Wednesday, April 2, 2014

Standard Deviation Lesson for MBF3C Class

I'm well into the One-Variable Statistics unit in the 11 college course. Most students are doing well, able to calculate mean, variance and Standard Deviation. 
However, I've been running into many problems trying to get the students to understand the meaning of Standard Deviation and how it could be applied to use in Statistics. 
Whenever I get into trouble with a topic, I tend to try and relate it to sports as much as possible. Helps me teach it a little bit better, and most students, especially those that watch sports, understand a little better. 
I came up with this question to see if it would help students gain a better understanding of SD. I've had some feedback from a peer, and would like to see if there are any other ideas out there to tweak this question or help use it in class. So far results have been pretty good, but any other ideas would definitely help more. 

This question will relate to the starting lineup for a major league baseball team and their pay:

The Detroit Tigers starting lineup had the following end of season batting averages from 2013:  
.237, .256, .265, .274, .279, .289, .303, .312 and .334
If the owner of the Detroit Tigers pays his starting lineup’s salaries based on last year’s batting average, how much will his payroll be if he pays on the following scale?
                                                              i.      $10 000 000 to each player within +3 S.D of the mean batting avg.
                                                            ii.      $7 500 000 to each player within +2 S.D of the mean batting avg.
                                                          iii.      $5 500 000 to each player within +1 S.D of the mean batting avg.
                                                           iv.      $3 000 000 to each player within -1 S.D of the mean batting avg.
                                                             v.      $1 750 000 to each player within -2 S.D of the mean batting avg.
                                                           vi.      $750 000 to each player within -3 S.D of the mean batting avg.

Any thoughts out there on improvement to this question? 

1 comment:

  1. If your students are having difficulties understanding meaning of Standard Deviation and how it could be applied to use in Statistics, consider using this website, http://www.mathsisfun.com/data/standard-deviation.html. This link has many graphics which can help illustrate what standard deviation is and how it applies to statics.

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