Ia final report

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Ia final report

  1. 1. What is the Relationship between the Human Birth Rates and the Human Death Rates?<br />IB Math Studies Internal Assessment<br />International School Bangkok<br />Student: Yuki Matsuda<br />Teacher: Mr. DeMille <br />Word Count:<br />What is the Relationship between the Human Birth Rates and the Human Death Rates?<br />Introduction<br />In this assessment, I have to find the relationship between Human Birth Rates and Human Death Rates in order to compare with another country so each country knows the result of birth rates and death rates. Basically, the birth rates and death rates are relating to whether the country is rich or poor. For example, there is no map in here but when I saw the birth rates map, it is surprising different than what I thought. For overall, the Africa’s continent, most countries are high birth rates, that’s means there are many babies are born in each day and each year. Also, when we see the death rates map, it is easy to see and very clearly results. The most high death rate area is also, Africa’s continent. The birth rate is very high but also death rare is also too high because the medical treatment is not so develop and many people do not know how to prevent pregnancy. In consequences, Africa’s continent, the birth rates and death rates are the highest area in the world.<br />Statement of Task<br />The main purpose of this investigation is to define the relationship between a country’s human birth rates and its human death rates. Basically, the birth rate is the ratio of total live births to total population in a specified community or area over a specified period of time. The birth rate is often expressed as the number of live births per 1,000 of the population per year. In addition, the death rate is the ratio of total deaths to total population in a specified community or area over a specified period of time. The death rate is often expressed as the number of deaths per 1,000 of the population per year. The birth and death rate can see in Health and Social Statistics and we can see many countries’ birth rate and death rate of different year.<br />Plan of Investigation<br />Following the data collection, I am going to do a scatter plot of the data and calculate the birth rate and death rate by showing correlation and regression line. Also, I am going to do a 2 on the data to show independent and dependent variables.<br />Collected Data<br />Table 1: Human Birth Rates and Human Death Rates for 18 Countries<br /> Birth rateDeath rateCountry20072006200519901985198019752007200620051990198519801975Australia 12.012.112.315.415.715.316.97.67.57.47.07.57.47.9Austria 8.78.78.811.611.612.012.59.89.89.710.611.912.212.8Belgium 10.310.410.512.611.512.712.210.310.310.210.611.211.612.2France 11.912.012.213.513.914.814.19.29.19.19.310.110.210.6Germany2 8.28.38.311.49.610.09.710.710.610.611.211.511.612.1Greece 9.69.79.710.211.715.415.710.310.210.29.39.49.18.9Ireland 14.414.514.515.117.621.921.57.87.87.89.19.49.710.6Israel 17.718.018.222.223.524.128.26.26.26.26.26.66.77.1Italy 8.58.78.99.810.111.214.810.510.410.39.49.59.79.9Japan 9.29.49.59.911.913.717.29.49.29.06.76.26.26.4Netherlands 10.710.911.113.312.312.813.08.78.78.78.68.58.18.3New Zealand 13.613.813.918.015.6—18.47.57.57.57.98.4—8.1Norway 11.311.511.714.312.312.514.19.49.49.510.710.710.19.9Panama 21.521.722.023.926.626.832.35.45.45.3————Portugal 10.610.710.811.812.816.419.110.610.510.410.49.69.910.4Switzerland 9.79.79.812.511.611.312.38.58.58.59.59.29.28.7United Kingdom 10.710.710.813.913.313.512.510.110.110.211.211.811.811.9United States 14.214.114.116.715.716.214.08.38.38.28.68.78.98.9<br />Table 1: This table presented the data that was collected from infoplease websites for human birth rates and death rates. These countries quite known in the world but each birth and death rate are completely different than other countries.<br />sum x: 212.8 correlation coefficient: -0.89439527<br />sum y: 160.3 covariance: -4.47290123<br />sum x2: 2716.3 slope: -0.40149492<br />sum y2: 1467.97 y-intercept: 13.65211771<br />sum xy: 1814.59<br />mean x: 11.82222222<br />mean: y: 8.905555556<br />standard deviation x: 3.337756325<br />standard deviation y: 1.498322107<br />Data Analysis/Mathematical Processes<br />We will start by looking at a Scatter plot of the collected data.<br />Graph 1 shows the Human Birth Rate vs. Human Death Rate plotted on a scatter plot. Also, it appears as if it is a negative correlation and the strength of the association is strong.<br />Standard Deviation Calculations<br />Standard Deviation measures the variability/dispersion of the particular variables. It is given by the following formula.<br />Sx=x2n-x2 Sy=y2n-y2<br />Sx=2716.318-11.822<br /> =150.81-139.765<br /> =11.1406<br />Sx=3.3377<br />3.34 is the standard deviation of x, human birth rates. This indicates a condensed range of data yet sufficient for a statistical analysis.<br />Sy=1467.9718-8.9052<br /> =81.5538-79.309<br /> =2.24497<br />Sy=1.498<br />1.498 is the standard deviation of y, human death rates. This indicates a condensed range of data although it still remains sufficient for a statistical analysis.<br />Least Squares Regression<br />Least Squares regression calculations identify the relationship between the independent variable, x, and the dependent variable, y. The least squares regression is given by the following formula:<br />y-y=SxySx2(x-x) where Sxy=xyn-xy<br />Sxy=1814.5918-(11.82)(8.905)<br />Sxy= -4.4729<br />Therefore:<br />y-8.906=-4.4729(3.33776)2 (x-11.822)<br />y-8.906= -0.4015(x-11.822)<br />y-8.906= -0.4015x+4.7465<br /> y= -0.4015x+13.6521<br />y= -0.4015x+13.6521 is the least squares regression formula for this particular set of data. As we see in the Graph 2, this data is exactly same as Graph 2.