Exploring the relationship between population size and gdp in differentiating developing and developed countries.

Under this mathematics internal assessment, I will investigate the difference between the population size and the GDP of developing and developed countries and provide a comparison. Throughout the investigation, I will focus on the use of statistical data and mathematics to delineate the relationship between population and GDP.

Since I was in grade school I had a curious mind towards economics, I find the relationship betwee n these variables intresting as one aspect can change the entire economical status of a country either developing or developed. To me it is more than just numbers and statistics; it has a deeper meaning. It explores the interaction between the human population and economic advancements. I am very interested in this topic's influence on society as it has more about people and their livelihood not necessarily focusing on graphs and mathematics. Looking at the dynamic that these variables connect on provides significant insights into issues such as societal disparities, as well as efforts to reduce poverty and community health. This aspect of economics taps into my passion for looking at real-world problems and solve them with the skills that I have. Which makes it not only intellectually enthusiastic but also personally interesting.

This internal assessment will examine the link between a country’s population and the respective GDP. The purpose of this inquiry is to establish how a country's population influences its GDP. Initially, I will evaluate univariate data by looking at population and GDP individually in developing and developed nations. This will include constructing four box and whisker plots to depict the spread and distribution of the data, allowing me to detect key statistical metrics such as the mean, range, interquartile range, and any outliers in the dataset. Box plots allow me to properly compare variables and do in-depth data analysis.

Following the investigation of univariate data, I will analyze bivariate data using scatter diagrams. These graphs will assist in determining whether there is a relationship between a country's population (differentiating between developed and developing countries) and its GDP. To measure this association, I'll use Pearson's Product Moment association Coefficient (r). If a correlation is found, I will investigate it further by calculating the line of regression, which may be able to forecast the correlation between the two variables. This bivariate study will shed light on the type and strength of the link between population and GDP, aiding in a full comprehension of the subject.

Overall, this study intends to use mathematical approaches to investigate the link between a country's population and GDP. I hope to understand the influence of population on economic production by evaluating both univariate and bivariate data. Through this thorough research, I hope to provide significant insights into the area of economics while also demonstrating the applicability of mathematical principles in real-world circumstances.

The countries used throughout my investigation have been divided into developed and developing countries using the Human Development Index (HDI) metric, whereby in this index the highest possible score is 1.0. The index while dividing these countries considers various factors which include; economic growth, life expectancy, health, education, and, standards of living (Human Development Index, n.d.)

Human Development Index - An integrated statistic that measures a country’s overall human development by considering life expectancy, education, and per capita income. Therefore, it provides a more holistic view of development than GDP alone.

Gross Domestic Product (GDP) -  According to the Oxford Dictionary, the total value of all the goods and services produced by a country in one year. It is a primary indicator of a country’s economic performance.

Developed Country - A developed country is characterized by a high GDP, advanced infrastructure, a well-developed industrial and service sector, and a high standard of living. Developed countries typically have low population growth rates.

Developing Country -  A developing country, often referred to as a less developed or underdeveloped country, is characterized by a lower GDP, limited industrialization, and often a higher population growth rate. A developing country is a country that is in the process of industrialization and economic growth.

Per Capita GDP - Per capita GDP is the GDP of a country divided by its population. It represents the average income of the citizens in a country which is a factor used to compare the standard of living among different countries.

To be able to generate a random list of developing and developed countries, I gathered all 214 countries from the World Data Bank. After collecting all of them for the data to be representative I used an online random sample generator to randomly select 15 developing and developed countries. If I used all the data provided by the World Data Bank it would be too much for the investigation thus, making the sample size too large. Using a random selection allowed me to examine the data in a representative manner. First of all, using the 214 countries provided by the World Data Bank, I then classified each country into either developing or developed according to the definitions provided above. Next, I placed the data into a list randomizer for both developing and developed countries after placing the data into alphabetical order for uniformity (Guide, n.d.).

See Table 1 -  population in a country in 2020 and the GDP of developing countries. (Appendix A) as well as Table 2: Populations and Gross Domestic Product of Developed Countries (Appendix B)

The first statistical exploration of the population and the gross domestic product (GDP), separately between the developing and developed countries on two different box and whisker diagrams. Using the GeoGebra Claasic App, I generated the diagrams. However, for data such as my range, interquartile range (IQR), and outliers, I used the five-figure summaries (most extreme values in my data set, the lower and upper quartiles, and the median) through my TI-84 Plus calculator. The table below is the five-figure summary for developing and developed countries.

