Probably few if any popular events offer such an abundance
of statistics teaching topics as the Olympics. The closest rival I can think of
would be the upcoming presidential election, which will be covered in a
separate post later this year. The only downside about the Olympics is that it
will be history by the time the fall semester starts. L
Here is my list – I do not claim completeness and will
update it as more ideas cross my mind:
1)
There will certainly be an abundance of graphs
related to the Olympics. Let the students find “good” and “bad” ones and
discuss them.
2)
I know that in ski jumping the min and max of the judges’ scores is
eliminated. I am sure there will be a discipline in the summer Olympics as well
where that applies.
3)
The most successful nation will be the one with
the most “total medals” (U.S. custom) or most “gold medals” (more European
custom) – this is just another example for the mode.
4)
The numeric score that determines the final rankings
comes in all types of scales . . . time and distance and other measures are obviously
on the ratio scale. Basketball teams’
points (2 for a win, 1 for a loss) during the preliminary round are on the interval scale. Decathlon scoring is on
the ordinal scale (there is an
exponent involved that makes it not on the interval scale). I just hope there
is no winner determined by something measured on the nominal scale. J
I am sure among gymnastics, dressage,
synchronized swimming, etc., experts can find additional interesting scales.
5)
Certain “mass” events like the marathon can be
used to teach creating histograms and to show skewness. You can also use it to compute mean, median, percentiles, standard deviation and variance. It is
also a good starting point to discuss the uselessness of modes in certain situations.
6)
Drug testing allows for all kinds of probability related questions – simple and conditional probability,
independence, etc. come to mind. You
are a drug-using cyclist. They will randomly test 5000 of the 12000 athletes.
What is the chance they will catch you? There are 500 cyclists at the Olympics
and they test 300 of them. What is the chance they will catch you now? You are
getting tested 4 times and thanks to your superior drugs, the chance that a
test returns a positive result is 25% each time you get tested. What is the
chance they will never catch you?
7)
The hypergeometric
distribution can also be used in the context of drug testing. 40 of the 290 weight lifters use drugs. If
20 of them are randomly chosen for drug tests that never fail to detect a drug
user, what is the chance that exactly 7 drug users will get caught?
8)
Guessing the medalist in some sport where you
have no prior knowledge allows for the coverage of permutations vs. combinations. What
is the chance you will guess the medalists correctly in the men’s 400m
free-style final if you don’t know anything about swimming? Or: The top three runners in the women’s 200
meter semi-final advance to the final. If you don’t know anything about track,
what is the chance you will guess the three women that advance correctly?
9)
The expected traffic chaos can be used to apply the
normal distribution: It takes you X minutes to get to the team
handball arena and X ~N(60, 152). What is the chance you will be
late for the game if you leave 78 minutes before the start?
10)
You can use the public transportation to frame
questions about the uniform distribution. The bus from the athletes’ village runs to
the stadium runs every 8 minutes, but not according to a printed schedule. What
is the chance a random athlete needs to wait between 3 and 5 minutes?
11)
Points scored in many sports (e.g. basketball)
can be assumed to be normally
distributed: In basketball points
for the USA~N(98,122). What is the chance they will score more than
90 points? The same works for most track and field disciplines.
12)
Differences
in normally distributed variables to determine the winner. E.g. Points for the USA are X~N(90,102)
and for Argentina are Y~N(85,202) . . . what is the chance that Argentin wins the basketball
game?
13)
In some disciplines you should be able to find correlations between certain physical
attributes of the athletes (height, weight, . . .) and their results. E.g. between the height of high jumpers and the
height they jump. You can use that also to discuss cause-and-effect and thus simple
regression analysis.
14)
You can find correlations between results in the heats and semifinals or
semifinals and finals (swimming, running, . . .).
15)
Proportions
can be found in basketball, skeet, etc… and allow for the binomial distribution: If
each time I shoot, the chance I hit the disk is 99%; what is the chance I hit
49 out of 50 disks?
16)
There is some research about a country’s
expected medal haul using multiple
regression analysis using population, GDP/capita and other variables. For
more, see:
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