1. IB Math Studies Standard Level Internal Assessment:<br />Literacy Rate and Population<br />Paige Carmichael<br />International School Bangkok<br />November 2010<br />IB Math Studies SL<br />Introduction<br />As Proverb once said, “In teaching others we teach ourselves” and by doing so, we may educate not only ourselves but also the world as a whole. In researching the correlation between the literacy rates of the top 20 countries by population, one would be able to determine the emphasis and availability of a good, solid education system. The investigation I am working on is directed to prove that as the population of a country increases, as does the literacy rate. To fairly evaluate the statistical analysis, I figured it would be best to start by making data tables of the top 20 countries by population and their literacy rates. To put the data into a different perspective, I also created a line and a bar graph to reiterate the visual correlation between the two sets of data. Finally, to further prove a possible correlation, I used scatter plots. The data collected was analyzed to show how the country’s populations are compared to the percent of literacy. <br />Hypothesis<br />As the population increases, the literacy rate will also increase.<br />The Measurements<br />The measurements will be taken from the official CIA website, which is highly accredited for the type of data that I am collecting. I will be collecting the literacy rates of the top 20 countries as ranked by population to determine the correlation between the two sets of data.<br />Mathematical Investigation:<br />Data Table:<br />PopulationLiteracy Rate1) China1,330,141,29583) 93.32) India1,173,108,018149) 66.03) United States310,232,86321) 99.04) Indonesia242,968,34288) 92.05) Brazil201,103,33098) 90.06) Pakistan184,404,791163) 54.27) Bangladesh156,118,464164) 53.58) Nigeria152,217,341139) 72.09) Russia139,390,20512) 99.510) Japan126,804,43321) 99.011) Mexico112,468,85585) 92.812) Philippines99,900,17781) 93.413) Vietnam89,571,13097) 90.314) Ethiopia88,013,491175) 35.915) Germany82,282,98821) 99.016) Egypt80,471,869148) 66.417) Turkey77,804,122105) 88.718) Iran76,923,300121) 82.319) Democratic Republic of the Congo70,916,439125) 81.120) Thailand67,089,50079) 94.1<br />(The numbers next to the literacy rate is the world rank of the country according by literacy rate)<br />With this data, I created both bar and line graphs to visually represent the data listed above in the table. I chose to separate the top ten from the bottom ten because of the space that all 20 countries took up and it was easier to read and analyze the data when there are fewer variables on the x-axis. This data will then be interpreted using the chi-squared method which will be explained below using the chart, calculator and equation format of determining the correlation between the two sets of data.<br />Line Graph:<br />Graph 1: Population of the top 10 countries in the world<br />Graph 2: Literacy rate of the top 10 most highly populated countries in the world<br />51435-454660<br />Graph 3: Population of the second 10 most highly populated countries in the world<br />Graph 4: Literacy rate of the second 10 most highly populated countries in the world<br />Bar Graph: <br />Literacy Rate vs. Population<br />-29210054610<br />534035120015<br />-29210097790428053531750<br />Graphs 5-6: To show the correlation between Literacy Rate and Population of the top 20 countries by population<br />Scatterplot<br />279400362585Literacy Rate vs. Population<br />177800396875<br />178435420370<br />Graph 7: The correlation between population and literacy rate can be seen by using a scatter plot of the original data<br />Interpretation of Results<br />Throughout the investigation, it can be inferred that there is no correlation between the population of a country and it’s literacy rate. The data graphs clearly show that just because whether a population is high or low, that does not determine how literate that the country is. Seeing as that it can by hypothesized that a country that is large would have a high literacy rate, they would correlate. This is not the case in this investigation. For all of the graphs showing population, it is a steady decrease as the population decreases, but the literacy graphs are all scattered and are not able to follow or do not correlate with the population graphs. <br />Validity<br />Seeing as there can be uncertainties in the data recorded, there is very little room for error when dealing with these certain subjects. These statistics were found on the official CIA website which is also valid, official information. Secondly, it was hard to comprehend how to compare graphs when the numbers are so drastically different, so, when creating the graphs, and uncertainty can be the even to uneven ratio of the numbers listed on the graphs used to compare the two sets of data.<br />Conclusion<br />In conclusion, the goal of this Internal Assessment was to investigate the correlation of the literacy rate of the top 20 countries by population. Through the use of bar graphs, scatter plots and line graphs, it can be seen that the re is no correlation between the two sets of data, therefore proving the hypothesis to be wrong. <br />