Exploring the Correlation Between GDP per Capita and Life Expectancy

This project investigates the relationship between GDP per capita (Purchasing Power Parity) and life expectancy across different genders and continents (Africa, Asia, and Europe). The study uses data from the World Bank (2015) and employs mathematical processes such as scatter graphs, bar graphs, standard deviation, and regression analysis to determine if a positive correlation exists between per capita GDP and life expectancy. The analysis includes summary statistics for each continent, frequency distributions of GDP, and calculations of average life expectancy for males and females. Scatter plots visually represent the relationship between GDP and life expectancy, while regression lines provide a quantitative measure of the impact of GDP on life expectancy. The conclusion indicates a positive, albeit small, impact of per capita GDP on life expectancy, with variations observed across continents and genders, supporting earlier research in the field. Desklib provides access to this and other solved assignments for students.

Effect of GDP per Capita (Purchasing
Power Parity/PPP)
On Life Expectancy
Introduction
Hypothesis: Relationship between GDP and life expectancy between genders in Asia,
Europe and Africa.
For my math studies project I am going find, if there are relation between PPP also known as
GDP and life expectancy is under observation considering two genders separately. In this
work I’ll trying to understand if there is positive relation between per capita GDP and life
expectancy of people.
The data for GDP and life expectancy was taken from the World Bank, the data is from 2015.
I will be using several mathematical processes to prove or disprove my hypothesis. The lower
process will be the scatter graph, bar graph and standard deviation (S.D). Lower processes
like scatter graph will be used in order to find the correlation between GDP and life
expectancy. The higher level process will be Regression Analysis (curve of best fit)
Mathematical Processes
Summary statistics of the variables
Africa: The means for per capita GDP, male life expectancy and female life expectancy were
found. Initially the frequency table for per capita GDP was found as in figure 1.

Figure 1: Per Capita GDP frequency distribution
The GDP wise country division was represented by a bar diagram. The distribution reflected
that most of the countries were in GDP per capita bracket of $ 750 to $ 3400.
Figure 2: Countries as par GDP per capita-Africa
The average GDP per capita was calculated as
= $5677.01. Average GDP was calculated
using Male life expectancy data on Africa which has been included in the master table.

The average male life expectancy was calculated as
Male Life Expec tan cy = Sum of life lenght of countries
Total number of countries =3002. 42
49 = 61.27. The average female
life expectancy was
Female Life Expec tan cy= Sum of life of females
Total number of countries =3181. 56
49 = 64.92
persons. The standard deviations (S.D) were respectively {using the formula
s= √ ∑ x2
n −( ∑ x
n )
2
} $6270.43, 6.08 and 6.72 persons (appendix table 10). The S.D value
for GDP indicated the huge disparity among the countries. The accumulation of the per capita
GDP was in the range (mean S.D), which was calculated as -$593.42 to $11947.44.
Between this limits there were 43 countries, hence
42
63 X 100=66 .67 % countries lied in the
interval.
Asia: The means for per capita GDP, male life expectancy and female life expectancy were
found. The frequency distribution has been provided in figure 3. The limits are GDP per
capita and unit was dollars.
Table 1: Frequency distribution for Asia
Lower
Limit
Upper
Limit Frequency
700 12200 16
12200 23700 7
23700 35200 4
35200 46700 3
46700 58200 2
58200 69700 2
69700 81200 2
81200 92700 0
92700 104200 1
104200 115700 0
115700 127200 1

The frequency distribution has been represented in bar diagram in figure 3. The distribution
curve was right skewed.
Figure 3: Countries as par GDP per capita-Africa
The average GDP per capita was calculated as
Avg GDP= Total GDP
Number of countries = $ 1060556 . 65
38 = $ 27909.38. Male life expectancy data
from master data was used. The average male life expectancy was calculated as
Male Life Expec tan cy = Sum of life lenght of countries
Total number of countries =2740 .63
38 = 72.12 persons. The standard
deviations (S.D) {using the formula
s= √ ∑ x2
n −( ∑ x
n )
2
} were respectively $ 29321.80,
6.03 and 6.49 persons (appendix table 11). From the mean GDP value compared to Africa
was much higher because of large number of developed and developing countries in Asia.
The average female life expectancy was
Female Life Expec tan cy= Sum of life of females
Total number of countries =2898 .38
38 = 76.27 persons.

