Question one
There are estimated to be 34,303,677 kangaroos in Australia (source: Australian Government 2011). Assuming that they are evenly distributed over the country (7,692,024 km²), how many would you see on the 877km drive from Melbourne to Sydney? You may assume that you can see an average of 1km from the car, and that the road is reasonably straight.
Question two
In New Zealand, there is the following breakdown of ethnicity and language. Languages spoken: 95.9% English, 4.2% Māori, 0.6% NZ Sign Language. Ethnic groups: 78.0% European / other, 14.6% Māori, 9.2% Asian, 6.9% Pacific peoples. (source: Wikipedia) What percentage of those speaking Maori are ethnically Maori?
There are 4.46 kangaroos per square kilometre. The number of square kilometres viewed is 877*2 + (pi * (1^2)) * 2 = 1757.14 km^2. The slight “trick” here is the area at the ends, remembering the area of a circle is pi*r^2.
To answer the question, the total number of kangaroos is (4.46 * 1757.14) = 7836.2, which can be rounded to 7836.
Question two
This is about assumptions – you can’t assume uniformly distributed, so cannot tell from the data given. For interest, 84% of Maori speakers are ethically Maori. I think it’s on the school syllabus now, which is why it isn’t a higher percentage.
Did you find the solution difficult or unusual?
This kind of result is quite normal for practical problem solvers who use maths to help businesses. They do not always have the problem statement clearly defined. To start to develop a solution to a real-world business problem they have to make certain assumptions. These assumptions are then updated as the results are analysed.
With thanks to the Tesco commercial science team.
