Math IA- Based on GDP of India

Student’s Name
Professor’s Name
Course
Date
Math IA: The Relationship between India’s States Population and GDP
Rationale
I have decided to focus this mathematical exploration towards one of the most interesting disciplines, economics. World economics is such a dynamic topic that a single analysis cannot be sufficient to conclude from available data and therefore one cannot effectively and efficiently make projections for future market trends from it. Present-day economies change from day to day based on market volumes exchanged as well as the currency value of the trading state/country/region. Being an ardent lover of extremes, I chose to take a closer look at how economies of highly populated nations perform. To suit my taste and curiosity, I chose to analyze India (the nation with the highest population in the whole world).
I did some research on the GDP of India and its relationship with the population at the state level, and the findings were quite shallow. I only found an equivalence comparison between the various states of India and other national GDPs of other nations. Interestingly, the GDP of some of the states of India matches that of other countries national GDP. Such is what I want to unearth; I want to check and see if there can be correlations between an internal factor, population, and the country’s GDP. It inspired me to closely study this to evaluate the available data to determine whether or not the two, GDP and population are related. I thus sourced the nation’s economic data and compared it to the population data from the 2011 national census.

I decided to explore the relations at the state level rather than at national level to ensure it is directed and focused and without too many assumptions. It was because of unequal distribution of the factors that drive the economy.
Introduction
The GDP of a nation is the value of all trading volume that takes place within its boundaries. It refers to the highest possible gross revenue generated by a country regardless of the nationality of those trading. The economic performance of a country is affected by very many factors both internally and externally. Common external factors include
foreign trade policies,
international economic sanctions and
the value of the trading currency.
Internal factors are from within the nation, and they include
population,
political stability,
availability of resources and
government incentives to encourage trade.
GDP is a common way to determine any economic improvements/changes in an economy. It is not the same for all nations as different countries move varied trade volumes. The same applies to a nation’s GDP: it reflects the whole countries trade value and not that of the various states that make up the nation. I intend to study the building blocks of the figures reflected at the national level from the grassroots. With a country of India’s stature comes a lot of mettle that dictates how most of the factors correlate. The population is big, and a big percentage are still struggling, the bonus point is this there is a ready market for their products. However, the deepening and the ever-widening gap between the rich and the poor. An example would be a comparison between Maharashtra and Bihar; Bihar is three times smaller than Maharashtra and its GDP as of 2014 more than four times lower than that of Maharashtra. However, these two states have almost the same number of citizens as of the 2011 census that was carried out.
India’s Background Economic Information
India’s economic history is an evolutionary one. It has grown through different phases and faced various challenges along its growth curve. Before the Second World War, the nation’s economy was considered from a subcontinent level; the Indian Subcontinent that comprised of present-day India, Bangladesh, and Pakistan. The three nations only achieved sovereignty after the World War II. The history begins from the time of the Indus Valley civilization (3300-1300 BC), a time when the economy only grew mainly on trade. 600 BC saw the nation’s trade volume increase significantly fueling urbanization and intensive trading before uniting with Bangladesh and Pakistan in 300 BC to form the then Maurya empire that covered nearly the entirety of the Indian subcontinent. After this union, the subcontinent then moved to an agricultural based economy thanks to the increased agricultural productivity sprouting from the Maurya Empire.
India experienced economic growth during the late medieval period after 1000 and was responsible for slightly above 30% of the subcontinent’s trade volume. It was later overtaken by Ming China in 1500 before regaining its lost status as the largest economy in 1700 and later lost it again under the British rule in the 18th century. During this second millennium, India adopted mixed trade, something it has carried to its present-day status. The Republic of India adopted new trade policies upon its formation in 1947. The policies were favourable to the economy until the nation suffered an economic crisis in 1991. After healing from the ‘deep wounds’ and spoils of the crisis, India has experienced significant growth, making big steps forward and a name for itself on the world’s economic map. India’s economy is now the tenth largest economy in the world. The country has moved from US$ 18 billion in exports in the 1990-91 financial year to US$ 245 million in the 2010-11 financial year (“How The Indian Economy Changed In 1991-2011”) Mumbai is the current trade and economic capital for India and boasts of numerous high-end facilities as well as enough infrastructure. The city also lies in the state the has the highest contribution to the countries GDP.
