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Transcript
Relationship between GDP per Capita and Gini Index
By: Ms. Bercovitz
Probability & Statistics
2/28/2012

STATEMENT OF QUESTION
In this report, the relationship between the Gini index and GDP per capita is being
investigated. The Gini index measures how equal the distribution of income in a country is. In
other words, the Gini index measures how big of an economic or income gap exists between
the rich and the poor in a country. A Gini index of 0 represents complete equality; a Gini index
of 100 represents complete inequality. GDP per capita is a measure of a country’s total
economic output divided by the total number of citizens. GDP per capita is one way in which a
country can measure its economic growth, and GDP per capita is often used as a way to
compare the economy of one country to another.
The essential question being asked in this report is, “Does a relationship exist between
the Gini index and GDP per capita, and if so, what is the nature of this relationship?” To gather
data for this investigation, Pearson Education’s Infoplease.com website was used as a means to
find economic statistics by country. GDP per capita (in thousands) is being used as the
explanatory variable, and Gini index is being used as the response variable. This is because I am
predicting that GDP, which is a measure of economic success, predicts how fair an economy is.
Below are the data and scatterplot for for Gini index and GDP per capita.

DATA
Chile
Honduras
Swaziland
Norway
Namibia
Lesotho
Sierra Leonne
Central African Republic
Botswana
Bolivia
Haitia
Colombia
Paraguay
South Africa
Brazil
Panama
Ecuador
El Salvador
GDP per capita (in thousands)
11.3
2.9
5
42.3
7
2.5
0.8
1.1
10.5
2.9
1.7
7.9
4.9
12
8.4
7.2
4.3
4.7
Gini
Index
54.9
53.8
50.4
25.8
74.3
63.2
62.9
61.3
60.5
60.1
59.2
58.6
58.4
57.8
57
56.1
53.6
52.4
Table 1: Gini Index and GDP per capita
(in thousands) for 40 different
countries. Gini index is a measure of
the economic equality of a country. A
Gini index of 0 means perfect
economic equality; a Gini index of 100
means perfect economic inequality.
Peru
Bangladesh
Finland
Bulgaria
Neterlands
Mongolia
France
Canada
Slovenia
Belgium
Japan
Germany
Romania
Hungary
Denmark
Ukraine
Argentina
Moldova
Slovakia
Pakistan
Tajikistan

5.9
2.1
30.9
9.6
30.5
1.9
29.9
34
21.6
31.4
31.5
30.4
8.2
16.3
34.6
7.2
13.1
1.8
16.1
2.4
1.2
52
33.4
26.9
29.2
30.9
32.8
32.7
32.6
28.4
33
24.9
28.3
31
26.9
24.7
28.1
51.3
33.2
25.8
30.6
32.6
SCATTER PLOT
Graph 1: Relationship between
GDP per capita and Gini index,
with GDP per capita displayed
in thousands. Included are a
least-squares regression line
and the accompanying
regression equation. The
correlation value for this
relationship is r=-0.58841.
Relationship between GDP per capita
and Gini Index y = -0.694x + 51.475
70
Gini Index
60
50
40
30
20
10
0
0
10
20
30
GDP per capita (in thousands)
40
50

INTERPRETATION OF DATA
The mean GDP per capita is $12.77 thousand, and the standard deviation is $12.17
thousand. This means that, on average, the countries’ GDP per capita values deviated from the
mean of $12.77 thousand by $12.17 thousand. Since the standard deviation is nearly as large
as the mean, we can say that the GDP per capita values are very widely ranging. The mean Gini
index is 43.32, and the standard deviation is 14.94. This means that, on average, the countries’
Gini indexes deviated from the mean of 43.32 by 14.94 units.
The relationship between GDP per capita (in thousands) and Gini value is negative and
linear with a correlation value of r=-0.58841, indicating a relatively weak relationship. In
general, as GDP per capita increases, the Gini value of a country decreases. This means that as
a country produces more goods on average per person, their overall economic equality
increases. In general, it appears that countries who are experiencing higher levels of economic
success and growth have higher levels of economic equality among their citizens.
The regression equation for the relationship between GDP per capital (in thousands)
and Gini value is y=-0.7224x+52.55, where y represents the Gini value and x represents the GDP
per capita. The slope of the regression equation is -0.7224; this means that Gini value
decreases by 0.7224 units for every thousand dollar increase in GDP per capita. Since a lower
Gini value corresponds to a more equal economy, this negative slope suggests that as GDP per
capita increases, economic equality increases. The y-intercept of the regression equation is
52.55. This means that when the Gini value is zero, the GDP per capita of a country would be
$52.55 thousand dollars, or $52,500 per person. In other words, if an economy were perfectly
equal (which is what a Gini value of zero means), each person would be producing on average
$5,255,000 worth of goods each year.
The residual plot for the data shows that there is a wide variation in the data,
particularly for countries which have low GDP per capita values. The residual plot shows that
the regression line is not a particularly good fit for our data.

INTERPRETATION OF OUTLIERS
There is one unusual point which can be identified as an outlier. Namibia has a GDP per
capita of $7 thousand and a Gini index of 74.3. Although we would expect Namibia to have a
high Gini index given its low GDP per capita, 74.3 is much higher than the rest of the data
points.

PREDICTION FROM REGRESSION LINE
We could use our regression line to make predictions about unknown data points. We
will predict the Gini Index of a country with a GDP per capita of $50 thousand and a GDP per
capita of $25 thousand. For a country with a GDP per capita of $50 thousand, the Gini Index
would be 13.9, and for a country with a GDP per capita of $25 thousand, the Gini Index would
be 33.2.

CONCLUSION
Overall, our essential question was, “Does a relationship exist between the Gini index
and GDP per capita?” It was found that there was a weak negative relationship between GDP
per capita and Gini Index. This is likely because as GDP per capita increases, on average more
individuals are making more money, which potentially makes an economy more equal. It is
important, however, to remember that GDP per capita is an average, meaning that a few very
rich individuals could pull the average up and make the GDP appear higher than it actually is.