The Relationship between the Population and Prisoner Population of Countries around the World
Mathematics Studies Standard Level Coursework
17th January 2016
Ruhi Rajani 001482-0017
North London Collegiate School
Mrs Buffham
Word Count: 2051
In this controlled assessment I will investigate whether the prisoner population of different countries is independent of the population of those countries. I will use a selection of countries that have been randomly selected using the Excel number generator, by assigning a random number to all of the countries presented by the World Bank, and using this number to choose the countries that were generated. I will do this to ensure that any form of bias is avoided, in compliance with the basis that random sampling is 'a sampling method in which all members of a group (population or universe) have an equal and independent chance of being selected'[1]. I will use a sample size of 64, due to the fact that this is a large enough sample size to come to a conclusion of whether the populations of countries and their prisons are connected, however this size is not too large that it would take an extremely long time to analyse the findings that this data presents. I decided to investigate this subject due to an interest in the legal system, and I wanted to find out if the populations of different countries played a large role on the number of people that were in prison on those countries or not.
In order to carry out this investigation, I used data from the World Bank[2] for the populations of each country. I then used the International Centre for Prison Studies[3] to collect the data regarding the prison populations of each country. I chose these institutions as they are well-respected organisations, and therefore are likely to have provided reliable data. I decided to use data from the year 2014, as there was data available for both population and prisoner population for that year. This is not as reliable as collecting data from other years, but this was enough data for the scope of this investigation. In order to measure the relationship between these two variables, the data had to be from the same year, in order for the results of the analysis to be accurate.
I will carry out simple and complex tests to discover the mean and standard deviation of the data, as well as calculating what percentage of the population in each country are prisoners, data which I will display on a graph. These tests will help to determine if there is a relationship between the populations of countries and the number of prisoners in each country. In order to determine independence of these two factors, I will conduct a chi-squared test.
My hypothesis is that the prisoner population of countries is not independent of the population of countries, due to the logic that if there are more people in a country, there are more people to commit crimes. However, I am, factoring an awareness that in less developed countries, for example, other causes such as overpopulation can also lead to crime because of a need to obtain food and money in order to cope with the conditions of that country.
Table 1. Raw Data Sample Test 1.
Country / Population (x) / Prisoner Population (y) / Percentage of Population who are PrisonersChina / 1,364,270,000 / 1,657,812 / 0.12%
India / 1,267,401,849 / 411,992 / 0.03%
USA / 318,857,056 / 2,217,000 / 0.70%
Indonesia / 254,454,778 / 161,692 / 0.06%
Brazil / 206,077,898 / 607,731 / 0.29%
Pakistan / 185,132,926 / 80,169 / 0.04%
Nigeria / 178,516,904 / 57,121 / 0.03%
Bangladesh / 158,512,570 / 69,719 / 0.04%
Russian Federation / 143,819,569 / 649,500 / 0.45%
Japan / 127,131,800 / 61,794 / 0.05%
Mexico / 125,385,833 / 255,138 / 0.20%
Philippines / 99,138,690 / 120,076 / 0.12%
Ethiopia / 96,958,732 / 93,044 / 0.10%
Vietnam / 90,730,000 / 142,636 / 0.16%
Egypt / 89,579,670 / 62,000 / 0.07%
Germany / 80,889,505 / 63,628 / 0.08%
Iran / 78,143,644 / 225,624 / 0.29%
