Is there a Correlation between average Gross Domestic Product per capita (GDP) and countries’ average life expectancy?

Range= 22.8

Interquartile range= 9.375

This parallel box and whiskers plot shows the difference in the distribution of average life expectancy in developed countries and developing countries within the sample. Both sets of data do not intersect at all, it can be seen that developed countries' box plot is placed in the top right and thus shows that developed countries contain higher values in comparison to developing countries. The reasoning for the distributions may be that individuals in developed countries have a higher standard of living as their GDP per capita is higher, more individuals are able to receive higher quality of medical care. This difference can also be seen through the median values, as the developing countries have a median life expectancy of 72.95, whereas the developed countries have a median life expectancy of82.2.

Range = 9904.5

Interquartile range = 5058.225

Range = 85679.30

Interquartile range = 2623.20.975

Range= 6.9

Interquartile range= 2.175

I referred to the World Bank’s 2020 database to find GDP per capita values for all 20 sample units. It is reliable because the World Bank collects their data by obtaining consecutive reports from each central bank of each country. On the other hand, I collected the data for life expectancy from a reliable source where they collect data from multiple sources such as CIA world factbook and the United Nations, therefore making the data reliable.

The third stage of my exploration is to directly investigate the relationship between GDP per capita and the average life expectancy within developed and developing countries. To do so, I will have to graph scatter diagrams to allow me to visually dictate the strength of correlation between the two variables in developed and developing countries both independently and dependently. I will then use Pearson’s correlation coefficient to dictate the strength of the relationship. If there is in fact a moderate or strong correlation, I will be able to create an equation predicting the average life expectancy based on the GDP per capita.

Table 1: Displaying the raw data for 20 countries’ GDP per capita and average life expectancy in Developing
countries 2020
Table 2: Displaying the raw data for 20 countries’ GDP per capita and average life expectancy in Developed
countries 2020

The second statistical stage of the investigation is to find the distribution for average life expectancy. Before finding the distribution, I first created another table for five-figure summaries for both sets of data. These values will be used in creating the box and whiskers plot that shows the distribution of average life expectancy for developed and developing countries. By showing my data in the form of a box and whiskers plot, I will be able to visually interpret five-figure summaries of the data and compare and contrast between the average life expectancy for developed and developing countries.

Table 4: The five-figure summaries for average life expectancy

The upper boundary:

=464905.5375

There are no outliers because no value is higher than the upper boundary value.

The lower boundary:

= -348378.3625

There are no outliers because no value is lower than the lower boundary value.

Graph 1, Set 2: Developed countries box and whiskers plot has a positively skewed distribution, meaning that the median is closer to the lower quartile of the plot for developed countries. This can also be shown by the relative proximity of its median value $51868.95 to its minimum value $31,419, instead of towards the maximum value,$117,098.40. The data is distributed along the range of $85679.30 US dollars and has an interquartile range of $262320.975. There are no outliers within this data set, and no extreme values lie below the lower boundary or above the upper boundary.

The first stage of my investigation was to find the distribution of GDP per capita (US dollars) in the sample. To further explore these distributions, I used my calculator to find the sample’s “five-figure summaries,” which consists of quartile value and range values. I will be using a box and whiskers plot to present my data. This is important as I will be able to visually dictate the “five-figure summaries” and compare the distribution of GDP per capita for both categories. Furthermore, an outlier test will be conducted on each box and whiskers plot to allow the identification of variables that may create a deviation in the distribution.

Table 3: The five-figure summaries for GDP per capita (US dollars)

I obtained my data sample through a random stratified sampling method, meaning that all sample countries were divided into two categories before being randomly chosen, so there is no bias in my decision-making. In order to ensure that the data is reliable and accurate, I have collected the data from the year 2020, and not the current year2021 as GDP per capita has not been collected fully. I used the United Nations list of countries and inserted them into two categories: Developed countries and developing countries. 20 countries were selected for each category, thus the sample consisted of 40 countries which ensured that the sample was large enough to be representative of excluded countries in my investigation.

The upper boundary:

=90.1875

There are no outliers because no value is higher than the upper boundary value.

The lower boundary:

=52.6875

There are no outliers because no value is lower than the lower boundary value.

Graph 2, set 1:The box and whiskers plot has a negatively skewed distribution, meaning that the median is closer to the upper quartile of the plot for developing countries. This can be also shown by the relative proximity of its median value 72.95 to its maximum value $77.1, instead of towards the minimum value, of 54.3. The data is distributed along the range of 22.8 and has an interquartile range of 9.375. There are no outliers within this data set, and no extreme values lie below the lower boundary or above the upper boundary.

The upper boundary:

=86.63

There are no outliers because no value is higher than the upper boundary value.

The lower boundary:

=77.9375

There is one outlier, United Arab Emirates, as its value at 77.8 is lower than the lower boundary at a average life expectancy of 77.9375

The United Arab Emirates' average expectancy rate lies below the lower boundary at 77.8. This number is expected as the GDP per capita of the United Arab Emirates is within one of the lower ranges in the developed countries category.

