Caribbean Examinations Council Secondary Education Certificate School Based Assessment Additional Math Project

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1 Caribbea Examiatios Coucil Secodary Educatio Certificate School Based Assessmet Additioal Math Project Does good physical health ad fitess, as idicated by Body Mass Idex, affect the academic performace of teeagers? Name of Cadidate: Shary Gittes Name of cetre: Harriso College Cetre Number: Year of Examiatio: 2016 Registratio Number:

2 Table of Cotets Purpose of Project..3 Method of Collectio 4 Presetatio of Data.5 Mathematical Kowledge/ Aalysis of Data..16 Discussio 29 Coclusio..30 Appedix..31 Bibliography..32 2

3 Purpose of Project Academic performace is the outcome of beig educated the extet to which a teacher, studet or istitutio has achieved their academic goals. This is usually measured i the form of assessmets. The study of Mathematics ot oly eables a perso to be a great accoutat or actuary, but learig it forces a studet to thik logically ad to solve problems usig the skill. Mathematics also is ot just simple regurgitatio, but a commo strategy is used to solve may differet problems, which therefore helps i life experieces. Takig Eglish as a subject eables the studets to lear the rules of grammar, puctuatio ad spellig, as well as eablig them to costruct a setece ad proouce words correctly. A good grasp of these priciples ehaces commuicatio skills ad improves your overall presetatio, as your writte laguage ad speech would be up to par. Body Mass Idex (BMI) is the measure of relative size based o the height ad mass of a perso. BMI is used as a screeig tool to determie whether a perso i uderweight, healthy, overweight or obese. If someoe s BMI is out of the healthy rage, they are at risk of health crises. A study carried out by Kayla Naticchioo of Joh Carroll Uiversity titled The Relatio betwee Obesity ad Academic Achievemet of School-age Childre showed that there was a lik betwee utritio ad weight i childhood ad academic achievemet. Her research showed that studets with poor utritio performed poorly i the classroom. The purpose of this project is to examie the relatioship betwee the health status of adolescets ad their academic performace i Eglish Literature ad Mathematics. The variables beig cosidered are 1) the health status of the studets as idicated by Body Mass Idex (Healthy (ormal BMI) ad Uhealthy (uderweight, overweight ad obese BMI)) 2) academic performace i two selected subjects (Mathematics ad Eglish Literature) 3) Geder (Male or Female) 3

4 Method of Collectio Forty studets i the fifth form year (20 girls ad 20 boys) were asked if they were willig to cotribute their weights ad heights to my Additioal Mathematics School-Based Assessmet. Those who coseted were weighed. The studets who were weighed were asked to remove their shoes ad ay articles from their pockets. Thereafter, their height was recorded usig a measurig tape. Each studet was asked to stad vertically agaist a wall ad the level at the very top of his/her skull was marked horizotally o the wall. The height was the distace betwee the groud ad the horizotal mark o the wall. The weight was recorded i pouds (lbs) ad height was recorded i iches. I order to calculate the BMI (Body Mass Idex) oe of the two followig equatios ca be applied: BMI = Weight (Kg) Height 2 (m 2 ) BMI = 703 Weight (lbs) Height 2 (ich 2 ) The latter equatio was applied. With the studets coset, their Eglish ad Mathematics marks attaied i the respective exams, which were give to them at the ed of the fourth year (promotioal exams), were provided ad used as a represetatio of their academic performace. The privacy of the studets were maitaied, therefore, o ames are listed. 4

5 Presetatio of Data Geder Weight (lbs) Height Height²(iches²) BMI State of Studet Eglish (%) Math(%) (iches) M Healthy M Healthy M Healthy F Obese F Healthy M Healthy M Overweight M Uderweight F Overweight M Overweight F Uderweight F Obese M Overweight M Healthy M Healthy M Healthy F Uderweight F Healthy M Healthy F Healthy F Overweight F Healthy F Healthy M Healthy F Obese F Healthy M Healthy M Overweight F Healthy F Healthy F Obese M Healthy F Healthy M Healthy M Healthy M Uderweight F Healthy M Healthy F Healthy F Healthy Table 1: Table Showig the BMI Results ad 2015 Mathematics ad Eglish Literature promotio marks (%) of 20 males ad 20 females. 5

6 Uderweight Healthy Overweight Obese 10% 10% 15% 65% Figure 1: A Pie Chart Showig the BMI Results of all of the Studets 6

7 20% 10% 70% Uderweight Healthy Overweight Figure 3: A Pie Chart Showig the BMI Results of the Male Studets 20% 10% 10% 60% Uderweight Healthy Overweight Obese Figure 4: A Pie Chart Showig the BMI Results of the Female Studets 7

