Math Studies Sl Internal Assessment

Dependency of a Boxers draw graze on R distributively and Gender Antonio Paolo Gomez Candidate No. 003902-006 Northbridge International naturalize Cambodia Math Studies Internal Assessment Word Count wholeness hundred sixty-five5 Statement of Task3 Plan3 Data4 Math Processes5 Simple math processes5 Pearsons Correlation Coefficient r7 Chi-Squ be8 discussion/Validity10 Conclusion10 Works Cited11 Statement of Task Boxing is a truly well known sport around the world, where two disciplined athletes face off in a ring, trading blows until one of them submits or until judges decide a winner.The sport revolves around throwing blows with their fists, and to organize said athletes, their characteristics atomic number 18 measured, and their accomplishments be recorded. Before a fight is held, a fighters profile is summarized, mentioning the persons height, weight, produce, and their win/loss record. All of what is mentioned is said to play a freehand give out in the flow of the mat ch. The purpose of this investigation is to determine if in that location is a relationship between a pugilists delve and his winning rate. The information that will be taken will be professional boxers measured clear up and their counts of wins and losses for winning rate.The measurement of a boxers reach is used to determine how far he can extend his punch. The measure of boxers reaches and their records of wins and losses will be used to determine if reach is one of the larger factors that affect an athletes chances in a match. Plan The investigation will include data ga at that placed from professional boxers, which are their reach and their counts of wins and losses. The data that will be dispassionate can be collected from official sites online, which have brief profiles of athletes measurements. I will be apply official sites since they tend to be up to date and have accurate and legit information.The amount of data collected will consist of 30 athletes, half of whom a re male and half are female. The data will be collected from official boxing sites such as BoxRec. com, which contains the profiles of numerous official boxers and their measurements, which includes their reach and wins and losses. The data for one athlete will consist of his reach and his win/loss record. I will attempt to avoid any professional athletes that are relatively new to the professional stage, so I will be looking at boxers with around at least five eld of experience.Once the data has been acquired, the data will be analyzed using different mathematical processes. A scatter dapple will be used to dapple out said data. The correlation coefficient r will be calculated. The test of independence will be used to determine if there is a addiction between a boxers sex and winning rate. Data Males Boxer dawn (cm) Win calculate (%) 1 170 90. 00 2 173 96. 77 3 183 96. 88 4 194 88. 57 5 183 87. 88 6 207 92. 31 7 177 94. 29 8 183 72. 34 9 201 100. 00 10 198 95. 24 11 198 80 . 77 2 179 86. 21 13 179 89. 29 14 183 87. 88 15 180 89. 66 Females Boxer Reach (cm) Win Rate (%) 1 165 89. 47 2 161 86. 67 3 167 66. 04 4 166 75. 00 5 162 81. 25 6 168 93. 33 7 163 76. 47 8 162 75. 00 9 159 88. 46 10 167 86. 21 11 176 80. 95 12 171 83. 87 13 168 82. 61 14 166 78. 95 15 169 90. 48 From the scatter plot using both male and female sets of data, we can predict that the calculated correlation would be weak and that a boxers win rate weakly correlates with his/her reach.This can be recognizen as the data points are spread and plotted quite far from the line of best fit. Math Processes Simple math processes Average Males * Reach in centimeters 170+173+183+194+183+207+177+183+201+198+198+179+179+183+180=2788 2788/15= 185. 8666667 cm * Win rate in percentage 90. 00+96. 77+96. 88+88. 57+87. 88+92. 31+94. 29+72. 34+100+95. 24+80. 77+86. 21+89. 29+87. 88+89. 66= 1348. 09 1348. 09/15= 89. 