Question

The table below shows the number of wins per season for the New England Patriots and Detroit Lions NFL teams from 2004 through 2012 Year New England Patriots Detroit Lions 10 12 16 3 7 2004 2005 2006 2007 2008 2009 2010 2011 10 13 2012 32. From the above table and using Xcel spreadsheet, a) Calculate the mean for each of the two teams b) Calculate the variance for each of the two teams c) Calculate the standard deviation for the two teams d) Calculate the coefficient of variation (CNfor the two teams e) Which of the two teams experienced more variability with games won per season?

Answer 1

Solution:

We have the following required formulae:

Mean = sum of all observations/number of observations

Variance = sum((each observation - mean)²)/(number of observations - 1)

Standard deviation = Variance^1/2

And, coefficient of variation = (standard deviation/mean)*100%

Then, 32)

a) For New England Patriots (NEP):

Mean = (14 + 10 + 12 + 16 + 11 + 10 + 14 + 13 + 12)/9 = 112/9 = 12.444

For Detroit Loins (DL):

Mean = (6 + 5 + 3 + 7 + 0 + 2 + 6 + 10 + 4)/9 = 43/9 = 4.778

b) For NEP:

Variance = [(14 - 12.444)² + (10 - 12.444)² + (12 - 12.444)² + (16 - 12.444)² + (11 - 12.444)² + (10 - 12.444)² + (14 - 12.444)² + (13 - 12.444)² + (12 - 12.444)²]/(9 - 1)

Variance = [2.421 + 5.973 + 0.197 + 12.645 + 2.085