IB Math Studies

1. Human Brain Development VS AgesIB Math Studies Internal AssessmentName: Siraphat (Ploy) PhataraprasitCourse: IB Math StudiesDate: December 2010School Name: International School of Bangkok (ISB)<br />Statement of Task:<br />As human grew older they’re brain cells tend to work slower. In this investigation I decided to prove that it is true that human whose age’s increases there speed of brain functioning will work slower. In order to prove this claim, the puzzle piece of equipment was given to 30 high school student of different ages from 15 to 19. Each of the students would solve the puzzle pieces within 20 second or less, and may only take it once anytime after math classes. The data that was taken will then be analyzed to show how the increase in ages affected the performance of the brain functioning in solving the puzzle.<br />Hypothesis:<br />As ages increases, the speed of brain functioning will work slower.<br />Measurements:<br />The ages of different students would be collected as well as the time they have using to solve the puzzle. The accuracy of time would be rounded into two decimal places to make sure that the answer is sufficient. The accuracy of time is important in order to know the differences between each of the participant brain development through ages. Moreover, the older the ages the more the brain work slower, so accuracy of the time is the only way of finding the differences. Therefore, data on different ages and time of people whose solve the puzzle will be collected as well as, Scatter Plot of the data, Median, Quartiles, Maximum and Minimum Values, Inter-quartile range, Outliers, Least Square Regression, Observed and Expected Value, and Chi-Square would be made. (Chi Square test is uses on the data to show the dependence of ages and brain development.)<br />Methodologies:<br />Investigation Methodology:<br />Find 30 high school students whose have math classes.<br />Create a data table with two column mark with; Ages and Time (per second.)<br />Explain how to solve the puzzle; time using the stop watch, and collected the data.<br />Puzzle pieces can only be done once per student!<br />Mathematical Investigation:<br />Collected Data:<br />Table 1: Ages and Time to solve puzzle for 30 students<br />#AgeTime (s)11514.1421514.1531613.5941614.0251614.4361614.4671614.5781617.1091713.59101713.59111714.31121714.39131714.41141714.42151714.43161714.43171714.45181714.46191714.46201714.59211716.38221814.39231815.01241815.24251815.26261815.31271815.56281914.57291915.03301916.38<br />This is the result of communicating and working with all 30 students in schools who took math classes right before taking the test. <br />Box of Whiskers Sample calculations: Age 17<br />Median: Number ordered from lowest to highest. N will be the number of terms in the series.<br />Formula: n + 12 13 + 12 142 7 = 14.43 seconds<br />Quartiles: numbers ordered form lowest to highest. N will be the number of terms in the series.<br />Q1 <br />Formula: n + 12 n = 7 7 + 12 82 4 = 14.39 seconds<br />Q3<br />Formula: n + 12 n = 7 7 + 12 82 4 = 14.46 seconds<br />Maximum and Minimum value: The number is founded from lowest and highest values of the series.<br />Maximum = 16.38 and Minimum = 13.59<br /> <br />Inter-quartile range: To find the inter-quartile range (IQR) both Q1 and Q3 have to be known first, then the first quartile is to be decreased from the third quartiles.<br />Equation Q3 – Q1 = IQR<br />Q1 = 14.39<br />Q3 = 14.46<br />14.46 – 14.39 = 0.07<br />IQR = 0.07<br />Box and Whisker plots Graph: Age 17<br />Minimum: 13.59 but an outlier<br />MQn: 14.31<br />Q1: 14.35<br />Q2: 14.43<br />Q3: 14.46<br />Max non Outlier: 14.59<br />Max Outlier 16.38<br />1313.2513.5013.751414.2514.5014.751515.16.4Time (s)<br />Because the outliers are so far away from Q1, Q2, and Q3, the box and whisker plot has to be hand draw.<br />Outliers<br />Q1 – (1.5 x IQR)<br />14.39 - (1.5 x 0.07)<br />14.39 – 0.105 = 14.285<br />Q3 + (1.5 x IQR) <br />14.46 + (1.5 x 0.07)<br />14.46 + 0.105 = 14.565<br />Data Table: The values calculated in parts 1-5<br />Age1516171819Q114.1414.0214.3915.0114.80Minimum14.1413.5913.5914.3914.57Median14.145 14.445 14.4315.2515.03Maximum14.1517.1016.3815.5616.38Q314.1514.5714.4615.3115.705IQR0.010.550.070.30.905Outlier Minimum14.12513.19514.28514.5613.4425Outlier Maximum14.16515.39514.56514.8617.0625<br />Least Square of Regression <br />y-y = SxySx2 (x- x) where Sxy = xyn - xy<br />Sxy = 7537.0230 - (17.067) x (14.704) <br />Sxy=0.2808 <br />Therefore:<br />y-14.704 = 0.28081.0622 (x- 17.067)<br />y-14.704 = 0.2644 (x- 17.067)<br />y-14.704 = 0.2644x – 4.5118 + 14.704<br />y=0.2644x+10.1922 <br />The least squared regression formula for this particular set of data is y=0.2644x+10.1922.<br />Null Hypothesis: The ages of solving the puzzle is independent of the speed of the brain development.<br />The table shows the frequency in both young and old age differences in the two puzzle completion time categories.<br />Age DifferencesYoung AgeOld Age1516171819Puzzle completion time10 – 15 seconds25126216 – 20 seconds01101Total261363<br />Observed Value<br />15 – 17 ages18 – 19 agesTotal10 – 152182916 – 20213Total23932Total30<br /> Expected Value<br />15 – 17 ages18 – 19 agesTotal10 – 1529(23)32 = 20.8429(9)32 = 8.162916 – 2023(3)32 = 2.169(3)32 = 0.843Total23932Total30<br />Chi-Squared:<br />x2= (fo-fe)2fe <br />fofefo- fe(fo-fe)2(fo-fe)2/fe2120.80.20.040.001923076988.2-0.20.040.004878048822.2-0.20.040.018181818210.80.20.040.05Total: 0.749829439<br />Therefore x2=0.75<br />Degree of Freedom = 2<br />Validity:<br />Throughout the processes of collecting the data there was a lot of amount of concern in it. <br />During the collecting of the data:<br />Explaining how to work on collecting the data was really tough. Because of some second language or others student communication with me was kind of hard to understand.<br />Student always come in a group so after asking one of the student to do the next one then know already what to do and have already seen the puzzle being solve so it is easy for them to work it out.<br />Students has lots of different mood and there tiredness, so most of the student brain may work slowly. Some may be lack of sleep, some may have such a quick understanding and done it very fast. <br />Conclusion:<br /> The main conclusion in this investigation was met and confirming that the ages and brain speed development is independent to each other. The chi-squared test has classify the result as stated that it is 0.75 non-significant because the degree of freedom is two and was in the ranges of independent not dependent to each other, therefore the answer was confirm and the hypothesis was met. So the speed of solving the puzzle is independent with the ages no matter what. <br />