Retiring to paradise
Problem
Charlie is hoping to retire soon. When he does, he would like to get away from it all and move to a country where he could have a lot of space and not feel overcrowded.
Alison has different plans for her retirement. She wants to live somewhere where there will be plenty of activity and she can make lots of new friends.
Here are some population data for eight countries they could move to.
From these data, what advice would you give Charlie and Alison about where each should settle?
| Country | Population |
| A | 1 366 718 000 |
| B | 158 571 000 |
| C | 138 740 000 |
| D | 61 017 000 |
| E | 21 767 000 |
| F | 21 284 000 |
| G | 4 692 000 |
| H | 3 536 000 |
"Hang on, this only tells me how many people live in the country altogether! I need to know how big each country is too!"
Here is the total land area for each country.
Would you change your advice to Charlie and Alison, based on these data?
| Country | Total land area (sq km) |
| A | 9 596 961 |
| B | 143 998 |
| C | 17 098 242 |
| D | 301 340 |
| E | 7 741 220 |
| F | 54 610 |
| G | 323 802 |
| H | 65 300 |
Below are some more data that Charlie and Alison have collected about the eight countries (you can download it in a spreadsheet here).
Analyse the data, and send us your choice of country for each of them, together with a clear explanation of why you think the data support your choices.
| Country | Percentage of population living in urban areas | Percentage of land covered by urban areas | Uninhabitable land (sq km) |
| A | 48 | 2.00 | 1 919 392 |
| B | 29 | 4.50 | 14 400 |
| C | 74 | 1.50 | 854 912 |
| D | 67 | 1.70 | 3 013 |
| E | 88 | 0.30 | 5 418 854 |
| F | 14 | 2.30 | 13 653 |
| G | 82 | 0.14 | 226 661 |
| H | 62 | 0.88 | 3 265 |
What other data might it be useful for Charlie and Alison to have, in order to make their decision?
Getting Started
Alison will want to live in an urban environment, and Charlie won't.
How could you find out the approximate urban population density and rural population density from the data you have been given?
Student Solutions
Based on the information in the first two tables most people agreed that Alison should live in B because it apparently has the highest population density and Charlie should live in E because it apparently has the lowest population density:
Population Density (based on total land area):
A = 142 people per sq km
B = 1101 people per sq km
C = 8 people per sq km
D = 202 people per sq km
E = 3 people per sq km
F = 390 people per sq km
G = 14 people per sq km
H = 54 people per sq km
(All results were rounded up to a whole number)
However, there was some confusion as to how to use the rest of the data:
Some suggested that Charlie should go and live in uninhabitable land! Are some of you wanting to get rid of Charlie? Alison perhaps...
Some didn't take into account that the population density would change after removing the uninhabitable land from the total land - Charlie and Alison would only be interested in the population density of the habitable land.
Some suggested suitable countries for Alison and Charlie, but didn't make it clear what calculations they had carried out to reach their conclusions.
The clearest analysis we received was from Komal, from India, who presented his results in this spreadsheet.
However, he assumed that Charlie would choose to live in an urban area. This didn't seem to take into account that Charlie "would like to get away from it all" - he'd be more likely to make his decision based on the population density of the non-urban areas.
Perhaps someone would like to work out the population density in the rural areas of each country.
Chris and Reiss from Wilsons' School suggested other information they might want to take into account before moving:
- The cost of living
- The crime rates
- The tax rates
- How much at chance of terrorist attacks the country is
- The climate
- What public transport there is
- What pension they'll get
- How good the doctors are
- How much doctors cost
- Life expectancy = Quality of Health
- The percentage of people in his/her age group
- Language
- Resorts
- How densely populated the coast is (if there is a coast)
- Housing
- Quality of the infrastructure
Teachers' Resources
Why do this problem?
This problem confronts students with the idea that when collecting data to try to answer a question it is important to identify all the relevant variables, and that an oversimplistic analysis with a limited amount of information can lead to the wrong decisions.
The problem also offers the opportunity for students to practise calculating ratios, percentages and proportions.
Possible approach
Introduce the problem, and display the population information from the problem (perhaps using this Powerpoint presentation), or hand out the first part of this worksheet.
"Based on this information, which country should Charlie settle in, and which country should Alison retire to?"
Accept students' answers together with their justification. If no-one suggests that more information is needed, pose the following question:
"Is there anything else that you think Charlie and Alison should take into account before they make their decision?"
Write up any suggestions on the board. Then hand out the second part of the worksheet or show the second slide:
"Charlie and Alison need to take into account the population density, rather than the population. Can you use these data to work out the population density and advise them?"
Allow the class some time to work out the population densities, collect together the answers, and note that the advice to Charlie and Alison will now be different. Then return to any suggestions students came up with about other factors, before handing out the final part of the worksheet or displaying the final slide.
"Here are some more data about the eight countries. Make a decision with your partner about how to analyse the data, and then work together to analyse them to see if your advice to Charlie and Alison would change. Be ready to explain any calculations you have made."
In a final plenary, students can share what they did and compare answers, as well as discuss any other factors that Charlie and Alison might wish to take into account.
If computers are available, this is an ideal opportunity for students to use spreadsheets to analyse data - the data are available to download here.
Key questions
What information is needed?
How can the available information be used to answer the question?
Does additional information change your original answer?
Possible extension
"Consider other contexts where additional information might cause you to change your mind."
Perhaps an interesting project for students would be to find some real examples from scientific or medical research where an initial finding was rejected as additional data came to light.
Possible support
Model the sort of calculations that students will need to do before presenting them with all the data.