8 40.0% % 50.0% % 60.0% % 70.0% % 80.0% % M A L E S T U D E N T S 2 1 F E M A L E S T U D E N T S Figure 5: A Stacked Colum Chart Comparig the Eglish marks of the Male Studets ad the Female Studets Stem Leaf Figure 6: A stem ad leaf diagram showig the overall Eglish marks for the males Stem Leaf Key: meas 55.6 Figure 7: A stem ad leaf diagram showig the overall Eglish marks for the females 8

9 20.0%-29.9% 30.0%-39.9% 40.0%-49.9% 50.0%-59.9% 60.0%-69.9% 70.0%-79.9% 80.0%-89.9% 90.0%-99.9% M A L E S T U D E N T S F E M A L E S T U D E N T S Figure 8: A stacked colum chart comparig the overall Math marks of the male ad female studets Stem Leaf Key: meas 86.7 Figure 9: A stem ad leaf diagram showig the Math marks of the male studets 9

10 Stem Leaf Key: meas 56.7 Figure 10: A stem ad leaf diagram showig the overall math marks of the female studets Healthy Males Uhealthy Males 60.0% % 70.0% % 80.0% % Figure 11: A bar chart showig the distributio of Eglish marks for Healthy ad Uhealthy males. 10

11 Number of Studets Stem Leaf Key meas 78.7 Figure 12: A stem ad leaf diagram showig the Eglish marks of the healthy males Stem Leaf Key meas 68.2 Figure 13: A stem ad leaf diagram showig the Eglish marks of the uhealthy males Healthy Males State of Males Uhealthy Males 30.0% % 40.0% % 50.0% % 60.0% % 70.0% % 80.0% % 90.0% % Figure 14: A Bark Chart Comparig the Math marks of healthy males ad uhealthy males 11

12 Stem Leaf Key meas 54.3 Figure 15: A stem ad leaf diagram showig the Math marks of the Healthy Males Stem Leaf Key meas 44.6 Figure 16: A stem ad leaf diagram showig the Math marks of the uhealthy males 12

13 State of Females Healthy Females Uhealthy Females Number of Studets 80.0% % 70.0% % 60.0% % 50.0% % 40.0% % Figure 17: A Bar Chart comparig the Eglish marks of the healthy females ad uhealthy females Stem Leaf Key meas Figure 18: A stem ad leaf diagram showig the Eglish marks of the Healthy Females Stem Leaf Key meas 88.9 Figure 19: A stem ad leaf diagram showig the Eglish marks of the Uhealthy Females 13

14 State of Females Healthy Females Uhealthy Females Number of Studets 90.0% % 80.0% % 70.0% % 60.0% % 50.0% % 40.0% % 30.0% % 20.0% % Figure 20: A bar chart comparig the Math marks of the healthy females ad the uhealthy females Stem Leaf Key meas 47.8 Figure 21: A stem ad leaf diagram showig the Math marks of the Healthy Females 14

15 Stem Leaf Key meas 76.5 Figure 22: A stem ad leaf diagram showig the Math marks of the Uhealthy Females 15

16 Mathematical Kowledge/Aalysis of Data: The followig eight (8) groups were cosidered: o ENGLISH Males (healthy) o ENGLISH Males (uhealthy) o ENGLISH Females (healthy) o ENGLISH Females (uhealthy) o MATH Males (healthy) o MATH Males (uhealthy) o MATH Females (healthy) o Math Females (uhealthy) A box-ad-whisker chart was plotted for each group, showig the lowest promotioal mark, the highest promotioal mark, the media mark, the lower quartile ad the upper quartile respectively. The media value (Q₂) is the value that divides the data ito two equal groups. It occurs i the ( +1 2 )th positio, where = the umber of values i the group. Whe this positio is ot a whole umber, the media i the mea of the mark immediately before the determied positio ad the oe immediately after it. The lower quartile (Q₁) is the media of the lower half of the data. It occurs i the ( +1 4 )th positio, where is the umber of values (studets) i the group. As with the media, whe this positio is ot a whole umber, the mea of the mark immediately before it ad the mark immediately after is foud to determie the lower quartile. The upper quartile (Q₃) is the media of the upper half of the data, occurrig i the 3 ( +1 4 )th positio, where is the umber of values (studets) i the group. The same rules for the lower quartile ad the media apply to this, i terms of the positio ot beig a whole umber. The iterquartile rage is the differece betwee the upper quartile ad the lower quartile i.e. Q₃ - Q₂. Figures show the box-ad-whisker plots for the eight (8) groups beig cosidered. 16