87% Average Females * Reach in centimeters 165+161+167+166+162+168+163+162+159+167+176+ 171+168+166+169= 2490 2490/15= 166 cm * Win rate in percentage 89. 7+86. 67+66. 04+75+81. 25+93. 33+76. 47+75+88. 46+86. 21+80. 95+83. 87+82. 61+78. 95+90. 48=1234. 76 1234. 76/15=82. 32 Average both genders * Reach in centimeters 2788+2490=5278 5278/30=175. 93 cm * Win rate in percentage 1348. 09+1234. 76= 2582. 85 2582. 85/30= 86. 095% We can see a small contrariety in win rate between the genders, with male boxers having a higher win rate by about 7%. We can see a bigger difference between the reach of the two genders but this would most likely be because men tend to grow and develop their bodies course larger than women.Standard passing Reach Males Sx=170-185. 872+173-185. 872+183-185. 872+194-185. 872180-185. 87215 Sx=10. 626 Females Sx=165-1662+161-1662+167-1662+166-1662+162-1662169-166215 Sx=4. 163 Both Genders Sx=170-175. 932+173-175. 932+183-175. 932+194-175. 932169-175. 93230 Sx=12. 798 We are able to see that the standard deflection is greater for the male boxers femal e boxers. We can arrogate that the pieces of data from the men are spread farther from the mean as compared to the data from the women. This means that in regards to the data collected, female boxers seem to be closer n their measured reach as compared to the males. The standard deviation for both groups surpasses the calculated standard deviation for the separate male and female groups, pith that as a whole range of data, the reaches recorded altogether are even more spread out from the comely as compared to the genders separately. Standard Deviation Win rate Males Sx=90-89. 872+96. 77-89. 872+96. 88-89. 872+88. 57-89. 87289. 66-89. 87215 Sx=6. 67 Females Sx=89. 47-82. 322+86. 67-82. 322+66. 04-82. 322+75-82. 32290. 48-82. 32215 Sx=6. 995 Both Genders Sy=90. 00-86. 0952+96. 7-86. 0952+96. 88-86. 0952+88. 57-86. 095290. 48-86. 095230 Sy = 7. 8087 We can see from the calculated standard deviations that the standard deviation for the win rate of males and females are close to each separate, meaning that both have pieces of data that are connaturally far from the calculated mean. In regards to all data recorded regardless of gender, the standard deviation is found to be slightly higher, meaning that the pieces of data for both genders are slightly farther from the mean as compared to the separate gender groups of data. Subject Reach Win Rate xy 170 90 15300 2 173 96. 77 16741. 21 3 183 96. 88 17729. 04 4 194 88. 57 17182. 58 5 183 87. 88 16082. 04 6 207 92. 31 19108. 17 7 177 94. 29 16689. 33 8 183 72. 34 13238. 22 9 201 100 20100 10 198 95. 24 18857. 52 11 198 80. 77 15992. 46 12 179 86. 21 15431. 59 13 179 89. 29 15982. 91 14 183 87. 88 16082. 04 15 180 89. 66 16138. 8 16 165 89. 47 14762. 55 17 161 86. 67 13953. 87 18 167 66. 04 11028. 68 19 166 75 12450 20 162 81. 25 13162. 5 21 168 93. 33 15679. 44 22 163 76. 47 12464. 1 23 162 75 12150 24 159 88. 46 14065. 14 25 167 86. 21 14397. 07 26 176 80. 95 14247. 2 27 171 83. 87 14341. 77 28 168 82. 61 13878. 4 8 29 166 78. 95 13105. 7 30 169 90. 48 15291. 12 sum 5278 2582. 85 455634 average 175. 9333 86. 1 15187. 8 Pearsons Correlation Coefficient r Covariance x-x(y-y)n or xyn-x y x=175. 93 y=86. 095 xy=455634. 04 455634. 0430=15187. 80133 15187. 80133-175. 9386. 095=41. 10789 Correlation r=SxySxSy Sxy=41. 10789 Sx=12. 798 Sy=7. 8087 41. 1078912. 798(7. 8087)=. 411344119 r=. 411344119 r2=. 1692039842Correlation coefficient r is calculated to be very weak, meaning that reach and win rate show very little correlation and that a boxers reach is not a big factor of his or her chances of victory. With low correlation between a boxers reach and win rate, I will now see if gender is a factor of an athletes win rate by calculating chi squared. Chi-Square Observed Values Numerical Numerical Total sept A B A+B Category C D C+D Total A+C B+D N Calculating Expected Values Numerical Numerical Total Category (A+B)(A+C)/30 (A+B)(B+D)/30 A+B Category (C+D)(A+C)/30 (C+D)(B+D)/30 C+DTotal A+C B+D N Int ervals have been decided by average of the winning rates of the two genders. (82. 