The growth and stability of the Indian economy may come as a surprise, but much of their improvement and development has yielded from the presence of two other strong economies; Russia and China. Russia’s economic growth started from back in the days during the industrial revolution and having spearheaded industrialization. China on the other has acted out of competition in a move to silence critics and leave an economic era on the map. International relations between most Eastern Europe nations and Eastern and South-east Asia nations and the US have also played a part in these markets and economies growing. A country benefits when its competitor is handed trade sanctions. Such a beneficiary has been India and China after The West and EU placed trade sanctions and destabilized Russia albeit, for a while, the nation has restarted economically and is now in an even better economic stand and still has resources. India has come back a stronger player in the global economics after its economic crisis nearly three decades ago ended. A key player in these comebacks from economic fails is the availability of a ready market for their products thanks to the population in those nations. China and India alone account for over 25% of the world’s population, both having hit over the one billion citizen’s mark.
Statement of Task
India is made up of 36 regions are comprising of 29 (twenty-nine) states and 7 (seven) union territories; this is from the 2011 census. The main purpose of this exploration is to investigate, deduce and validate relationships between the GDP of a state and its population in all the 36 regions within it. I gathered data on the country’s population and GDP to help me in determining any relations. The data used in this investigation is sourced online from India’s Census 2011 (“List of States With Population, Sex Ratio And Literacy Census 2011”) and Worldatlas (Sawe) websites.
Plan of Investigation
From the collected data available, I generated two charts with Excel; one to give an outlook of population distribution in the states and another to show the contributions of the regions/states to the national GDP. From this visual display, one can then easily deduce the inputs of the various states.
I will carry out statistical procedures on the dataset for a simple analysis. Among them are measures of central tendency (mean) and measures of dispersion (standard deviation). I will then do calculations to determine the Pearson’s correlation coefficient, r2 to help in determining the standpoint of my assessment.
Collected Data
The data used in this study is as shown in Table one below. It is the raw data that encompasses my topic of interest.
# State Population Area(Km2) Density Literacy GDP in 2014- ‘15 (US$ bn)
– India 1210854977 3287240 382 74.04 1670.00
1 Uttar Pradesh 199812341 240928 829 67.68 150.00
2 Maharashtra 112374333 307713 365 82.34 250.00
3 Bihar 104099452 94163 1106 61.80 60.00
4 West Bengal 91276115 88752 1028 76.26 120.00
5 Andhra Pradesh 84580777 275045 308 67.02 77.00
6 Madhya Pradesh 72626809 308252 236 69.32 75.00
7 Tamil Nadu 72147030 130060 555 80.09 150.00
8 Rajasthan 68548437 342239 200 66.11 85.00
9 Karnataka 61095297 191791 319 75.36 100.00
10 Gujarat 60439692 196244 308 78.03 110.00
11 Orissa 41974218 155707 270 72.87 40.00
12 Kerala 33406061 38852 860 94.00 59.00
13 Jharkhand 32988134 79716 414 66.41 26.00
14 Assam 31205576 78438 398 72.19 24.00
15 Punjab 27743338 50362 551 75.84 47.00
16 Chhattisgarh 25545198 135192 189 70.28 27.00
17 Haryana 25351462 44212 573 75.55 58.00
18 Delhi 16787941 1483 11320 86.21 67.00
19 Jammu and Kashmir 12541302 222236 56 67.16 13.00
20 Uttarakhand 10086292 53483 189 78.82 18.00
21 Himachal Pradesh 6864602 55673 123 82.80 12.00
22 Tripura 3673917 10486 350 87.22 4.00
23 Meghalaya 2966889 22429 132 74.43 3.30
24 Manipur 2855794 22327 128 76.94 2.10
25 Nagaland 1978502 16579 119 79.55 2.70
26 Goa 1458545 3702 394 88.70 7.30
27 Arunachal Pradesh 1383727 83743 17 65.38 2.10
28 Puducherry 1247953 490 2547 85.85 3.10
29 Mizoram 1097206 21081 52 91.33 1.50
30 Chandigarh 1055450 114 9258 86.05 4.30
31 Sikkim 610577 7096 86 81.42 1.80
32 Andaman and Nicobar Is 380581 8249 46 86.63 0.92
33 Dadra and Nagar Haveli 343709 491 700 76.24 0.36
34 Daman and Diu 243247 111 2191 87.10 0.16
35 Lakshadweep 64473 30 2149 91.85 0.06
36 Telangana 35193978 112,077 314 66.46 64.00

The states with a population below ten million people were grouped into others to reduce the dataset in question, and the figures balanced considering the extremely small values (those grouped) would easily be dropped as outliers in the dataset. It resulted in a concise dataset as shown in Table 2 that was then subsequently used in the analysis.
Data Presentation
We start by observing the revenue share of the states in the national GDP on a pie-chart. This chart was generated from the dataset in Table one of the (collected data). The chart will indicate the percentage the various states contribute to the national GDP.

