed will not be equal to the 85th car; the 85.16th(85/101) or 84th car will more likely be the 85th percentile speed. This brings back to the initial question why the answer would be C.43 instead of D.45; the 84th car is within the range 40-44.

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Kram,

rounding the result to the nearest integer, and then taking the value that corresponds to that rank. (Note that the rounded value of n is just the least integer which exceeds .)

Of course, this will *increase* the speed of the 85th percentile speed. And in our subject, we agreed it was "at or below", so I think that cancels out the rounding.

You lost me on

The 85th percentile speed will not be equal to the 85th car; the 85.16th(85/101) or 84th car will more likely be the 85th percentile speed. This brings back to the initial question why the answer would be C.43 instead of D.45; the 84th car is within the range 40-44.

You are saying the 85th percentile speed is something faster than the 85th fastest vehicle, yes?

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You lost me on

The 85th percentile speed will not be equal to the 85th car; the 85.16th(85/101) or 84th car will more likely be the 85th percentile speed. This brings back to the initial question why the answer would be C.43 instead of D.45; the 84th car is within the range 40-44.

You are saying the 85th percentile speed is something faster than the 85th fastest vehicle, yes?

I must have typed it wrong, that 85.16th should have been 84.16th which is the same as 85/101. I am saying that the 85th percentile speed out of 100 sample vehicles is less than the speed of the 85th car. In order for the 85th car to be the 85th percentile, there should be 101 sample cars because the percentile ranges from 0% to 100% which has 101 values. The median which is also the 50th percentile will only be true if the percentile range is based from 0% to 100% because it has an odd number of samples and 50 is the midpoint.

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With 100 observations, the percentiles (1% to 100%) range from the 1st observation (1%) to the 100th observation (100%)... remember, "at or below". I don't think there's such a thing as the 0th percentile.

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(1) No sir. Please see my post #32 (and jaa's #17). Look at the cumulative column. The cumulative frequency %'s for this problem's speed intervals is 2, 13, 31, 60, 84, 97 and 100%. Since 85% falls between the cumulative 84% and the 97%, interpolation is required to determine the 85th percentile speed.

I wasn't clear... I was talking about the measured speeds, not the binned speeds. So this difference leads us to:

(2) This would be true of there were no recorded speed intervals (bins). If 100 unique speeds were recorded and placed in order then, yes, the 85th fastest speed would be the 85th percentile speed. But per this problem and per many agency's method, the cars passing are counted in a speed interval range (20-24, 25-29 ....... 50-54) . Once speed intervals are used (such as in this problem) and the 85th fastest car falls in one of these intervals, then interpolation is required to solve for the 85th percentile speed. Does that make sense?

I think we're getting somewhere! (1)

Regardless of how speeds are recorded (as measured or binned), they are surely measured in mph. Putting the speeds in bins (whatever their size) only has the effect of losing some (important!) information but the underlying measurement remains unchanged. In this problem of ours, the 85th fastest vehicle is very clearly in the 45-49 bin. So why should any decision on how to create bins (the bigger, the worse for losing information) affect this absolute truth: the 85th fastest vehicle is, without question, traveling between 45 and 49 mph. (2)

To specifically address your last sentence, it makes perfect sense to me: once you know which bin the 85th fastest car falls in, you need to interpolate to solve for the 85th percentile speed. Because there are enough data points, I think it's even fine to linearly interpolate even though the distribution of speeds is best assumed to be normal. (3)

(1)

(2) Yes, you could argue that information is lost. But per the accepted method that many (most?) agencies (and the problem at hand) use to calc the 85th percentile speed, speed intervals (bins) are used during recording/observation and once they are used at the observation stage the, say, 47.8 mph is "lost" and is now placed in the 45-49 bin. Once this is done, the speed is now a 47 mph. Period. That's why the answer to this problem is C (I actually think the answer is closer to 42mph than 43mph but I guess the closest answer is still C). You have 24 cars traveling at an average of 42mph adding up to a cumulative % of 84 (just shy of the 85% we are looking for). You have 13 cars traveling at 47 adding up to a cumulative 97%. The 85% we are looking for is so much closer to the 84% so we know the 85% speed is also going to be closer to the 84% speed (42mph). So, without any additional calcs we can see that the 85% speed will be a little above 42mph but much closer to 42 than 47. Thus, answer C. I hope I am clear. It's easy to think the answer but hard to type it.

(3) I think you lost me. Do you see why the answer is C? I'll try to explain more clearly if not.

