# Differences in wealth and life expectancy of the countries of the world

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Introduction

Maths GCSE Coursework

Maths Coursework

Introduction

For my mathematics coursework I have been given the task of finding the differences in wealth and life expectancy of the countries of the world. To my aide I shall have the World Factbook Data which was given to me by my maths teacher.

The World Factbook Data contains the Gross Domestic Product (GDP) per capita; this is the economic value of all the goods and services produced by an economy over a specified period. It includes consumption, government purchases, investments, and exports minus imports. This is probably the best indicator of the economic health of a country. It is usually measured annually.

Another thing the data contains is the Life expectancy at birth. Life expectancy is called the average life span or mean life span, in this case of the countries or continents. This informs me of the average age a person in the specified country is likely to like to.

Using this data I shall try to prove hypotheses that I shall personally predict before carrying out the investigation.

For my investigation I shall be using varieties of different ways to presenting my data and results. I shall use graphs, charts as well as tables to make the data easier to read and understand for the reader. This would enable me also to keep organised and follow what I have to do.

To develop my work I shall use very reliable as well as advanced methods to prove my hypotheses. These shall consist of Spearman's rank correlation coefficient, box plots, standard deviation aswell as histograms.

Bearing my hypotheses in mind, I think that it would

Middle

1.33

71-80

33

75.5

3.67

81-90

3

85.5

0.33

Total

60

6.67

This was extended work to give me more information indirectly concerning hypotheses one.

This data shows me that the modal group for population life expectancy worldwide is the 71-80 age range. Unsurprisingly the economically worst off continent, Africa, was the only continents to have any country with a Population Life Expectancy of below 40. On the other hand Asia, not being the second worst economically continent, alongside with Africa, had countries with Life Expectancy lower then 60. To summarise so far in my investigations only South America has not fitted in with my first hypotheses.

Standard Deviation

Standard deviation is the most commonly used measure of statistical dispersion. It is a measure of the degree of dispersion of the data from the mean value. It is simply the "average" or "expected" variation around an average.

Standard deviation would show me how spread out the values in the sets of data are. It is defined as the square root of the variance. This means it is the root mean square (RMS) deviation from the average. It is defined this way in order to give us a measure of dispersion that is:

I have chosen this method because although the scatter graph and histograms do show population distribution they do not give a precise and exact answer. This can easily be obtained by using standard deviation.

- A non-negative number, and

- Has the same units as the data.

Interpreting Standard deviation

Interpreting standard deviation is quite easy to read. A large standard deviation indicates that the data points are far from the mean and a small standard deviation indicates that they are clustered closely around the mean. In this case 0.9 is a large standard deviation and 0.1 is a small standard deviation.

The formula for standard deviation is;

Σƒx²-x ²

√ Σƒ

Standard Deviation

Asia

Male Life Expectancy | Mean | Deviation | Deviation² |

42.27 | 68.45 |

Conclusion

Countries | Male Life Expectancy | Female Life Expectancy |

Mozambique | 37.83 | 36.34 |

Niger | 42.38 | 41.97 |

South Africa | 44.39 | 43.98 |

Swaziland | 39.10 | 35.94 |

Zambia | 35.19 | 35.17 |

Apart from these few countries, (which just prove that men can live longer then women!) my hypotheses was correct, because worldwide females tend to live longer then males.

Looking at my investigation I feel in order for this data to be more accurate I would certainly need to have some minor adjustments, like the size of my data. I feel this did affect my results as the size of the data resulted in me being restricted from significant data that was not chosen due to my method of sampling.

If this investigation was done again I would actually stick with the same methods, however I would expand my database and also use an even wider variety of representing my data (for example I could use the cumulative frequency graph). This would enable me to have a more accurate set of results.

Spearman’s Rank Correlation

Asia

Afghanistan | Bangladesh | Cyprus | Gaza Strip | Jordan | Malaysia | Maldives | Mongolia | Oman | Qatar | Saudi Arabia | Syria | United Arab Emirates | West Bank |

13 | 10 | 1 | 14 | 6 | 7 | 8 | 11 | 4 | 9 | 3 | 5 | 2 | 12 |

14 | 13 | 2 | 9 | 1 | 8 | 12 | 11 | 7 | 10 | 5 | 3 | 4 | 6 |

-1.00 | -3.00 | -1.00 | 5.00 | 5.00 | -1.00 | -4.00 | 0.00 | -3.00 | -1.00 | -2.00 | 2.00 | -2.00 | 6.00 |

1 | 9 | 1 | 25 | 25 | 1 | 16 | 0 | 9 | 1 | 4 | 4 | 4 | 36 |

6 x 136 | 816 | Σd² | 136.00 | ||||||||||

n = 14 so: p = 1- | 14 (196-1) | = 1 - | 2730 | = 1- 0.2989011 | Correlation | 0.7010989 |