17 Figure 23: A box-ad-whisker plot showig the Eglish marks of healthy ad uhealthy males Figure 24: A box-ad-whisker plot showig the Eglish marks of healthy ad uhealthy females 17

18 Figure 25: A box-ad-whisker plot showig the Mathematics mark of healthy males ad uhealthy males Figure 26: A box-ad-whisker plot showig the Mathematics marks of healthy females ad uhealthy females 18

19 The mea ad stadard deviatio for each of the eight specified groups were calculated. The formulas used were: mea = X i stadard deviatio = (X i mea) 2 X i represets the sum of all the marks for a specified group. represets the umber of studets i a specified group. Tables 3, 4, 5, 6, 7, 8, 9 ad 10 show the results of these calculatios for the eight specified groups beig cosidered. N.B.= d.p. = decimal places The statistics for the eight specified groups are summarized i Table

20 χ (χ mea) (χ mea)² Σ Number of studets 14 Mea x = Σx i Mea= = ( 4 d.p.) Stadard deviatio σ = Σ(x mea)2 Stadard deviatio= = To 2 d.p.= 7.22 Table2: A table showig the calculatio of the mea ad stadard deviatio of a set of marks obtaied by healthy males i Eglish 20

21 χ (χ mea) (χ mea)² Σ Number of studets 6 Mea x = Σx i Mea = = Stadard deviatio = σ = Σ(x mea)2 Stadard deviatio= = To 2 d.p. = 5.57 Table 3: A table showig the calculatio of the mea ad stadard deviatio of a set of marks obtaied by uhealthy males i Eglish 21

22 χ (χ mea) (χ mea)² Σ Number of studets 12 Mea x = Σx i Mea = = Stadard Deviatio σ = Σ(x mea)2 Stadard Deviatio= = To 2 d.p. = Table 4: A table showig the calculatio of the mea ad stadard deviatio of a set of marks obtaied by healthy females i Eglish 22

23 χ (χ mea) (χ mea)² Σ Number of studets 8 Mea x = Σx i Mea = = Stadard Deviatio σ = Σ(x mea)2 Stadard Deviatio = To 2 d.p. = 7.26 Table 5: A table showig the calculatio of the mea ad stadard deviatio of a set of marks obtaied by uhealthy females i Eglish. 23

24 χ (χ mea) (χ mea)² Σ Number of studets 14 Mea x = Σx i Mea = = (4 d.p.) Stadard Deviatio σ = Σ(x mea)2 Stadard Deviatio = = To 2 d.p. = Table 6: A table showig the calculatio of the mea ad stadard deviatio of a set of marks obtaied by healthy males i Mathematics 24

25 χ (χ mea) (χ mea)² Σ Number of studets 6 Mea x = Σx i Mea = = 58.3 Stadard Deviatio σ = Σ(x mea)2 Stadard Deviatio = = To 2 d.p. = Table 7: A table showig the calculatio of the mea ad stadard deviatio of a set of marks obtaied by uhealthy males i Mathematics 25

26 χ (χ mea) (χ mea)² Σ Number of Studets 12 Mea x = Σx i Mea = = ( 4 d.p.) Stadard Deviatio σ = Σ(x mea)2 Stadard Deviatio = = To 2 d.p. = Table 8: A table showig the calculatio of the mea ad stadard deviatio of a set of marks obtaied by healthy females i Mathematics 26

27 χ (χ mea) (χ mea)² Σ Number of studets 8 Mea x = Σx i Mea= = Stadard Deviatio σ = Σ(x mea)2 Stadard Deviatio= = To 2 d.p. = Table 9: A table showig the calculatio of the mea ad stadard deviatio of a set of marks obtaied by uhealthy females i Mathematics 27

28 Eglish Math Males Females Males Females healthy uhealthy healthy uhealthy healthy uhealthy healthy uhealthy N Lowest Score (%) Highest Score (%) Media Iterquartile Rage Mea ( d.p.) Stadard Deviatio ( 2 d.p. ) % passes 100% 100% 91.6 % 100% 85.7% % % 62.5% Table 10: A summary of the statistical results for the eight specified groups of fifth formers 28