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ptatohed,

There are 100 vehicles for which their speed was recorded. In what bin was the 85th fastest vehicle?

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With 100 observations, the percentiles (1% to 100%) range from the 1st observation (1%) to the 100th observation (100%)... remember, "at or below". I don't think there's such a thing as the 0th percentile.

rounding the result to the nearest integer, and then taking the value that corresponds to that rank. (Note that the rounded value of n is just the least integer which exceeds .)

The first part of the equation quoted from Wikipedia is the following:

One definition of percentile, often given in texts, is that the P-th percentile () of N ordered values (arranged from least to greatest) is obtained by first calculating the (ordinal) rank

which suggests that the percentile is from 0% to 99% and includes 0%. After looking at this equation again, I am wrong that there should be 101 values which is from 0% to 100%. The values range from 0% to 99%; if each of the 100 speeds is compared to the percentiles the following would happen: The speed of the 1st vehicle would be 0% because it is not faster than any other vehicle. 2nd vehicle to the 1st percentile until the 85th vehicle which would then be the 84th percentile.

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I guess since there are different ways of calculating percentiles that give different results, then it will be hard to agree on the same answer; however the 85th fastest car in a sample size of 100 is not necessarily the 85th percentile in my opinion. If there are 100 numbers from 1 to 100 and the following equation is used the 85th percentile would be 85.5; however if the percentile function of Excel 2003 is used, 84.15 would be the 85th percentile. Assigning each number to the percentile (1 to 0%, 85 to 84%, 100 to 99%) results in the 84 being the 85th percentile.

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I guess since there are different ways of calculating percentiles that give different results, then it will be hard to agree on the same answer; however the 85th fastest car in a sample size of 100 is not necessarily the 85th percentile in my opinion. If there are 100 numbers from 1 to 100 and the following equation is used the 85th percentile would be 85.5; however if the percentile function of Excel 2003 is used, 84.15 would be the 85th percentile. Assigning each number to the percentile (1 to 0%, 85 to 84%, 100 to 99%) results in the 84 being the 85th percentile.

Is there a way to edit a post if you make a mistake?

84.15 should be 85.15 and 84 being the 85th should be 86 being the 85th.

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Is there a way to edit a post if you make a mistake?

84.15 should be 85.15 and 84 being the 85th should be 86 being the 85th.

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ptatohed,

There are 100 vehicles for which their speed was recorded. In what bin was the 85th fastest vehicle?

Il, trust me, I get your point. Yes, the 85th vehicle was in the 45-49 mph speed interval. But the question is not asking "what was the speed of the 85th vehicle?". The question is "what is the 85th percentile speed?". This needs to be calculated. The calculations are previously included in this thread so I don't want to go through them again.

Again, if there were 100 recorded individual speeds, the speed of the 85th fastest car would be the answer (of course, we have no idea what this is in this problem). But, once speed intervals/bins are used in the data collection as they are here and we now have so many cars traveling at 42mph and so many cars traveling at 47, and the 85th percentile speed is somewhere in between, we must use the correct linear interpretation calculations to derive the 85th % speed (calcs previously posted). The best answer is C.

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Il, trust me, I get your point. Yes, the 85th vehicle was in the 45-49 mph speed interval. But the question is not asking "what was the speed of the 85th vehicle?". The question is "what is the 85th percentile speed?". This needs to be calculated.

OK, so here's a fundamental difference we have. The more I think of it, the better and better this problem is looking as a great problem for the PE exam. Equations should never be blindly followed and especially not when you know they violate the underlying principles. Much earlier in this thread I wrote about the "plug and chug" mentality.

Again, if there were 100 recorded individual speeds, the speed of the 85th fastest car would be the answer (of course, we have no idea what this is in this problem).

And another big disagreement here: of course we have an idea what speed each and every car is travelling because we assume they are normally distributed. 100 samples are surely in the realm of the large numbers.

And let me ask you to do this final thing... putting away all previous discussion in this thread: Go back to the fundamentals of 85th percentile speeds (I gave this http://onlinemanuals.txdot.gov/txdotmanuals/szn/determining_the_85th_percentile_speed.htm but there are surely other sources). And ask yourself this: can binning speeds change the underlying principles of 85th percentile speeds? That is, can the throwing away of information (exact MPH speed) in favor of the convenience for collecting tick marks in a bin on a form, change the underlying process that drives the use of 85th percentile speeds?