Figure SEQ Figure * ARABIC 1: Graphical representation of the explored data

Calculation of Basic Data Statistics
Reduced Dataset for statistical analysis
State Population(x) GDP(y) x^2 y^2
Uttar Pradesh 199812341.00 150.00 39924971615900300 22500
Maharashtra 112374333.00 250.00 12627990717194900 62500
Bihar 104099452.00 60.00 10836695906700300 3600
West Bengal 91276115.00 120.00 8331329169493220 14400
Andhra Pradesh 84580777.00 77.00 7153907837923730 5929
Madhya Pradesh 72626809.00 75.00 5274653385522480 5625
Tamil Nadu 72147030.00 150.00 5205193937820900 22500
Rajasthan 68548437.00 85.00 4698888215142970 7225
Karnataka 61095297.00 100.00 3732635315518210 10000
Gujarat 60439692.00 110.00 3652956369054860 12100
Orissa 41974218.00 40.00 1761834976711520 1600
Kerala 33406061.00 59.00 1115964911535720 3481
Jharkhand 32988134.00 26.00 1088216984801960 676
Assam 31205576.00 24.00 973787973491776 576
Punjab 27743338.00 47.00 769692803382244 2209
Chhattisgarh 25545198.00 27.00 652557140859204 729
Haryana 25351462.00 58.00 642696625537444 3364
Delhi 16787941.00 67.00 281834963019481 4489
Jammu and Kashmir 12541302.00 13.00 157284255855204 169
Uttarakhand 10086292.00 18.00 101733286309264 324
Telangana 35193978.00 64.00 1238616087464480 4096
Others 26225172.00 45.70 687759646429584 2088
 
Sum 1246048955 1665.70 110911202125670000 190180
Mean:
The mean of the population per state was calculated by dividing the sum of the respective population values by the number of states.
Mean population = National population/Number of states.
= 1246048955/36
= 34612470.
I used the same approach to calculate the mean Gross Domestic Product (GDP) of a state.
Mean GDP = National GDP/Number of states.
= 1665.70/36
= 46.27
Standard Deviation:
Standard deviation is a measure of central tendency that describes how data is spread from the mean. The calculation of the standard deviation for the population uses the formula shown below:

where x is the population,
n the number of entries in the dataset (in this case 36)
Sx is the standard deviation of the population
Standard deviation = {(sum of x squared/n) – the square of the mean}0.5.
= {(110911202125670000/36) – 346124702}0.5
= 42819254
42819254is the standard deviation of variable x, the population of each state in India.
The calculation of the standard deviation for the Gross Domestic Product uses the formula shown below:
Standard deviation = {(the sum of y squared/n) – the square of the mean}0.5.
= {(190180/36) – 46.27}0.5
= 53.9631
53.9631 is the standard deviation of variable y, GDP of each state of the 36 Indian states.Table 3 below provides a summary of the above statistics
Statistical summary of the dataset
Sum 1246048955 1665.70
Mean 34612471 46.27
Standard Deviation 42819254 53.9631
Least Squares Regression
Least squares regression is a method used in fitting a dataset. A function of an independent variable is fixed to another function (one for the dependent variable) to help deduce a function of the line of fit. It results in a function that can then be used to predict other any other variable given variable of the pair, for example, finding an independent variable given a dependent variable. The following formulae give the least squares regression:

where y is the GDP,
S2x is the variance
n the number of variables.
Sxy = (2075543744343.5/36) – 34612470 * 46.27
= 56052493096
Sx 2 = 42819254* 42819254
= 1833488529975500
y – 46.27 = {(1833488529975500/56052493096) (x – 42819254)}
y = {(1866242179588710/56052493096) (x – 42819254)} + 46.27
= 32710.20482(x – 42819254) + 46.27
= 32710.20482x – 1400626575128.73 + 46.27
= 32710.20482x.– 1400626575175
Therefore; y ≈ 33924.54x – 1400626575175 is the equation derived from the regression fit. This equation can be used to further model projections for the inputs of each state in future GDPs.
Pearson’s Correlation Coefficient
Pearson’s correlation coefficient is a statistical method of determining the extent of the relationship between two variables. I derived the coefficient so that it can help me determine how strong the GDP of the states of India relate to their respective populations. To do the calculations, I used the following equation:

