Variance of Professional Athletes’ Salaries
Topic
Analyzing Professional Athletes’ Salaries using Variance and Standard Deviation
Vocabulary
 Mean
 Median
 Mode
 Range
 Difference from mean
 Squared Difference
 Variance
 Standard Deviation
Student Exploration
What is your favorite sport? What do professional athletes in that sport earn?
What is your favorite sport? Pick ten athletes from your favorite sport and record all of their salaries in the table below (in the “Athlete’s Salary, \begin{align*}x\end{align*}
Then find the following information for those ten athletes’ annual salary.

1. Find the mean, \begin{align*}\overline{x}\end{align*}
x¯¯¯ .  2. Find the median.
 3. Find the mode.
 4. Find the range.
 5. Complete the table by calculating the difference from the mean (deviation from the mean) and the squared difference (squared deviation).
Athletes’ Salary \begin{align*}x\end{align*} 
Deviation from mean, \begin{align*}x\overline{x}\end{align*} 
Squared deviation, \begin{align*}(x\overline{x})^2\end{align*} 

 6. Calculate the variance. Again, the variance is a measure of the dispersion and its value is lower for tightly grouped data than for widely spread data. What does the variance say about your data? Explain.
 7. Calculate the standard deviation. Again, the standard deviation measures how closely the data clusters around the mean. It is the square root of the variance.
 8. What makes calculating the standard deviation different from calculating the range?
 9. What must be true about a data set if the standard deviation is 0? Explain.
 10. Use technology to check the mean, standard deviation, and variance that you found in #1, 6 and 7. For stepbystep instructions on how to use your calculator to check these revisit the “read” tab of the “Applications of Variance and Standard Deviation” chapter/concept.
Websites for Pro Athletes’ Salaries:
Major League Soccer in U.S. (MLS): http://www.mlsplayers.org/salary_info.html
European Soccer Players: http://www.forbes.com/2009/04/08/highestpaidsoccerplayersbusinesssportsmoneysoccervalues09players.html
International Soccer Players: http://www.theoffside.com/worldfootball/futebolfinances100bestpaychecks2011.html
NBA: http://www.draftexpress.com/nbaplayersalaries/
WNBA: must research by individual athlete
NFL: http://www.spotrac.com/nfl/
Rugby: must research by individual athlete
Professional Golfers’ Association (PGA): http://www.pgatour.com/r/stats/info/?109
Extension Investigation
Research a second sport and ten new professional athletes’ salaries. Complete questions 19 for the second set of athletes. Them compare the variance and standard deviation for the two different sports.
Resources Cited
Major League Soccer in U.S. (MLS): http://www.mlsplayers.org/salary_info.html
European Soccer Players: http://www.forbes.com/2009/04/08/highestpaidsoccerplayersbusinesssportsmoneysoccervalues09players.html
International Soccer Players: http://www.theoffside.com/worldfootball/futebolfinances100bestpaychecks2011.html
NBA: http://www.draftexpress.com/nbaplayersalaries/
WNBA: must research by individual athlete
NFL: http://www.spotrac.com/nfl/
Rugby: must research by individual athlete
Professional Golfers’ Association (PGA): http://www.pgatour.com/r/stats/info/?109
Connections to other CK12 Subject Areas
 Variance of a Data Set
 Standard Deviation of a Data Set
 Applications of Variance and Standard Deviation