HW#2 1. The given table below shows the average property damage caused by tornad

Question

HW#2 1. The given table below shows the average property damage caused by tornadoes over a 50-year period in each of the states. The distribution is strongly skewed to the right. (a) Give the five-point summary. (b) Show that there are no suspected outliers according to the 1.5xIQR rule. (c) Find the mean property damage. Explain why the mean and median differ so greatly for this Damage(Smillions) State Damage(Smillions) 51.88 0.00 3.47 40.96 3.68 Pennsylvania 17.11 Puerto Rico 0.05 Rhode Island 0.09 South Carolina 17.19 South Dakota 10.64 Tennessee 23.47 88.60 3.57 0.24 California 2.26 Delaware 37.32 0.34 0.26 7.42 62.94 53.13 49.51 49.28 24.84 27.75 0.53 2.33 Washington 2.37 West Virginia 2.14 Wisconsin 31.33 Wyoming 1.78 29.88 84.84 43.62 68.93 0.26 Mississippl Nevada 0.10 New Hampshire 0.66 2.94 New Mexico New York North Carolina 14.90 North Dakota14.69 81.94 -” F6

Explanation / Answer

(a) The 5-point summary is given below.
Min. Q1 Median Q3 Max.
0.00 2.17 12.66 35.82 88.60

(b) We identify an observation as an outlier if is less than Q1 - (1.5 * IQR) or greater than Q3 + (1.5 * IQR). Here, IQR = Q3 - Q1.
Here, Q1 - (1.5 * IQR) = - 48.305 and Q3 + (1.5 * IQR) = 86.295.
Checking the observations and these cutoffs, we conclude that the damage value of $88.6 million (of Texas) is a suspected outlier.

(c) The mean is 21.92.
This dataset has a mean value which is greater than that of the median. This happens in case of a positively skewed distribution where, more precisely, mean > median > mode. Since we have provided with the information that the distribution is strongly skewed to the right (or, positively skewed), we can say that the mean value being greater than the median value is justified.

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