Question

28. The Australian Open is the first of the four Grand Slam professional tennis events held cach year. Victoria Azarenka beat Maria Sharapova to win the 2012 Australian Open wom- en's title (Washington Post, January 27, 2012). During the tournament Ms. Azarenka's serve speed reached 178 kilometers per hour. A list of the 20 Women's Singles serve speed leaders for the 2012 Australian Open is provided below. DATA file Australian Open Serve Speed (km/h) 191 190 187 187 Player S. Williams S. Lisicki M. Keys L. Hradecka J. Gajdosova J. Hampton B. Mattek-Sands F. Schiavone P. Parmentier N. Petrova Serve Speed (km/h) 179 178 178 178 178 Player G. Arn V. Azarenka A. Ivanovic P. Kvitova M. Krajicek V. Dushevina S. Stosur S. Cirstea M. Barthel P. Ormaechea 187 181 178 178 177 181 179 179 179 177 177 a. b. Compute the mean, variance, and standard deviation for the serve speeds. A similar sample of the 20 Women's Singles serve speed leaders for the 2011 Wimbledon tournament showed a sample mean serve speed of 182.5 kilometers per hour. The variance and standard deviation were 33.3 and 5.77, respectively. Discuss any difference between the serve speeds in the Australian Open and the Wimbledon women's tournaments. ir nuity index for various areas of Southern

Answer 1

a)

X	(X - X̄)²
191	101.00
190	81.90
187.0	36.60
187	36.60
187	36.60
181	0.00
181	0.003
179	3.802
179	3.802
179	3.802
179	3.802
178	8.702
178	8.702
178	8.702
178	8.702
178	8.702
178	8.702
177	15.602
177	15.602
177	15.602

	X	(X - X̄)²
total sum	3619	406.95
n	20	20

mean =    ΣX/n =    3619.000   /   20   =   180.9500
                      
sample variance =    Σ(X - X̄)²/(n-1)=   406.95   /   19   =   21
                      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (406.95/19)   =       4.628

b)

wibbledon tournament serve speeds have greater mean with greater variation than that of Australian Open