29 Discussio: With referece to Table 10 o the previous page ad careful examiatio of the figures, clear comparisos ca be made. It was observed that healthy males achieved higher mea marks i Mathematics ad Eglish tha healthy females. However, uhealthy females attaied higher mea marks tha uhealthy males i both Eglish ad Mathematics. The highest mea mark was calculated by the marks of females ad the lowest mea mark was calculated by the marks of males. Geerally, from the data, it ca be cocluded that females, whether healthy or uhealthy, did better tha all males. Healthy idividuals seemed to have doe better tha uhealthy idividuals, with the exceptio of the females i the Eglish exam. The highest media calculated from the data collected was from uhealthy females i Eglish ad the lowest media was calculated from the marks of uhealthy males i Mathematics. Females did better tha the males i terms of media marks. Healthy idividuals also seemed to have doe better i this area, with the exceptio of uhealthy females who surpassed healthy females. The highest iter-quartile rage was calculated from the marks obtai from uhealthy males i the Mathematics ad the lowest was calculated from uhealthy females i Eglish. Whe calculated, the iter-quartile rages for the healthy studets were higher tha those of uhealthy studets for both Mathematics ad Eglish, with the exceptio of the males who did Mathematics; the iter-quartile rage of the uhealthy males was higher tha that of the healthy males. This shows the level of variatio betwee the middle rage (the values from Q₁ to Q₃) The highest stadard deviatio was calculated from the marks of the uhealthy females i Mathematics whereas, the lowest stadard deviatio was calculated from the marks of the uhealthy males i Eglish. The stadard deviatios of the uhealthy participats were lower tha those of the healthy participats. However, for Mathematics, the stadard deviatio of the healthy participats were lower tha those of the uhealthy participats. The highest overall score was achieved by a healthy female i Mathematics ad the lowest overall score was attaied by a uhealthy female. With respect to the passes see i the lowest scores category, 33.3% of the passes was attaied by a healthy idividual ad 66.7% was attaied by uhealthy idividual. 60% of the lowest scores that were ot passes were attaied by healthy studets ad 40% by uhealthy studets. All males (uhealthy ad healthy) passed the Eglish examiatio. The majority of the females passed the Eglish exam, however, those who failed the exam were healthy. I Mathematics, the umber of passes of the healthy studets were higher tha the umber of passes of the uhealthy studets. 29

30 Coclusio: The aim of this expressio was to determie whether or ot BMI is liked to academic performace. Takig ito cosideratio the results of the studets, bar charts, pie charts ad stem ad leaf diagrams were created. The data was also used to create box-ad-whisker plots ad to calculate the mea ad stadard deviatio of the marks. With referece to the results, it ca be cocluded that BMI does, i some cases, ifluece a perso s academic performace. All results prove this, with the exceptio of the females, i terms of the Eglish examiatio. It was therefore determied healthy studets have better problem solvig skills tha uhealthy studets have. However, the chage of tred appears with the uhealthy females, as they appear to have a better uderstadig of their laguage ad its usage i compariso to healthy females. Despite that, healthy males did better i Eglish tha uhealthy males A limitatio experieced i this project was that studets may have eate immediately before beig weighed, which makes them appear heavier as they really are. Aother limitatio is that BMI does ot take muscle mass ito cosideratio. Therefore, whe the BMI of a healthy, muscular perso is calculated, they appear to be uhealthy (overweight or obese), causig a healthy perso to be placed i the uhealthy category. I additio, the Eglish ad Mathematics results used to determie the child s academic performace was just oe test, ad a sigle test caot determie the brilliace of a child as accurately as a series of tests would. Factors determiig a child s itelligece iclude, but are ot limited to, the child s eviromet ad the gees of their parets. 30

31 Appedix: To determie their BMI rage, the followig BMI table was used after cosultig various BMI charts. Uderweight Healthy Overweight Obese BOYS < >27.0 GIRLS < >

32 Bibliography: Why Study Eglish Laguage ad Literature? Math Forum: Ask Dr.Math : FAQ The Relatioship Betwee Obesity ad Academic Achievemet Of School-age Childre tplahvimh4khdmagkqfgg3mam&url=http%3a%2f%2fcollected.jcu.edu%2fcgi%2fviewcot et.cgi%3farticle%3d1008%26cotext%3dhoorspapers&usg=afqjcnehhq9jt15riuabamvvl Rq8J3GBrw Divisio of Nutritio, Physical Activity ad Obesity About Child & Tee BMI What is BMI chart for females? WHO Growth Charts for Caada BMI For Childre Body Mass Idex &sa=x&ved=0ahukewjafbuknplahvb9h4khtzuadaq_auibigb#tbm=isch&q=bmi+charts+for +girls&imgrc=tcj4llt2dbqvfm%3a Healthy Kids Healthy Weight: What We Are & What We Ca Do The Role of Geetics i IQ ad Itelligece 32

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