Life expectancy

Background Description One of the best ways to grasp the significance of the change of life expectancy is to understand its history. As it was stated above, the life expectancy of people around the world has become longer from the past with human evolution.
According to Rorabaugh, Critchlow, and Baker, life expectancy was only about 35 years in 1600s in England because about two-thirds of children died before four years old. The life expectancy of Colonial America was also about 25 years in Virgin colony, and about 40 percent of children in New England died before reached adulthood (p.47-48). However, the life expectancy of children increased rapidly during the Industrial Revolution; in fact, the percentage of children who were born in London and died before 5 years old decreased from 74.5% 1730-1749 to 31.8% in 1810-1829 (p.62-63).
Although the life expectancy around the world has increased dramatically in these decades, there are still various problems which should be concerned. GDP, the index to explain the affluence of the countries, is one of the largest reasons to decide life expectancy, because GDP is related with other various functions, such as health expenditure, mortality rate, food self-sufficiency, the amount of resources, and so on. It is the fact that life expectancy in developed countries is longer than the one in developing countries.
In this way, there are various reasons and elements to determine life expectancy of human. It is important and necessary to examine these causes and effects to decrease the gap between developed countries and developing countries and to make people in the world fairer.

Statement of the Research Objective The main purpose of this project is to analyze a number of data of human life expectancy of 147 different countries. Moreover, the research expects to examine the difference of life expectancy among these countries including developed and developing countries. Furthermore, the research organizes the result and causes which influence life expectancy, such as health expenditure, birth rate, death rate, mortality rate, GDP, and improved water sources.

Data Sources
The data of the life expectancy at birth of 147 countries in 2011 is from the website of Human Development Reports. The data is a cross-sectional data, but some countries lack of the original data of 2011, which are omitted from this research. The data is cited from: https://data.undp.org/dataset/Life-expectancy-at-birth-years-/7q3h-ym65 Statistical Analysis
I. Numerical Methods
According to the table 1 in Appendix:
Mean = 69.52
A typical country is expected to have a life expectancy at birth of 69.52 years.

Median = 71.13
50% of countries have a life expectancy at birth of at least 71.13 years and half had a life expectancy at birth of at most 71.13 years.

Minimum = 45.10
The lowest life expectancy at birth is 45.10 years.

Maximum = 82.70
The highest life expectancy at birth set is 82.70 years.

Range = 37.59
The life expectancy at birth of the highest country differs from the lowest country by 37.59 years.

Standard Deviation = 9.41
9.41 years is a measure of the spread of actual score around expected life expectancy at birth of 69.52 years.

Skewness = - 0.71
The skewness indicates an asymmetric tail and it is skewed to lower to the left.

Kurtosis = - 0.36
The data is characterized by a relatively flat distribution.

Q1 = 62.98
The bottom quarter (25%) of countries have a life expectancy at birth of 62.98 years or less (at most 62.98 years).

Q2 = 71.13
Half (50%) of countries have a life expectancy at birth of at least 71.13 years, and half at most 71.13 years.

Q3 = 76.22
The top quarter (25%) of countries have a life expectancy at birth of 76.22 years or more (at least 76.22 years).

IQR = 13.24
13.24 years is the difference between the third quartile and the first quartile.

Z-score
Z = (X -μ ) / σ , μ = Mean, σ = St. Dev.
Sierra Leone has the lowest life expectancy, 44.84 years old, and Z-score is -2.59.
Switzerland has the highest life expectancy, 82.70 years old, and Z-score is 1.40.
The lowest life expectancy in Sierra Leone is 2.59 Standard Deviation below average.
The highest life expectancy in Switzerland is 1.40 Standard Deviation above average.
20th Percentile = 61.29
The top 80% of countries has a life expectancy in at least 61.29 years old.

30th Percentile = 66.34
The second top 70% of countries has a life expectancy in at least 66.34 years old.

60th Percentile = 74.06
The second bottom 40% of countries has a life expectancy in at most 74.06 years old.

90th Percentile = 80.74
The bottom 10% of countries has a life expectancy in at most 80.74 years old.

Empirical Rule
Approximately 68% of life expectancy is within 1 standard deviation from the mean between 60 and 79 years old.
Approximately 95% of life expectancy is within 2 standard deviations from the mean between 51 and 88 years old.
Approximately 99% of life expectancy is within 3 standard deviations from the mean between 41 and 98 years old.

