Question

During one​ year, there were 10 hurricanes recorded. Their maximum wind​ speeds, in miles per hour​ (mph), were as shown in the following table. Consider these storms a population of interest. Obtain the following parameters for the maximum wind speeds. Use the appropriate mathematical notation for the parameters to express your answers. a. Mean b. Standard deviation c. Median d. Mode e. IQR Max wind (mph) 80 100 115 85 105 85 110 90 95 110 a. The population mean is represented by x overbar eta Upper M x overbar sigma s mu and is equal to nothing.

Answer 1

a) The population mean is estimated by the sample mean as xbar = (1/n) sum(Xi) , where Xi is the ith observation, i=1(1)n, n being the total number of observations. Here xbar = 97.5 (mph)

b) The population standard deviation is estimated by the sample standard deviation, s= ((1/(n-1))sum(xi-xbar)²)^0.5 , i=1(1)n.

Here s = 12.30402

c) Median = average value of the 2 middle most elements in the sorted dataset. Here median = 97.5

d) Mode = the number of observation occurring the maximum number of times. Since the observation 85 and 110, both occurs twice and the other observations occur once, so the dataset is a bimodal dataset with modes being 85 and 110.

e) The Interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1), i.e. IQR = Q3-Q1 = 22.5.

(The answers are obtained using R-software. Code and output are attached below).