The Australian Open is the first of the four Grand Slam professional tennis events held each year. Victoria Azarenka beat Maria Sharapova to win the 2012 Australian Open women'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.

a. Compute the mean, variance, and standard deviation for the serve speeds.
b. 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.

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Player S. Williams S. Lisick Playe 3 G. An V Azarenka A. Ivanovic PKvitova M. Krajicelk 179 178 178 178 178 178 178 190 L. Hradecka J. Gajdosova B. Mattek-Sands F. Schiavone P. Parmentier N. Petrova 179 179 179 S. Cirstea M. Barthel P Ormaechea