Tuesday, 26 June 2012

Lesson Sketch: Relative frequency - A lesson on calculating the risks of sport

Another basic one here. Why do it? Because you can't repeat the 'checking to see if a dice is fair' activity year on year forever. Step one - Ask pupils to put a list of common sports in to the order of how dangerous they think the sports are:

American Football, Football, Gymnastics, Ice Hockey, Swimming, Wrestling, Field Hockey, Skiing, Water Polo, Equestrian, Golf, Skydiving

Step 2 - Show the number of deaths for each sport and proclaim American Football to be the most dangerous!

Sports
Deaths in US colleges in the last 5 years in five years
American Football
55
Football
6
Gymnastics
1
Ice Hockey
1
Swimming
8
Wrestling
3
Field Hockey
0
Skiing
2
Water Polo
1
Equestrian
1
Golf
0

Ask what is wrong with your statement. Why have so many more people died in American Football than any of the others? Get that we also need to know how many people actually took part. Show them the third column of the table along with the formula for relative frequency:



Sports
Deaths in colleges
in five years
Participation in colleges
in five years
American Football
55
2’079’069
Football
6
841’963
Gymnastics
1
57’613
Ice Hockey
1
128’898
Swimming
8
475’953
Wrestling
3
188’272
Field Hockey
0
156’370
Skiing
2
33’974
Water Polo
1
39’968
Equestrian
1
10’489
Golf
0
62’528

Pupils put the sports in order of their danger of death. One thing I like about this is that the data (got from here) is not really adequate for most of them and it gives plenty of room for discussion.


Step 3 - Show pupils this pdf: http://www.uspa.org/Portals/0/MembershipSurveys/memsurvey09.pdf

Ask how we can work out the relative frequency of deaths in skydiving using this data. Pupils will probably go for the 16 deaths over 2.5 million jumps, but for the result to be comparable to the previous task it would make more sense to do the number of deaths over the 32'177 members. This is because all the other sports will be played throughout the year and it is counted as deaths per participant rather than deaths per game. An interesting and fairly advanced conversation to be having with your pupils - YAY!