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

Extracts from this document...

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

...read more.

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;

image12.png

Σƒx²-x ²

          Σƒ            image11.png

Standard Deviation

Asia

Male Life Expectancy

Mean

Deviation

Deviation²

42.27

68.45

...read more.

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-image04.png

14 (196-1)

=  1 -image04.png

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

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-image04.png

15 (225-1)

  =  1 -    image04.png

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

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)image05.png

  =  1 -    image06.png

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

1

0

0

1

1

1

  6 x 4.00

24

Σd²

4.00

n = 6    so:   p = 1-image07.png

6 (36-1)

  =  1 -    

210image07.png

 = 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

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)image09.png

  =  1 -    

720image10.png

 = 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

0

0.25

0.25

0

image11.png

  6 x 0.50

3image11.png

Σd²

0.50

n =4   so:   p = 1-

4 (16-1)

  =  1 -    

60

 = 1- 0.05

Correlation

0.50

        

...read more.

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