How does the speed of runner vary over the course of a marathon (a distance of 4

Question

How does the speed of runner vary over the course of a marathon (a distance of 42.195km)? Consider determining both the time to run the first 5 km and the time to run between the 35-km and 40-km points, and then subtracting the former time from the latter time. A positive value of this difference corresponds to a runner slowing down toward the end of the race. The accompanying histgram is basd on times of runners who participated in sevral different Japanese marathons.

What are some interesting of this histogram? what is a typical difference value? Roughly what proportion of the runners ran the late distance more quickly than the early distnace?

I don't wnat a copy from http://www.stat.rice.edu/~dcox/Stat305/Hw01/node2.html

thank you

Explanation / Answer

The marathon is a long-distance running event of 42.195 kilometres (26 miles 385 yards) that can be run either as a road race or off-road.There may be a few outliers around 700 seconds or around 11.67 minutes.

histogram for the aligned part of the model. This slope matches precisely to the eyeball fit of the cumulative finish time plot.A histogram of the rates shows the same damped exponential distribution, reinforcing the reason for the good model fit. Notice that the histogram has an even more exponential look than the Hawaii Triathlon. Since the Portland Marathon contains a huge number of female walkers (more so proportionally than Hawaii), the effect of censoring beyond the cut-off point becomes reduced even further. Again, one can ultimately imagine that if more couch potatoes who dream of finishing a marathon (a huge, huge number!) eventually entered, that the censored region would likely get populated, or at least fleshed out.

Typical difference value

Mode - 50-100 range

Mean - 200-250 range

Medien - 150 - 200 range

Proportion of the runners ran the late distance more quickly than the early distance

It's depending on your size and the intensity of your run.Here sample size n say 500, and maybe 1,000 on the outside. Thus, the proportion of runners ran the late distance more quickly than the early distance is around 10/1000 and 10/500

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