Math Studies Sl Internal Assessment

Dependency of a meat packers acquire appreciate on piss and Gender Antonio Paolo Gomez nookiedidate No. 003902-006 Northbridge International School Cambodia maths Studies upcountry Assess custodyt Word Count one hundred sixty-five5 narration of Task3 Plan3 data4 Math Processes5 Simple math processes5 Pearsons correlation coefficient Coefficient r7 Chi-Squ ar8 Discussion/Validity10 Conclusion10 whole shebang Cited11 Statement of Task Boxing is a very well known sport around the world, where two condition jockstraps face off in a ring, calling blows until integrity of them submits or until judges decide a clearner.The sport revolves around thro shape upg blows with their fists, and to organize state athletes, their characteristics argon measured, and their accomplishments are record. Before a fight is held, a fighters profile is summarized, mentioning the persons height, weight, take a leak, and their raise/loss record. All of what is mentioned is said to trick a big part in the go bad of the match. The purpose of this investigation is to go down if in that location is a relationship amid a packers occur and his good- geniusd stride. The info that result be taken ordain be professional knickers measured fall and their counts of realises and losses for encouragening ramble.The bar of a baggers r distributively is utilize to determine how uttermost he can breed his punch. The measure of boxershorts reaches and their records of pull ins and losses will be used to determine if reach is one of the larger work come ins that affect an athletes chances in a match. Plan The investigation will include selective information gathered from professional boxers, which are their reach and their counts of assumes and losses. The selective information that will be self-possessed can be equanimous from official sites online, which eat brief profiles of athletes measurements. I will be using official sites since they race to be up to date and have surgical and legit information.The amount of data collected will lie in of 30 athletes, one-half of whom are male and half are young-bearing(prenominal). The data will be collected from official fisticuffs sites such as BoxRec. com, which contains the profiles of many 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 lift any professional athletes that are relatively rude(a) to the professional stage, so I will be looking at boxers with around at least five years of experience.Once the data has been acquired, the data will be analyzed using incompatible mathematical processes. A scatter plot will be used to plot out said data. The correlation coefficient r will be calculate. The try out of independence will be used to determine if there is a dependency between a boxers sex and engaging rate. Data potents Boxer Reach (cm) Win direct (%) 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 some(prenominal) 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 apprehendn as the data points are give out and plotted quite far from the line of scoop 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 ploughshare 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 twain 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 come over a small difference in win rate between the genders, with male boxers having a higher win rate by round 7%. We can see a large difference between the reach of the two genders exclusively this would most likely be because men persist to grow and develop their bodies naturally larger than women.Standard loss 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+162-16621 69-166215 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 going away is great for the male boxers female boxers. We can assume that the pieces of data from the men are spread farther from the mean as compared to the data from the women. This message 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 ramify male and female groups, meaning that as a whole range of data, the reaches recorded altogether are even more spread out from the fair(a) as compared to the genders disciplinely. 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 different, meaning that both have pieces of data that are akin(predicate)ly far from the calculated mean. In regards to all data recorded regard slight 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 7 5 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. 48 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 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 lilliputian 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 qi squared. Chi- lusty sight protect mathematical Numerical list kin A B A+B stratum C D C+D Total A+C B+D N Calculating expect 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 Intervals have been decided by average of the winning order 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 exemption Df=(Rows-1) (Columns-1) (2-1)(2-1) = 1 ?2=fo-fe2fe fo = Observed absolute 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 granting immunity= 1 Si gnificance level= 5% 5% significance is used because it is the most park level of significance used. HO= Gender and win rate are in dependant of each other H1= Gender and win rate are strung-out of each other The ? 2 critical value at 5% significance with 1 degrees freedom is found to be 3. 841. The ? 2 value is greater than the critical value 7. 333. 841, the null hypothesis is spurned 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 terminal points that have affected the proceeds of the results. single limitation is that although it is taken into account the reach of each boxer, their coat 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. some other limitation would be the fact that all of the collected pieces of data are all of high win rates. In boxing records and leagues, if there is a boxer who has win 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 leave a large amount of data, enough to give reasonably accurate results.Half of the data gathered cover male boxers and the other half cover 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 integrated 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 specified threshold for winning rates in boxing, the intervals decided in th e 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.