Math 203B                                                            Name(s):  ___________________________             ___
Activity 1:  Mean and Median, January 26, 2001

The table below reports the weights of rowers on the 1996 U.S Olympic men's rowing team.
 

Name Event Weight Name Event Weight
Auth LW double sculls 154 Klepacki Four 205
Beasley Single sculls 224 Koven Eight 200
Brown Eight 214 Mueller Quad 215
Burden Eight 195 Murphy Eight 220
Carlucci LW four 160 Murray Four 205
Collins, D. LW four 155 Peterson, M. Pair 210
Collins, P. Eight 195 Peterson, S. LW double sculls 160
Gales Quad 205 Pfaendtner LW four 160
Hall  Four 195 Schneider LW four 158
Holland Pair 195 Scott Four 208
Honebein Eight 200 Segaloff Eight, coxswain 121
Jamieson Quad 210 Smith Eight 207
Kaehler Eight 210 Young Quad 207
  1. Use your calculator to produce a histogram of these weights.  Include your histogram--don't forget to label the axes!  Comment on some of the striking features of this distribution.

 





 
 
 
 

  1. Use your calculator to calculate the mean and median of these weights (type them into the list L1 and then run 1VarStats).

 
 
 



  1. If you were told only the mean and median weights, but you were not given the individual weights or shown a visual display of the weights, would you have a complete understanding of the distribution of rowers' weights?  Explain.





  1. In what direction (increase or decrease) do you predict the mean and median to change if the coxswain (Segaloff) is removed from the analysis?  Explain briefly.

 
 
  1. Now remove the coxswain and use your calculator to recalculate the mean and median.  Record the results in the third column of the table.
 
whole team
without
coxswain
also without
lightweights
with max at
324
with max at
2224
Mean 191.85        
Median 202.5        
Was your prediction about the direction of change correct?


  1. Which measure (mean or median) do you guess will change more if all of the lightweight rowers and the coxswain are removed from the analysis?  Explain briefly.

 
 
 
 
 
 
  1. Remove the lightweight rowers (LW four, LW double sculls) and the coxswain from the analysis, and recalculate the mean and median.  Record these in the table.  Which measure was more affected?  Was your prediction correct?

 
 
 
 
 
  1. Now suppose that the heaviest rower weighed 324 pounds instead of 224.  Calculate the mean and median after making this change (still with the coxswain and lightweights removed).  Record the results in the table.

 
  1. Finally, suppose the heaviest rower's weight had inadvertently been recorded as 2224 rather than 224.  Recalculate the mean and median with this change.  Record the results in the table.
How many rowers weigh less than this mean?

 
Do you think these values are extreme enough to draw attention to the typographical error?  Explain.

 
 
 
 

A measure whose value is relatively unaffected by the presence of outliers in a distribution is said to be resistant.
 

  1. Based on these calculations, would you say that the mean is resistant?  Explain.








  2. Based on these calculations, would you say that the median is resistant?  Explain.