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you can't say anything about your speed relative to the mean. You can only infer information about your speed relative to the median or about the percentile. The mean and the median can only coincide when the distribution is normal and the population includes one element whose value is exactly equal to the mean and is also the median.

If $n$ people pass you, and you pass $n$ people, you can say that you are in the middle $1/(2n+1)$ of the pack. If $x$ people pass you, and you pass $y$ people, you can say that your percentile is $100 (y)/(x+y)$. You can be more certain about your relative velocity with more knowledge acquired: by passing more people, or letting more people pass you. Or if not "more certain", you have more precision in the knowledge of your relative velocities percentile as the number of observations increases.

• If $(x+y)=0$, you have no knowledge of your relative velocity in the population.

• If $(x+y)=m$, then you know your percentile in the velocity distribution to the nearest $(m+1)$-th partile, or nearest $1/(m+1)$ fraction. If $m=4$, you can only know your quintile (which definitely is a word), since $m+1=5$.

If you don't know the underlying distribution of the velocities of the population, you can't infer a lot about your own absolute velocity. If you don't pass or get passed by many people, you can't know much about your relative velocity.

I have to admit to using this when I run to keep pace. I get spurred to run faster if I start getting passed by more people than I myself am running past. Of course, being passed by a muscular athletic jogger is more of an incentive. So adding more factors about the athletic prowess of each individual relative to you could also tell you more. But if the only collection acquired about your relative speed are the two integers, then only your percentile in the unknown velocity distribution can be inferred.

As to Aaron Meyerowitz about the static observor, there is a problem with changing the frame of reference of the observer if you do not take into account the absolute velocity in the frame of reference of the ground. Some runners may actually be running facing in the other direction, and converting to the static observer does not account for that,

Example: you are in a car driving west on a highway. You can infer your velocity rank or percentile relative to the west-bound vehicles by keeping track of how many west-bound vehicles pass you and how many of them you pass. If you accidentally include the east-bound vehicles on the other side of the road, you will come to the erroneous conclusion that you are going very fast indeed, as you are "passing" many vehicles oriented and bound in the eastern direction.

But, when you change the frame of reference to a static observer on the track, you have to look at what direction the runner is facing in order to make sure that you are only counting the runners facing the same direction and running in the same direction as you.

Strangely enough, I once saw someone walking backwards on a sidewalk, though not on the oval-track at the local junior high school.

4 spelling mistakes fixed

you can't say anything about your speed relative to the mean. You can only infer information about your speed relative to the median or about the percentile. The mean and the median can only coincide when the distribution is normal and the population includes one element whose value is exactly equal to the mean and is also the median.

If $n$ people pass you, and you pass $n$ people, you can say that you are in the middle $1/(2n+1)$ of the pack. If $x$ people pass you, and you pass $y$ people, you can say that your percentile is $100 (y)/(x+y)$. You can be more certain about your relative velocity with more knowledge acquired: by passing more people, or letting more people pass you. Or if not "more certain", you have more precision in the knowledge of your relative velocities percentile as the number of observations increases.

• If $(x+y)=0$, you have no knowledge of your relative velocity in the population.

• If $(x+y)=m$, then you know your percentile in the velocity distribution to the nearest $(m+1)$-th partile, or nearest $1/(m+1)$ fraction. If $m=4$, you can only know your quintile (which definitely is a word), since $m+1=5$.

If you don't know the underlying distribution of the velocities of the population, you can't infer a lot about your own absolute velocity. If you don't pass or get passed by many people, you can't know much about your relative velocity.

I have to admit to using this when I run to keep pace. I get spurred to run faster if I start getting passed by more people than I myself am running past. Of course, being passed by a muscular athletic jogger is more of an incentive. So adding more factors about the athletic prowess of each individual relative to you could also tell you more. But if the only collection acquired about your relative speed are the two integers, then only your percentile in the unknown velocity distribution can be inferred.

As to Arron Aaron Meyerowitz about the static observor, there is a problem with changing the frame of reference of the observer if you do not take into account the absolute velocity in the frame of reference of the ground. Some runners may actually be running facing in the other direction, and converting to the static observer does not account for that,

Example: you are in a car driving west on a highway. You can infer your velocity relative to the west-bound vehicles by keeping track of how many west-bound vehicles pass you and how many of them you pass. If you accidentally include the east-bound vehicles on the other side of the road, you will come to the erroneous conclusion that you are going very gast fast indeed, as you are "passing" many vehicles oriented and bound in the eastern direction.

But, when you change the frame of reference to a static observer on the track, you have to look at what direction the runner is facing in order to make sure that you are only counting the runners facing the same direction and running in the same direction as you.

Strangely enough, I once saw someone walking backwards on a sidewalk, though not on the oval-track at the local junior high school.

3 middle third

you can't say anything about your speed relative to the mean. You can only infer information about your speed relative to the median or about the percentile. The mean and the median can only coincide when the distribution is normal and the population includes one element whose value is exactly equal to the mean and is also the median.

If $n$ people pass you, and you pass $n$ people, you can say that you are in the middle $1/(2n+1)$ of the pack. If $x$ people pass you, and you pass $y$ people, you can say that your percentile is $100 (y)/(x+y)$. You can be more certain about your relative velocity with more knowledge acquired: by passing more people, or letting more people pass you. Or if not "more certain", you have more precision in the knowledge of your relative velocities percentile as the number of observations increases.

• If $(x+y)=0$, you have no knowledge of your relative velocity in the population.

• If $(x+y)=m$, then you know your percentile in the velocity distribution to the nearest $(m+1)$-th partile, or nearest $1/(m+1)$ fraction. If $m=4$, you can only know your quintile (which definitely is a word), since $m+1=5$.

If you don't know the underlying distribution of the velocities of the population, you can't infer a lot about your own absolute velocity. If you don't pass or get passed by many people, you can't know much about your relative velocity.

I have to admit to using this when I run to keep pace. I get spurred to run faster if I start getting passed by more people than I myself am running past. Of course, being passed by a muscular athletic jogger is more of an incentive. So adding more factors about the athletic prowess of each individual relative to you could also tell you more. But if the only collection acquired about your relative speed are the two integers, then only your percentile in the unknown velocity distribution can be inferred.

As to Arron Meyerowitz about the static observor, there is a problem with changing the frame of reference of the observer if you do not take into account the absolute velocity in the frame of reference of the ground. Some runners may actually be running facing in the other direction, and converting to the static observer does not account for that,

Example: you are in a car driving west on a highway. You can infer your velocity relative to the west-bound vehicles by keeping track of how many west-bound vehicles pass you and how many of them you pass. If you accidentally include the east-bound vehicles on the other side of the road, you will come to the erroneous conclusion that you are going very gast indeed, as you are "passing" many vehicles oriented and bound in the eastern direction.

But, when you change the frame of reference to a static observer on the track, you have to look at what direction the runner is facing in order to make sure that you are only counting the runners facing the same direction and running in the same direction as you.

Strangely enough, I once saw someone walking backwards on a sidewalk, though not on the oval-track at the local junior high school.

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