Who's the Best?
In this problem, we needed to find a way to use the Olympic medal tally in order to work out which country is the most athletic.
Joe and Matthew, from Chatham Grammar School, both considered the total number of medals which countries have won in the previous three Olympics. Matthew thought that because there were the most number of events in the 2008 Olympics, the top five medal winning countries from this Olympics would be the most athletic.
Matthew then ranked these five countries according to the number and type of medals won using a weighted points system. He gave 15 points for gold, 10 points for silver and 5 points for bronze, and then divided the sum of these scores by the number of Olympic games the country had participated in.
| Country |
# Olympics attended |
Total # gold medals |
Total # silver medals |
Total # bronze medals |
Total weighted score |
Total weighted score / # Olympics attended |
| USA |
27 |
946 |
765 |
662 |
25 137 |
931 |
| Russia |
4 |
108 |
97 |
110 |
3 724 |
931 |
| China |
7 |
163 |
117 |
106 |
4 144 |
592 |
| Germany |
25 |
374 |
439 |
469 |
12 350 |
494 |
| Great Britain |
28 |
220 |
277 |
269 |
7 420 |
265 |
Because the USA and Russia had the same (and highest) result, Matthew then recalculated the USA weighted score for the past 4 Olympic games only, when Russia also competed. For the past 4 Olympics, the USA had 153 gold medals, 133 silver medals and 120 bronze medals. So the new total weighted score is $153*15+133*10+120*5=4224$, and the average over
the four Olympics is 4224/4=1056. He thus concluded that the USA is the most athletic nation.
Elliott, from Wilson's School, considered the number of medals won and the population size. He first listed the countries according to the number of gold medals achieved in the 2008 Olympics.
Elliott then calculated a weighted score from the medal tally: $$ \text{Total Score} = \Big( 3 \times \text{# Gold medals} + 2 \times \text{# Silver medals} + 1 \times \text{# Bronze medals} \Big)\times 10^7 $$
He multiplied the weighted score by $10^7$ so that the Overall Results would be reasonable sized numbers: $$\text{Overall Result} = \text{Total Score} \div \text{Population} $$
From this, he ranked the countries according to their overall score, and concluded that Jamica is the most athletic nation.
Well done to Will and Ellie from Roundwood Park School who used the same method as Elliot.
Olie and Dan from Baston Primary School and Owen and Jack from Chatham Grammar School all started to think about using population size and the wealth of countries as a way to determine the most athletic country. Jack and Owen also thought about using the Human Development Index to indicate how wealthy and developed a country is.
Can you find a mathematical method to find the most athletic nation using information about the number of medals, population size and country wealth? Or perhaps you could consider other data, such as sporting event results, population age, prevalence of obesity, and investment in Olympic althetes to determine which country is the most athletic.
