1 Mountainback The following data are from the Tussey Mountainback, a local 50 m

Question

1 Mountainback The following data are from the Tussey Mountainback, a local 50 mile ultramarathon which is divided into 12 stages (aka "legs") so that it can also be run as a relay race. The race starts and finishes at the same point on Tussey Mountain and the course goes through the Rothrock State Forest Leg | Mileage | Elev. (ft) | Tot. Climb (ft) | Tot. Climb (mi) | Climb Grd ( Tot. Desc ft Tot. Desc (mi) Desc Grd 5.05 4.2 2.26 773 887 -228 478 498 1301 -649 -470 472 369 558 -481 885 2.78 6.03 112 887 315 372 583 29 0.42 2 3.8 5.6 3.4 87 1.42 4.95 2.87 6.63 3.71 .75 4. 1 6.85 1.87 2.36 1.16 3.25 0.56 3.8 0.75 1.3 2.55 2.64 2.35 2.84 0.3 2.95 3.89 1.83 5.11 .16 4.49 3.3 2.75 6 1330 147 189 553 398 819 112 3.7 1.3 2.9 659 0.35 1.1 10 5.3 1.2 3.3 0.9 290 592 12 3.3 a) Create a box plot and a histogram to display the distribution of the mileage and elevation change for each leg of the race b) For each variable above, what is something the histogram tells you that the boxplot does not? What is something the boxplot tells you that the histogram does not? c) For each variable above, write whether you expect the mean to be be close to the median, much higher, or much lower. Why? Calculate the mean...were you right?

Explanation / Answer

(a)

R code is give as:

mileage<-c(3.2,4,3.8,5.6,3.4,4.1,3.7,4.3,2.9,5.5,5.3,4.2)
mileage
hist(mileage)
boxplot(mileage)

Elev_ft<-c(773,-887,-228,478,-498,1301,-649,-470,472,-369,558,-481)
Elev_ft
hist(Elev_ft)
boxplot(Elev_ft)

For Elev.(ft)

(b)

Boxplot does not show the missing or space in between 4.5 to 5.0 while histogram shows the space in between 4.5 to 5.0. Histogram displays frequencies for a group of data, rather than an individual data point; therefore, no spaces are present between the bars.

By the help of the boxplot third and first quartile can be easily identify and it also halp to identify the extreme values and interquartile range while histogram is not able to show the quartiles, extreme values and interquartile range.

(c)

In the case of Mileage, the mean is 4.166 is close to the median that is shown by boxplot. But in case of Elev.(ft) mean is 0 that is much higher than median.

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