The low average life expectancy in the United Arab Emirates led me to believe that it was due to other foreign factors that lowered the average life expectancy. After investigating, I found that the United Arab Emirates was the most preferred country to be living in for young people, however, whilst the population lived in extreme wealth, it records lowest life expectancy due to the good life, the various opportunities, and lifestyle choices such as obesity, unhealthy eating habits and lack of physical activity. Another surprising factor was deaths among children were relatively high, hence the reason why the low life expectancy in the country.

Graph 2, set 2: The box and whiskers plot has a positively skewed distribution, meaning that the median is closer to the lower quartile of the plot for developing countries. This can be also shown by the relative proximity of its median value of 82.2 to its minimum value 77.1, instead of towards the maximum value, of 84.7. The data is distributed along the range of 6.9and has an interquartile range of 2.175.

The United Arab Emirates average expectancy rate lies below the lower boundary at 77.8. This number is expected as the GDP per capita of the United Arab Emirates is within one of the lower ranges in the developed countries category.

As a student studying economics in IB, I have a fond interest in studying economics trends. I try to input this interest within my daily life, whether it is through my IB Group 4 project which explored the effects of GDP per capita on the life expectancy of the country, or in my lessons where I learn about the effects of GDP per capita on a country. My interest in economics inspired me to use my Math IA as a platform to investigate the factors that could correlate to the GDP. During my research, I have found a number of factors that are affected by GDP per capita of a country, such as standard of living, rate of pollution, life expectancy, and literacy rate. One that I have found interesting was thatof the relationship between GDP per capita and pollution in the States. It shows that there is a relationship between the two variables; however, pollution rises at a noticeably slow rate in comparison to GDP per capita. This led me to decide on my two variables for my investigation. The type of exploration I will be conducting is an application investigation using statistics to investigate if there is a correlation between the GDP per capita and a country's life expectancy.

I will use univariate and bivariate mathematics to help me explore the relationship between the two variables. Through this investigation, I hope to gain knowledge on countries' GDP trends while learning to apply textbook mathematics outside of school.

To explore the univariate data, I will first compile the quantitative information on average life expectancy and GDP per capita; the data will be categorized into classifications of ‘developed countries’ and ‘developing countries to minimize deviation. I will then use the box and whiskers plot to explore the distribution of data for developed and developing countries separately and combined; by doing so, I will be able to dictate the variability of the data. Due to the range of geographical factors and living conditions between the countries, it is expected that there will be outliers. The range, interquartile range, and outlier test will be calculated for these outliers' sets of data.

I will also be using Bivariate mathematics to investigate the relationship between GDP per capita and each country's life expectancy. Scatter plots and Pearson’s Product Moment Correlation Coefficient will also be used to determine the strength of the relationship of the two variables. If these methods show that GDP per capita and a country’s life expectancy correlate, I will be using the least square method to create an equation estimating a country’s life expectancy based on their GDP per capita. The equation will be tested using a country that was excluded from the sample. Furthermore, I will be using a two-way chi-squared test for independence to determine whether the two variables are independent of one another. If the results of the chi-square test suggest that variables are indeed dependent on one another but the scatter diagram shows that there is no linear relationship, Spearman’s rank-order correlation will be used to determine whether or not the two variables co-vary. Personally, I believe that the higher GDP per capita, the higher a country’s life expectancy.

These numerous tests will allow me to answer the question, “Is there a correlation between average Gross domestic product per capita (GDP) and a country’s life expectancy?”

The upper boundary:

=7010 + 1.5 x 5058.225

=14597.3375

There are no outliers because no value is higher than the upper boundary value.

The lower boundary:

= -5635.5625

There are no outliers because no value is lower than the lower boundary value.

Graph 1, Set 1: In developing countries, the box and whiskers plot has a positively skewed distribution, meaning that the median is closer to the lower quartile of the plot for developing countries. This can also be shown by the relative proximity of its median value $3490.40 to its minimum value $595.5 instead of towards the maximum value,$10,500. The data is distributed along the range of $9904.5 US dollars and has an interquartile range of $5058.225.There are no outliers within this data set, and no extreme values lie below the lower boundary or above the upper boundary.

Gross Domestic Product per capita: GDP is the total measure of a country’s economic value of goods and services within a time period. GDP per capita is the annual GDP divided by the population.

Developed country: Developed nations can generally be categorized as countries that are more industrialized and have higher per capita income levels.

Developing country: A poor agricultural country that is seeking to become more advanced economically and socially.

Life expectancy: The estimate of the average number of additional years that a person of a given age can expect to live.

This parallel box and whiskers plot shows the difference in distribution between the GDP per capita values of developed countries and developing countries within the sample. Visually, the plot shows that developed countries have a much greater GDP per capita than developing countries. This is expected as developed countries, by definition, are countries with a GDP per capita greater than $12 000 US dollars and developing countries, by definition are countries, with GDP per capita lesser than $12 000 US dollars. This difference can also be observed through the median values of both sets of data, whereas the developing countries' GDP per capita has a median value of $3490.40 and the developed countries GDP per capita has a medium value of $51,868.95.

The reasoning for the large range is that these two categories (developing and developed) include a large variety of countries correlated to different social factors. For example, countries such as China and Malaysia have been rapidly growing as a country, with an increase in income and other factors. However, it is just a matter of time that these countries become developed countries. When countries chose are placed in a category with countries such as Sudan with a population of 25% in extreme poverty and with a GDP at just 595.50, it is expected for a large distribution to occur.