The examination of population and GDP statistics for emerging nations gives useful insights into the economic dynamics of such countries. With the average size being 41,900 it demonstrates a significant diversity in population numbers in developing countries.This variance is emphasized by the broad interquartile range (IQR) of 33,898.1, which indicates that the middle 50% of nations have populations varying from 10,001 to 44,899. The population size range is very enormous, extending from the dataset's lowest to the maximum population size of 212,557,278.4. This large range demonstrates the significant demographic variability among developing nations, emphasizing the importance of detailed assessments that account for these differences. Similarly, the average GDP of 4,320 demonstrates the variation in economic production across emerging nations. The IQR for GDP of 4,316.7 highlights this variety, with the middle 50% of nations having GDPs ranging from around 3.4 to 8,736. The range of GDP numbers, 10,264, highlights the variations in economic success across emerging countries. The outlier test finds probable extreme values in population and GDP that may reflect nations with distinct economic or demographic features. These outliers may require more examination to determine the underlying causes of their remarkable performance or circumstances.

The mean GDP value of 36053.33 suggests that, on average, the economic output within the considered region or country hovers around this figure. However, the substantial interquartile range of 17781.9 points to significant GDP variability across different regions or sectors. This variability stems from various factors, including differences in economic development, industries, infrastructure, and resource distribution. The broad range of 82833.5 further underscores the diversity in GDP levels, showcasing a considerable gap between the lowest and highest values. This wide spectrum reflects a diverse economic landscape within the region or country. Utilizing upper and lower boundaries in an outlier test helps pinpoint extreme values that deviate significantly from the norm. The upper boundary of 48872.85 and lower boundary of 31090.95 act as thresholds beyond which GDP values are considered outliers. These outliers may indicate exceptional economic performance or downturns in specific sectors or regions, necessitating further exploration into their causes and implications.

The mean population of 1873.33 represents the average population size in the region or nation under consideration. However, the wide interquartile range of 25156.5 indicates significant variation in population numbers among different locations or demographic groupings in the region. This fluctuation might be caused by variables such as migratory patterns, birth and death rates, and government policies that influence population distribution. The range of 50700 emphasizes the huge contrast between the smallest and biggest population numbers within the area or country. Such a wide range shows that demographic compositions and population density vary by geography.

The following statistical investigation focuses on the link between two variables: the development status of the population in industrialized nations and the related gross domestic product (GDP). This analysis will involve producing different scatter diagrams for developing and developed nations, followed by a synthesis of findings to determine an overall link. To improve the precision of the results, I will use Pearson's Product Moment Correlation Coefficient (PPMCC) approach with my TI-84 Plus calculator to create a linear regression model that predicts one variable based on another. Following that, I will go to Table B (Fig 3) to assess the strength of the association and ensure a thorough review of the data.

This can be used to describe the measure of two random variables, and it is also used to measure the strength of their relationship with the values ranging from -1 and 1. The value of r is then calculated when solving the line of the regression equation for the data set shown above, and this will also show the strength of the correlation. I utilized materials that were available at geographyfieldwork.com to generate graphical representations of developing and developed countries.

Where r is = 0.236

This suggests no correlation between the population of a developing country and the gross domestic product per capita. Therefore there is no observable correlation between the population and gross domestic product per capita. While observing the graph it shows that random points with the line of best fit have only one point of contact in the scatter plot, proving that there is no relationship between the two variables.

Where r is = 0.1402

This suggests a weak positive correlation. Therefore, though there is a relationship between the two variables it is not strong thus making it a not good predictor of the variables. Even while observing the graph it clearly shows a weak positive correlation. However, to solidify these results, A Pearson Product Moment Correlation Coefficient test is necessary.

The Pearson product-moment correlation coefficient is critical for analyzing the link between a country's population and GDP. It quantifies the magnitude and direction of the association, giving statistical evidence to support or disprove my hypothesis. This strategy allows for more exact analysis, which helps to progress the exploration's aims.

The method clearly stated is a measure of the strength and direction of association between the two variables. As mentioned above my variables are the population and the correlation between the developed and developing countries in terms of the gross domestic product per capita. To do this I would need to use the formula presented below-

\(r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}} \)

Where-

r is used to represent the correlation coefficient

xi is the value for my x-variables in my sample

x̄ is the mean variable for the x-variables

yi is the value for the y-variable in my sample

ȳ is the mean for the mean variables

Results of the Pearson correlation indicated that there is a non-significant small positive relationship between population and the gross domestic capital per capita.

Results of the Pearson correlation indicated that there is a significant large positive relationship between Population and the Gross domestic product per capita.