32+89. 87)/2=86. 095 Observed Data Values Win rate 86% Win rate ? 86% Total Male 2 13 15 Female 9 6 15 Total 11 19 30 Calculated Expected Data Values Win rate 86% Win rate ? 86% Total Male 5. 5 9. 5 15 Female 5. 5 9. 5 15 Total 11 19 30 Degrees of Freedom Df=(Rows-1) (Columns-1) (2-1)(2-1) = 1 ?2=fo-fe2fe fo = Observed Frequency fe = Expected Frequency ?2=1-323+7-7. 527. 5+7-4. 524. 5+5-323+8-7. 527. 5+2-4. 524. 5 Chi Square Value Table o fe fo-fe (fe-fe)2 (fo-fe)2/fe 2 5. 5 3. 5 12. 25 2. 227272727 13 9. 5 -3. 5 12. 25 1. 289473684 9 5. 5 -3. 5 12. 25 2. 227272727 6 9. 5 3. 5 12. 25 1. 289473684 sum 7. 033492823 ?2= 7. 033 Degrees of freedom= 1 meaning level= 5% 5% importee is used because it is the most common level of significance used. HO= Gender and win rate are fissiparous of each other H1= Gender and win rate are dependent of each other The ? 2 critical value at 5% significance with 1 d egrees freedom is found to be 3. 841. The ? 2 value is greater than the critical value 7. 333. 841, the null hypothesis is rejected and it can therefore be assumed that a boxers win rate is dependent of his or her gender. Discussion/Validity The investigation carried out to observe the correlation of Win rate and reach and win rate and gender has a few limitations that have affected the outcome of the results. One limitation is that although it is taken into account the reach of each boxer, their size and weight places them in different classes for professional fights. This means that fighters would normally be fighting people that have similar size, and theoretically, similar reach.With similar reach between two fighting boxers, the outcome of an athletes history of fights really could have been affected by other factors such as tactics and strength. Another limitation would be the fact that all of the collected pieces of data are all of high win rates. In boxing records and league s, if there is a boxer who has won 90% of his matches, there should also be a boxer who has lost that many of his matches as well. The collected data covers 30 pieces. This is done to supply a large amount of data, enough to give reasonably accurate results.Half of the data gathered covered male boxers and the other half covered female for the purpose of investigating the dependency of win rate on gender with chi squared. One limitation in regards to the genders, is that there is no co-ed boxing, meaning that females and males do not compete with each other and are separated into two genders for boxing matches. Although there is no condition threshold for winning rates in boxing, the intervals decided in the chi squared tables can be justified as the below and above averages for the average win rates of the two genders.Conclusion The found ? 2 value of 7. 033 rejects the null hypothesis, that Win rate for boxers is independent of their gender and accepts the alternative hypothesis, that a boxers win rate is dependent of a boxers gender. The extent of this calculation is affected by the nature of the data collected. The data that was collected for males and females consisted of high win rate percentages, and in boxing, when there is an individual who has won 70% of his matches, there is sure to be an athlete who has lost 70% of his matches as well.The investigation shows that there is a very low correlation between reaches and win rate for boxers regardless of their gender. This outcome could have been affected because of one of the mentioned limitations above, where boxers of similar size and weight are placed in the same class and fight, so reach becomes less of a factor for victory as compared to strength, speed, and tactics. Works Cited Boxrec Boxing Records Ratings. 4 November 2012 . Boxrec. Boxrec Boxing Records.