Turkey / 75,837,020 / 165,033 / 0.22%
D. Rep. Congo / 74,877,030 / 22,000 / 0.03%
Thailand / 67,725,979 / 314,303 / 0.46%
France / 66,201,365 / 66,864 / 0.10%
UK / 64,510,376 / 95,605 / 0.15%
Italy / 61,336,387 / 52,144 / 0.09%
South Africa / 54,001,953 / 159,241 / 0.29%
Myanmar / 53,437,159 / 60,000 / 0.11%
Colombia / 47,791,393 / 120,905 / 0.25%
Spain / 46,404,602 / 64,835 / 0.14%
Ukraine / 45,362,900 / 71,325 / 0.16%
Argentina / 42,980,026 / 64,288 / 0.15%
Algeria / 38,934,334 / 60,220 / 0.15%
Poland / 37,995,529 / 75,691 / 0.20%
Morocco / 33,921,203 / 76,000 / 0.22%
Peru / 30,973,148 / 74,486 / 0.24%
Madagascar / 23,571,962 / 18,719 / 0.08%
Australia / 23,490,736 / 35,804 / 0.15%
Romania / 19,910,995 / 29,312 / 0.15%
Niger / 18,534,802 / 7,116 / 0.04%
Netherlands / 16,854,183 / 12,638 / 0.07%
Malawi / 16,829,144 / 12,156 / 0.07%
Ecuador / 15,982,551 / 25,902 / 0.16%
Zambia / 15,021,002 / 17,160 / 0.11%
Rwanda / 12,100,049 / 55,618 / 0.46%
Cuba / 11,258,597 / 57,337 / 0.51%
Greece / 10,957,740 / 11,988 / 0.11%
Haiti / 10,461,409 / 10,266 / 0.10%
Portugal / 10,397,393 / 14,293 / 0.14%
Hungary / 9,861,673 / 17,716 / 0.18%
Sweden / 9,689,555 / 5,779 / 0.06%
Austria / 8,534,492 / 8,241 / 0.10%
Israel / 8,215,300 / 18,658 / 0.23%
Switzerland / 8,190,229 / 6,923 / 0.08%
Serbia / 7,129,428 / 10,031 / 0.14%
Libya / 6,253,452 / 6,187 / 0.10%
Denmark / 5,639,565 / 3,481 / 0.06%
Norway / 5,136,475 / 3,710 / 0.07%
Ireland / 4,612,719 / 3,791 / 0.08%
New Zealand / 4,509,700 / 8,641 / 0.19%
Croatia / 4,236,400 / 3,853 / 0.09%
Jamaica / 2,721,252 / 4,050 / 0.15%
Iceland / 327,589 / 147 / 0.04%
Barbados / 286,066 / 884 / 0.31%
Greenland / 56,295 / 116 / 0.21%
Monaco / 38,066 / 23 / 0.06%
Tuvalu / 9,894 / 11 / 0.11%
In order to calculate these percentages I used the following equation: prisoner populationpopulation×100
For example:
prisoner population of Chinapopulation of China×100 = 1,657,8121,364,270,000×100=0.12151 = 0.12%
These percentages display that there is a relationship between the prisoner population and the population of countries. There are however certain outliers which are significant, with the USA having a higher percentage (0.7%) than most countries, and India having a lower percentage (0.03%) than most countries, both of these countries having two of the biggest populations out of all of the countries. There are several countries, such as Rwanda, Cuba and the Russian Federation which have a significantly higher prisoner population than the countries that have a similar sized smaller population to them, but the majority of these countries follow the trend of there being a general positive correlation.
I decided to present this information on a scatter graph to display the correlation as one that is more significant.
This graph presents a problem in the claim that there is a correlation, due to the range of populations meaning that the data is not spread out, and highly concentrated in the bottom left corner of the graph. However, it clearly shows the outliers, with the USA having an incredibly large prisoner population and a lower population than both China and India, which are the other two major outliers. India has a much lower prisoner population than other countries which are seen to have a significantly lower population than it. These anomalies could be to do with the larger land mass of these countries, combined with their large population. It could also potentially be due to the rigorousness of the legal systems in those countries, perhaps with the USA having a more rigorous system than other countries.
This table displays the process used to find the mean and standard deviation of the data.
Table 2.
Population (x) / Prisoner Population (y) / (x-[1] http://www.businessdictionary.com/definition/random-sampling.html
[2] http://data.worldbank.org/indicator/SP.POP.TOTL
[3] http://www.prisonstudies.org/highest-to-lowest/prison-population-total?field_region_taxonomy_tid=All&=Apply