<br />Pearson’s Correlation Coefficient<br />Pearson’s correlation coefficient indicates measure the strength and direction of association. It is given by the following formula:<br />r=SxySxSy<br />r=-4.472901233.337756(1.498327107)<br />r=-0.894395<br />r2= -0.894395 which, according to the coefficient of determination chart on pg 581 of textbook, represents a “strong correlation”.<br />This graph displayed calculation of the least squares regression line.<br />Graph 2 indicates that there is a strong positive linear correlation. This is also indicated through the value of the correlation coefficient, -0.894395. <br />Chi-Square Test<br />The Chi-square test is the test we use to find if two classifications from the same sample are independent. The following formulas are used:<br />Observed Values:<br />B1B2TotalA1aba+bA2bdc+dTotala+bb+dN<br />Calculations of Expected Values:<br />B1B2TotalA1a+b(a+c)Na+b(b+d)Na+bA2a+c(c+d)Nb+d(c+d)Nc+dTotala+cb+dN<br />The χ2 test examines the difference between the observed and expected values<br />χ2=(Observed value fo-expected value fe2expected value <br />Null (Ho) Hypothesis: Human birth and death rates are independent<br />Alternative Hypothesis: Human birth and death rates are not independent. <br />Table 2: Observation Values<br />Human Death Rate<br />5-88.1-11Total5-121111212.1-19426Total51318<br />Table 2 shows the observed values for Human Birth Rate vs. Human Death Rate. <br />Table 3: Calculations for the Expected Values<br />Human Birth Rate<br />5-88.1-11Total5-125(12)1813(12)181212.1-195(6)1813(6)186Total 51318<br />Table 3 shows the individual calculations for each of the expected values.<br />Table 4: Expected Values<br />Human Birth Rate<br />5-88.1-11Total5-123.338.671212.1-191.674.336Total 51318<br />Table 4 shows the expected values, retrieved by the calculations in table 2.<br />Degrees of freedom measures the number of values in the calculation that can vary:<br />Df=(r-1)(c-1)<br />Df= (2-1)(2-1)<br /> = (1)(1)<br /> = 1<br />Table 5: Table of Critical Values<br />fofefo-fe(fo-fe)2(fo-fe)2fe13.33-2.335.42894.4289118.672.335.4289-5.571141.672.335.42891.428924.33-2.335.42893.7289Total4.0156<br />χ2=4.0156<br />Critical value at 5% significance level is 3.841. As the chi square value (4.0156) > than the critical value which is 3.841 so the null hypothesis is rejected and the human birth and death rate are dependent.<br />Discussion<br />Data Interpretation<br />For the beginning, the data is clearly shown about human birth rate and human death rate in 18 countries in order to show that different countries have different results about human birth and death rates. In Graph 1 is shown the dot point of human birth and death rate but in Graph 2 clearly shows the negative linear correlation, it appears to be very strong. This is supported by the value of r= -0.4015, which was calculated in Pearson’s Correlation Coefficient section. Thus, this data represents the human birth rate of 18 countries does not have much effect on the human death rate. <br />In addition, the standard deviation of x, which is human birth rate is 3.34 and also the standard deviation of y, which is human death rate is 1.498. These results show that human birth and death rate are low, that means there are almost no change. <br />Finally, the chi-square test demonstrates that as the critical value is less than the chi-square value because critical value at 5% significance level is 3.841% but chi square is value is 4.0156. Thus the null hypothesis is rejected and the alternative hypothesis, which states that the human birth rate and the human death rate are dependent. <br />Limitations<br />One large limitation of the data collected was old resources about the human birth rate and human death rate because this resource was published in 2007 so there was already 3 years were past. It means the human birth and death rate become change over 3 years because some countries economically better and some are not so it could be affect to the human birth and death rate too. <br />Major limitation to the human birth and death rate data are that there were 18 countries appear on the collected data but most of the countries are Europe, some Asia and United Sates but there are no Africa continent and South America continent so it is hard to define how this country is different than other countries. <br />For the limitation of the math part, the main one would be data of chi-square. There are not problem for the result of the chi square but for the observation value and expectation value are some differences and it is better to be close because observation value and expectation value are always related. <br />Conclusion<br />In this Internal Assessment, the main thing that I have to find is the relationship between Human Birth Rate and Human Death Rate. Basically, according to the data, there is a negative linear correlation between human birth and death rates. Furthermore, the standard deviation, least square regression and pearson’s correlation coefficient are also significant because these calculation relates to the graph. It can be concluded that there may in fact exist a dependent relationship between the human birth rate and the human death rate of 18 countries.<br />Work Cited<br />“Crude Birth and Death Rates for Selected Countries”. Infoplease. 2007. <http://www.infoplease.com/ipa/A0004395.html>.<br />“Birth rate figures for countries”. Wikipedia. 2008. <http://en.wikipedia.org/wiki/File:Birth_rate_figures_for_countries.PNG>.<br />“Death rate world map”. Wikipedia. March 31, 2006. <http://en.wikipedia.org/wiki/File:Death_rate_world_map.PNG>.<br />

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