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 striking features of this distribution.
2. Use your calculator to calculate the mean and median of these
weights.
3. 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.
4. In what direction do you predict the mean and median to change
if the coxswain is removed from the analysis? Explain briefly.
5. Now remove the coxswain and use your calculator to recalculate
the mean and median. Record the results in the table (on the next
page). Was your prediction about the direction of change correct?
6. 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.
7. 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?
8. Now suppose that the heaviest rower weighed 324 pounds instead
of 224. Calculate the mean and median after making this change (still
with the lightweights and coxswain removed). Record the results in
the table.
9. Finally, suppose the heaviest rower's weight had inadvertently
been recorded as 2224 rather than 224. Recalculate the mean and median
with this change. How many rowers weigh less than the mean?
Do you think these values are extreme enough to draw attention to the typographical
error? Explain.
| whole team | without
coxswain |
also without
lightweights |
with max at
324 |
with max at
2224 |
|
| Mean | 191.85 | ||||
| Median | 202.5 |
A measure whose value is relatively unaffected by the presence of outliers in a distribution is said to be resistant.
10. Based on these calculations, would you say that the mean
is resistant? Explain.
11. Based on these calculations, would you say that the median
is resistant? Explain.