Here's what I'm understanding you to say: You agree the 85th fastest vehicle is the definition of the 85th percentile speed. You agree the 85th fastest vehicle is in the 45-49 bin. You want to use an equation that assumes all speeds in a bin are actually at the mean of the bin, even though you know this is not representative of reality. You come up with an answer that you know does not reflect reality. All in favor of following an FDOT recommended process.

Still, I appreciate the discussion especially since we've kept it civil of late! I find this problem fascinating... not sure exactly why.

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Still, I appreciate the discussion especially since we've kept it civil of late! I find this problem fascinating... not sure exactly why.

I think the rest of us find it fascinating that we're flogging this horse of a question to no end.

It's time to call it a day on this one. The method of calculating the 85th percentile is really a no-brainer and doesn't merit an academic exercise.

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It's time to call it a day on this one. The method of calculating the 85th percentile is really a no-brainer and doesn't merit an academic exercise.

Keep telling yourself that... :-)

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Il, trust me, I get your point. Yes, the 85th vehicle was in the 45-49 mph speed interval. But the question is not asking "what was the speed of the 85th vehicle?". The question is "what is the 85th percentile speed?". This needs to be calculated.

OK, so here's a fundamental difference we have. The more I think of it, the better and better this problem is looking as a great problem for the PE exam. Equations should never be blindly followed and especially not when you know they violate the underlying principles. Much earlier in this thread I wrote about the "plug and chug" mentality. (1)

Again, if there were 100 recorded individual speeds, the speed of the 85th fastest car would be the answer (of course, we have no idea what this is in this problem).

And another big disagreement here: of course we have an idea what speed each and every car is travelling because we assume they are normally distributed. 100 samples are surely in the realm of the large numbers. (2)

And let me ask you to do this final thing... putting away all previous discussion in this thread: Go back to the fundamentals of 85th percentile speeds (I gave this http://onlinemanuals...ntile_speed.htm but there are surely other sources). And ask yourself this: can binning speeds change the underlying principles of 85th percentile speeds? That is, can the throwing away of information (exact MPH speed) in favor of the convenience for collecting tick marks in a bin on a form, change the underlying process that drives the use of 85th percentile speeds?

Here's what I'm understanding you to say: You agree the 85th fastest vehicle is the definition of the 85th percentile speed. You agree the 85th fastest vehicle is in the 45-49 bin. You want to use an equation that assumes all speeds in a bin are actually at the mean of the bin, even though you know this is not representative of reality. You come up with an answer that you know does not reflect reality. All in favor of following an FDOT recommended process. (3)

Still, I appreciate the discussion especially since we've kept it civil of late! I find this problem fascinating... not sure exactly why.

(1) It appears that you are continuing to look at this problem from a mathematical point of view instead of an engineering point of view. I do very much disagree with your lack of appreciation for pre-established engineering formulas/equations. They are there for a reason! They have been established and agreed upon by engineers before us. Who are we to disregard industry standards and use our own? Why reinvent the wheel? There is an established and agreed upon procedure for determining the 85th percentile speed from collected data. Period. You don't need to agree with it or even like it. But it is the correct way of solving this problem. And it is the answer to this problem and to the original poster's question. I'm actually surprised you think this is such a good problem for the PE exam given that the correct solution is derived from the previously shown method leading to answer C. With all due respect, you'd get this problem wrong if you answered D on the exam. Do you not agree with that?

(2) You are right, we do disagree here. I think that once the exact speed is thrown out in exchange for speed interval tick marks during the data collection, we now no longer know the exact speed each of the cars within an interval was traveling.

(3) Yes, you summed up my answer correctly. I see absolutely no problem with using an industry accepted method to calculate the 85th % speed even if it does not reflect reality as you say it. The same way I'd order 18" pipe even if my calculations showed a 16.2" diameter was needed given my Q (because I know that they don't make 17" pipe). If I calculated a design speed of 54, I'd post 50, not 55. If I was designing curb and gutter on street plans for the City of Anyville, I'd sure as heck use their City Standard Plan for C&G (even though I may personally prefer Std 120-2 of the SPFPWC), if I was calculating the Q coming off of a proposed developed site, I might use a coefficient of runoff a little higher than "reality", to be conservative. Etc. etc.

I hope you get my point. Again, with all due respect, the answer to the original question is C and the previous calculations are correct. That answers the question asked by the original poster.

I'm not really interested in going back and forth any longer about how the answer "should be" this or that. The correct answer is C. If you have questions about how C is derived, I'd be happy to answer. But if you continue to simply repeat yourself that the answer "should be" D, then there isn't much more I can say. Thanks.

Edited by ptatohed