85th Percentile Speed Question

[ptatohed]

That's what I found too and since 85 would be into the next speed range the 45 MPH answer seemed logical.

In the solutions they graphed the frequency vs. the speed. However when they drew a horizontal line from 85% they didn't intersect the graphed information and called it 43.5 MPH and I was confused because if they intersected the graphed line with the 85% line it would've been higher that 43.5 MPH. Seems like a fine line between answers C and D.

The traffic engineer in my office told me there is an equation for questions like that but couldn't remember what it was. I would think if we had to graph anything in the actual test the answer would be a lot clearer and have a larger difference in the answers than 2 MPH.

ceg, could you please post the actual solution? Thanks.

 

[IlPadrino]

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.

This is incorrect. If the vehicle counts were doubled (i.e. total of 200 cars in the sample set), you would still think the 85 percentile speed is 45 mph because of your "bin" theory. This is why the vehicle count versus percentile must be mutually exclusive.

OK... you refuse to address the questions/points I make, so there's not much more I can do for you with this discussion. You don't understand percentiles well enough to know that when there are 100 values (as in this problem), the 85th percentile is, by definition, the 85th largest value when put in rank order. Your counter about what happens when there are 200 vehicles or binned values has nothing to do with the DEFINITION of percentile.

 

[IlPadrino]

If you had to do this calculation for a client ... say in Florida ...and you were required to put your stamp on it, would you really stray from the standard? I didn't think so.

Hell, yeah... I absolutely would. This isn't the case of ignoring some mandatory code requirements (e.g. IBC, NEC, ACI, etc.). Major provided a state publication which has the explicit purpose "to provide guidelines and recommended procedures for establishing uniform speed zones on State, Municipal, and County roadways throughout the State of Florida." It's a *guide* with *recommended procedures*. If you're not smart enough to understand the science and math behind the topic, you've got no business being an engineer.

And, yeah, this is one of my pet peeves: engineers who simply plug-and-chug and claim the incorrect answer isn't their fault because they followed someone's formula.

 

[IlPadrino]

According to DISTRIBUTION OF VEHICLE SPEEDS AND TRAVEL TIMES by DONALD S. BERRY AND DANIEL M. BELMONT of UNIVERSITY OF CALIFORNIA:

"The speeds of vehicles past a point on a highway tend to have a roughly normal distribution except when traffic volume exceeds the practical capacity of the highway."

The data bins certainly look normally distributed to me.

Now you're just being contrary. Your bin theory does not comply to a normal distribution graph; it would a stepped (layer cake) graph. If you visualize the data as a bell-curve graph, then you have to assign a single value within each bin, like a trend line. You would then use this line to determine your percentile vs. speed graph (i.e. the area under the bell curve at each interval divided by the total number in the sample set).

As for your suggestion to assume a normal/linear distribution within each bin, your boundary conditions for each bin would be based the output of the previous bin and the input of the next bin. Does this sound like a realistc approach?

Now you're just f*cking with me... bin theory (what the hell is that?) has nothing to do with how random values are distributed. Do you deny the (intuitively obvious) fact that traffic spot speeds are usually normally distributed? Of course there are exceptions (I gave two) but that doesn't change the fact that the bin counts in this problem appear to be normally distributed, too.

I don't understand what you wrote: "your boundary conditions for each bin would be based the output of the previous bin and the input of the next bin. Does this sound like a realistc approach?"

You must recognize that each vehicle has a specific speed (measured to whatever number of significant digits you're instrument gives you) regardless of how you tally counts on a form.

Would you please answer this question... if the 85th vehicle (in rank order from slowest to fastest) was really going 43 mph, then doesn't the bin count for 40-44 have to be 25 instead of 24?

 

[IlPadrino]

This is one of those classic examples of people blindly applying a standard that somebody established years ago without actually thinking about it critically.

This is where an educated engineer with a license would bang their heads against a wall with an unlicensed, state DOT plan reviewer, because it doesn't follow the book answer, and you can clearly see that the book answer is not right.

What he said!

 

[IlPadrino]

Post #32 is the clear winner in this debate and would get the correct answer in the exam.... which is what it's all about, right?

You wouldn't find a problem like this on the exam because exam questions are written by engineers who understand the principles behind the subjects and every question is peer reviewed. 43 is an answer that is inconsistent with the reality of the data provided.

 

[mrt406]

For what it's worth, I'll throw my hat in and formally agree with sac and ptatohed. From my understanding and experience, the 85th percentile speed is most definitely a calculated speed, not a counted speed. More specifically, a speed that's calculated specifically using the equation previously provided by sac and the numerous examples provided by others.

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.

http://www.dot.state.fl.us/trafficoperations/Operations/Studies/MUTS/Chapter13.pdf

As for....

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 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.

Finally, I'd also like to mention that I don't particularly support, or respect, the idea of telling someone they're not "smart enough" to understand the concept behind a problem simply because you don't agree with their solution.

 

[sac_engineer]

You don't understand percentiles well enough to know that when there are 100 values (as in this problem), the 85th percentile is, by definition, the 85th largest value when put in rank order.

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.

 

[sac_engineer]

Bravo mrt406!

The process of solving this question is about calculation, not just by adding some numbers then determining which bin the next highest number falls into.

Another example of an acceptable calculated value is the number of people per household: 2.59. Common sense tells you that there's no such thing as a 0.59 person, but it's calculated, just like the 85th percentile. Maybe we need to occupy the offices of the US Census Bureau and stand up for the 0.59!

 

[IlPadrino]

Finally, I'd also like to mention that I don't particularly support, or respect, the idea of telling someone they're not "smart enough" to understand the concept behind a problem simply because you don't agree with their solution.

My comment wasn't directed at anyone in particular but rather it was addressed to those engineers who use guides without understanding the concepts behind them. I apologize for not writing more clearly.

I stand by my point: if you don't understand the fundamentals of a topic, you'd better not just plug-and-chug your way to an answer and then throw a stamp on it.

 

[IlPadrino]

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

You can also read about percentiles at http://en.wikipedia....wiki/Percentile and http://www.itl.nist.gov/div898/handbook/prc/section2/prc252.htm

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

 

[IlPadrino]

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.

 

[ptatohed]

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).

 

[IlPadrino]

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.

 

[Kram]

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

 

[IlPadrino]

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?

 

[Kram]

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?

 

[ptatohed]

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?

 

[IlPadrino]

(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.

 

[IlPadrino]

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.