Coefficient of Variation = C.V. = (σ / µ) * 100 = 13.54%

II. Graphical Methods
Interpretation of Frequency according to the table 2:
• In this data of 147countries’ life expectancy at birth, 70-75 years is the most prevalent category.
• The second prevalent category of life expectancy at birth is the years between 75 and 80 years old.
• The least prevalent category of life expectancy at birth is the years between 45 and 50 years old.

Interpretation of relative frequency according to the table 3:
• 30% of countries have the highest life expectancy at birth between 70 and 75 years old.
• 20% of countries have the second highest life expectancy at birth between 65 and 70 years old.
• 5% of countries have the lowest life expectancy at birth between 45 and 50 years old.
• The percentage between the countries which has the life expectancy of 45 and 50 years old is almost same as the ones of 50 and 55 years old.

Interpretation of Cumulative Frequency according to the table 4:
• This is an asymmetrical distribution.
• The area chart is skewed to the left.
• The mean has been pull to the left of the median by the long “left tail” of the distribution, the few relatively small data values.

Interpretation of Cumulative Relative Frequency according to the table 5:
• The majority countries have life expectancy above 65 years old.
• Almost all of countries have the life expectancy below 80 years old.

According to figure 1 shows the circumstance as the following:
• 62 countries have the highest life expectancy between 70 and 79 years old.
• 39 countries have the second highest life expectancy between 60 and 69 years old.
• Only 6 countries have the lowest life expectancy between 40 and 49 years old.

III. Tabular Methods
Interpretation according to the table 6 as the following:
• The data distribution is categorized into 7 categories with 5 ranges.
• 70 to 75 years old is the prevalent life expectancy in this data.
• The highest life expectancy (80 to 85 years old) is 14.29% of total 147 countries.
• The lowest life expectancy (45 to 45 years old) is 4.08 of total.
• The numbers of countries which have the life expectancy between 50 to 55 years old, and ones which have between 55 to 60 years old are almost same.
• There are at least 101 countries which have life expectancy below 70 to 75 years old.
• The number of countries which have the life expectancy longer than 70 years old is 83 countries (56.47%).

Discussion of the Possible Outliers
Table 7 shows the information as the following:
Min 45.10
Q1 62.98
Q2 71.13
Q3 76.22
Max 82.70
IQR 13.24
1.5* IQR= 19.86
3.0*IQR= 39.72
Outer Fence 1 = 23.26
Inner Fence 1 = 43.12
Inner Fence 2 = 96.08
Out Fence 2 = 115.94

• The value between Inner Fence 1 and Inter Fence 2 is mild outlier.
• The value between Out Fence 1 and Out Fence 2 is extreme outlier.
• There is no outlier.
• The largest out fence is 115.94 on the .
• The other inner fence is 43.92.
• The other out fence is 96.08.

Limitations of the Study There are various elements which influence to the accuracy of the data set; for example, the causes of death, the difference of life-span between genders, and the numbers of immigration have an influence to the data set more than a little. First, some people unfortunately would die before their durations of life due to diseases, accidents, or wars, and these factors cause the change of the life expectancy of the whole population. Second, the difference of life expectancy between male and female is also one of the causes to influence the data set. Female’s life expectancy is longer than male’s in general; however, this data set shows only total life expectancy which is not completely accurate. Third, the number of immigrants may cause the change of the data set as well. If people from a country which has a low life expectancy immigrant to a country which has a high life expectancy, that will decrease the life expectancy of the country which has high. In this way, there are some causes which influence to the data set of life expectancy; therefore, it is not a perfect interpretation of life expectancy to use only this data set.

Conclusion, Summary, and Policy Recommendations According to the data set of the life expectancy at birth of 147 countries in 2011, it was found that there are various differences and characteristics of life expectancy at birth and how they are different from each other in a global view. Most countries, 56.47% of total, have a life expectancy longer than 70 years old; however, there are still a huge gap between developed countries and developing countries. Through this analysis, various reasons which influence the data set are inferred, such as, economies, medical systems, and resources. Developed countries which have high GDP and abundant resources can usually provide a number of health expenditure including health insurance; on the other hand, the amount of money for health expenditure is limited in developing countries. In this way, it can be concluded that the gap between developed countries and developing countries is occurred because of economic gap. As it was stated above, the life expectancy at birth is influenced by various elements; therefore, people should give more attention to these factors, such as, GDP, health expenditure, and resources. People will be able to have medical care easily if the governments of each countries provide public medical insurance system. Those who are in countries which do not have affluent water resource or infrastructures will be able to get water and move around places easily if the governments provide infrastructures such as water wells and bridges. The life expectancy increases with economic development; therefore, people should think about economic growth and take actions toward it to increase the life expectancy.