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Typically, the statistical data collected on atmospheric conditions are pertinen

ID: 3133393 • Letter: T

Question

Typically, the statistical data collected on atmospheric conditions are pertinent to temperature (T in degree F), saturated vapor pressure (SVP in mb), wind-speed (WS in mph) and wind-chill index (WCI in deg. F). Relevantly, answer the following questions: (a) Estimate with reason(s) the average performance of random WCI trend versus the temperature (T) fluctuation observed in a day-time measurement schedule as tabulated: (b) Under certain weather conditions, the WCI is functionally decided and influenced jointly by the ambient temperature (T) and the prevailing wind-speed (WS) conditions. Hence evaluate with reason(s) the average performance trend of WCI versus the temperature (T) changes observed in a measurement schedule as tabulated: (Give reason for your answer). (c) The observations in a measurement schedule of a particular day on the random wind-speed (WS) fluctuation versus the temperature (T) are as tabulated. Estimate with reason(s) on the average performance trend of WS on that day.

Explanation / Answer

mean = sum(x*f) / sum(f)

var = sum(x^2*f) / sum(f) - mean^2

Overall mean = (10.22148+9.880359+10.17289+11.03854)/4 = 10.17289

where g1 is the skewness.

a4 and g2 are the measure of kurtosis.

g1 = m3 / m2^(3/2)

a4 = m4 / m2^2

m2 = sum(x-mean)^2*f

m3 = sum(x-mean)^3*f

m4 = sum(x-mean)^4*f

x f xf x^2f (x-mean)^2 (x-mean)^2*f (x-mean)^3*f (x-mean)^4*f 0 3 0 0 104.4786534 313.4359602 -3203.779398 32747.36704 5 10 50 250 27.26385339 272.6385339 -1423.576652 7433.177017 10 14.15 141.5 1415 0.04905339 0.694105474 -0.15373048 0.034048227 15 18 270 4050 22.83425339 411.016561 1964.050857 9385.256302 45.15 461.5 5715 154.6258136 997.7851606 -2663.458923 49565.83441 g1 -0.08451 a4 2.073091287 g2 -0.926908713