where r is the square root of Pearson’s correlation coefficient,
Sxy is the standard deviation of the dataset
Sx is the standard deviation of the population of Indian states
Sy is the standard deviation of the GDP of the various states in India.
r = 56052493096/ (42819254*53.9631)
= 24.25823398
r2 = 588.461916
≈ 588.46
One ANOVA test
A one-way ANOVA test was done to test the hypothesis that, at 95% confidence intervals, the GDP of Indian states is directly influenced by their various population/demographics. I carried out a test using the Analysis Tool Pack to generate one-way ANOVA test results as shown in Table 3.
Anova: Single Factor SUMMARY Groups Count Sum Average Variance Population(x) 21 1.22E+09 58086847 1.97E+15 GDP(y) 21 1620 77.14286 3156.029 x^2 21 1.1E+17 5.25E+15 7.63E+31 y^2 21 188092 8956.762 1.94E+08 ANOVA Source of Variation SS dfMS F P-value F critBetween Groups 4.34E+32 3 1.45E+32 7.578415 0.000159 2.718785
Within Groups 1.53E+33 80 1.91E+31 Total 1.96E+33 83        
Table3: Excel generated ANOVA test results.
In the above result/output, the p-value indicates that the hypothesis is not sufficiently supported.
Discussion
The entirety of this exploration through India’s economic data on GDP and its census dataset has had missing links and ‘jumps’ within it. India has 29 states that are fully independent on most fronts. A further seven regions represent union territories that are upcoming or just started recently. As a result, they tend to lag behind in many issues; a possible explanation of the range depicted in the dataset Lakshadweep is a good example and fits the bill of all the characteristics of an outlier. It is possible to drop it, but there are more others with the same characteristics. As a result, I generalized them into workable groups from to reduce the number of outliers in the dataset. Such extremes confirm that indeed there is no big relationship between the two variables.
With the issue of lower extremes already covered within the generalizations, there remains ‘bigger’ outliers on the upper end that pose serious troubles would they be dropped. The top six states regarding GDP revenue generation are possible outliers and strangely account for more than half, 53.3% of the national GDP. Should these states be dropped from the dataset, there won’t be an account any accurate to represent the economy of India.
The range of the datasets also got exposed as a limitation of this investigation by the standard deviation; a figure that is higher than the minimum. It is an indication that the spread of the data is not consistent. The inconsistency is not just on one variable but on both variables. There may be other factors that affect the GDP of a country, but to India, the population is not a key player in controlling financial markets as well as the economy.
It can be derived from the original raw data by the observation that the GDP of Indian states is a little influenced by the size of the state. These are possibly a reflection of the fact that having more land translates to more potential of having natural resources.
The Pearson’s correlation coefficient is usually a number between -1 (negative one) and +1 (a positive one). Our finding from the calculations of Pearson’s correlation coefficient was 588. This figure is therefore not within the range (-1 < x > 1). It is another sign that implies there is little to no relation between population and the GDP of in Indian states. That raises a point of concern over the living conditions in states the nation. Jammu and Kashmir is a very big state in India regarding physical resources. That does not reflect on the population or the economic advantages and gains sourced from those places. West Bengal is the direct opposite of Jammu and Kashmir; it is small in size, but that does not limit it economically. The state generated more than 120 million dollars as of the 2013-2014 financial year. That is not the only place that it is ahead of Jammu and Kashmir, W, Bengal has a higher population.
Conclusion
Along with the challenges mentioned in the discussion. There is no party to the data that supports Population being the driver of the economy. I aimed to find out if the population and state economic development are related in any way and by how much. My findings from the Pearson’s correlation coefficient also backed my word that indeed there was no relationship between population and economic growth in the states. The states have probably grown thanks to other factors like good working conditions and availability of resources. I recommend that a future assessment and study on the Indian economy try to investigate the relation between the size of a state and its economic and financial output.
Works Cited
“How The Indian Economy Changed In 1991-2011.” The Economic Times. N.p., 2011. Web. 14 Feb. 2018.
“List Of States With Population, Sex Ratio And Literacy Census 2011.” Census2011.co.in. Web. 14 Feb. 2018.
Sawe, Benjamin. “Indian States By GDP.” WorldAtlas. N.p., 2017. Web. 14 Feb. 2018.