The accumulation of the per capita GDP was in the range (mean S.D), which was
calculated as -$1412.41 to $57,231.18. Between this limits there were 33 countries, hence
33
38 X 100=86 . 84 % countries lied in the interval.
The disparity in GDP was also prominent from the S.D value. Mean life expectancy rates of
72.12 and 76.27 for males and females were also higher compared to African life expectancy
values. Total 38 countries were studied under Asia.
Europe: The frequency distribution has been provided in figure 4. The limits are GDP per
capita and unit was dollars.
Table 2: Frequency distribution of countries-Europe
Lower Limit Upper
Limit Frequency
10750 19050 5
19050 27350 6
27350 35650 6
35650 43950 6
43950 52250 4
52250 60550 1
60550 68850 2
68850 77150 0
77150 85450 0
85450 93750 0
93750 102050 1
The frequency distribution has been represented in bar diagram in figure 3. The distribution
curve revealed that countries in Europe were distributed comparatively in even manner based
on GDP per capita.

Figure 4: Countries as per GDP per capita-Europe
The average GDP per capita was calculated as
Avg GDP= Total GDP
Number of countries = $ 1098842. 96
31 = $35446.54. Male life expectancy data
from master data was used for this calculation. The average male life expectancy was
calculated as
Male Life Expec tan cy = Sum of life lenght of countries
Total number of countries =2404 . 24
31 = 77.55 persons.
The S.D value {using the formula
s= √ ∑ x2
n −( ∑ x
n )
2
} was $17830.91 (table 12 in
Appendix) and the value suggested that the continent was having countries with very close
values of GDP level. High GDP influencing life expectancy rates to move to the greater sides
were also visible. Total 31 countries were studies within Europe.
The average female life expectancy was
Female Life Expec tan cy= Sum of life of females
Total number of countries =2566. 82
31 = 82.8 persons.

Mean GDP for the continent was highest among the three continents. Life expectancy rates
for males and females on average were and which were also the highest in the study.
Scatter graphs
Africa:
The continent with 49 countries has the most skewed data among all three continents.
Figure 7: Scatter diagram for male life expectancy in Africa
Scatter plot was indicative of the fact that major number of countries were condensed within
$ 7000 GDP values and average life expectancy were positive but not on the higher side.

Figure 8: Scatter diagram for female life expectancy in Africa
Female life expectancy was also not very promising. Major points in the data were between
50 years to 65 years of age group, for low GDP countries.
Asia: The continent had 38 countries in the study.
Figure 9: Scatter diagram for male life expectancy in Asia
GDP clustering in Asia is also on the lower side below $30000 but better than African
continent.

Clustering for life expectancy was between 65 years to 75 years. Level of correlation was
positive and high. It was also observed that life expectancy was over 75 years in the countries
having more than $50000 GDP per capita.
Figure 10: Scatter diagram for female life expectancy in Asia
Female life expectancy was also clustered in the age bracket of 65 years and 80 years. The
female group also had lower life expectancy range compared to males in Asia for higher level
GDP countries.
Europe: The continent had 31 countries in the study.

Figure 11: Scatter diagram for male life expectancy in Europe
GDP clustering in Europe was the best of the three continents. Clustering for life expectancy
was between 70 years to 80 years. Level of correlation was positive and very high. It was also
observed that life expectancy was near 80 years in the countries having more than $50000
GDP per capita.
Figure 12: Scatter diagram for female life expectancy in Asia
Female life expectancy was also clustered in the age bracket of 77 years and 85 years. The
female group also had a high life expectancy range compared to males in Europe for higher
level GDP countries

Regression line (line of best fit

Table 3: Africa Descriptive table
AFRICA 2015/GDP(in $)X
MALE/LIFE
EXPECTANCY
(Y)
FEMALE/LIFE
EXPECTANCY
(Z)
sum 278173.52 3002.40 3181.53
square 3505788848.24 185779.00 208784.11
n 49 49 49
SD 6270.43 6.08 6.72
MEAN 5677.01 61.27 64.93
The SD value in table 3 was calculated using the formula
s= √ ∑ x2
n −( ∑ x
n )
2
and the mean
was calculated using the formula x
−
= ∑ x
n .
Africa: The regression equation for y on x is y=a+bx , where
b=
∑
i=1
n
( xi −x
−
)∗( yi − y
−
)
∑
i=1
n
( xi−x
−
)2
and a=∑ y−b∗∑ x
n .
Hence,
b=700542. 95
1926595316. 79 =0 .00036 and
a=3002. 42−0 .00036∗278173 .51
51 =56 . 91
The regression line for males was y=0 . 00036 x+ 56. 91
The regression line for predicting life expectancy based on GDP was found. For linear
regression model line of best fit is found as ( y − y
−
) =b yx ( x −x
−
) .
The above calculation was done using table 3 and table 5. The regression coefficient was
where r is the correlation coefficient.
, were the standard deviation of life expectancy and PPP (GDP per capita).