Spearman’s Rank Correlation

Africa

Countries | Burundi | Cape Verde | Cote d’Ivoire | Egypt | Gabon | Liberia | Libya | Madagascar | Morocco | Mozambique | Niger | South Africa | Sudan | Swaziland | Zambia |

GDP-per capita | 15 | 8.5 | 8.5 | 5.5 | 3 | 11 | 2 | 12.33 | 5.5 | 10 | 12.33 | 1 | 7 | 4 | 12.33 |

Population Life Expectancy | 10 | 4 | 11 | 2 | 7 | 8 | 1 | 6 | 3 | 14 | 12 | 9 | 5 | 13 | 15 |

d | 5.00 | 4.50 | -2.50 | 3.50 | -4.00 | 3.00 | 1.00 | 6.33 | 2.50 | -4.00 | 0.33 | -8.00 | 2.00 | -9.00 | -2.67 |

d² | 25 | 20.25 | 6.25 | 12.25 | 16 | 9 | 1 | 40.0689 | 6.25 | 16 | 0.11 | 64 | 4 | 81 | 7.1289 |

6 x 308.3067 | 1849.8402 | Σd² | 308.3067 | ||||||||||||

n = 15 so: p = 1- | 15 (225-1) | = 1 - | 3360 | = 1- 0.550547679 | Correlation | 0.499452321 |

Spearman’s Rank Correlation

Europe

Countries | Belarus | Bosnia and Herzegovina | Faroe Islands | Finland | Guernsey | Macedonia | Malta | Man, Isle of | Norway | Portugal | Slovakia | Sweden |

GDP-per capita | 11.5 | 11.5 | 4 | 2 | 6 | 10 | 8 | 5 | 1 | 7 | 9 | 3 |

Population Life Expectancy | 12 | 11 | 4 | 6 | 2 | 9 | 5 | 7 | 3 | 8 | 10 | 1 |

d | -0.50 | 0.50 | 0.00 | -4.00 | 4.00 | 1.00 | 3.00 | -2.00 | -2.00 | -1.00 | -1.00 | 2.00 |

d² | 0.25 | 0.25 | 0 | 16 | 16 | 1 | 9 | 4 | 4 | 1 | 1 | 4 |

6 x 56.50 | 339 | Σd² | 56.50 | |||||||||

n = 12 so: p = 1- | 12 (144-1) | = 1 - | 1715 | = 1- 0.1976676 | Correlation | 0.8023324 |

Spearman’s Rank Correlation

Oceania

Countries | American Samoa | Australia | French Polynesia | Palau | Papua New Guinea | Vanuatu |

GDP-per capita | 4 | 1 | 2 | 3 | 6 | 5 |

Population Life Expectancy | 3 | 1 | 2 | 4 | 5 | 6 |

d | 1.00 | 0.00 | 0.00 | -1.00 | 1.00 | -1.00 |

d² | 1 | 0 | 0 | 1 | 1 | 1 |

6 x 4.00 | 24 | Σd² | 4.00 | |||

n = 6 so: p = 1- | 6 (36-1) | = 1 - | 210 | = 1- 0.114285714 | Correlation | 0.8857143 |

Spearman’s Rank Correlation

North America

Countries | Anguilla | Aruba | Belize | Costa Rica | Dominica | El Salvador | Netherlands Antilles | Saint Vincent and the Grenadines | Trinidad and Tobago |

GDP-per capita | 5 | 1 | 7 | 4 | 6 | 8 | 2 | 9 | 3 |

Population Life Expectancy | 2 | 1 | 9 | 3 | 5 | 7 | 4 | 6 | 8 |

d | 3.00 | 0.00 | -2.00 | 1.00 | 1.00 | 1.00 | -2.00 | 3.00 | -5.00 |

d² | 9 | 0 | 4 | 1 | 1 | 1 | 4 | 9 | 25 |

6 x 54.00 | 324 | Σd² | 54.00 | ||||||

n = 9 so: p = 1- | 9 (81-1) | = 1 - | 720 | = 1- 0.45 | Correlation | 0.55 |

Spearman’s Rank Correlation

South America

Countries | Argentina | Guyana | Suriname | Venezuela | ||

GDP-per capita | 1 | 3.5 | 3.5 | 2 | ||

Population Life Expectancy | 1 | 4 | 3 | 2 | ||

d | 0.00 | -0.50 | 0.50 | 0.00 | ||

d² | 0 | 0.25 | 0.25 | 0 | ||

6 x 0.50 | 3 | Σd² | 0.50 | |||

n =4 so: p = 1- | 4 (16-1) | = 1 - | 60 | = 1- 0.05 | Correlation | 0.50 |

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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