ADD Maths Sba Draft 1

8/16/2019 ADD Maths Sba Draft 1

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Caribbean Examination Council Secondary Education Certificate School Based

Assessment Additional Mathematics

Does good health (as indicated by Body Mass Index) influence academic

performance?

Name of student:

Candidate number:

School code:

Name of school:

Territory:


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Table of Contents

Title Page

Purpose of Project……………………………………………………………………!

Method of Data "ollection……………………………………………………………#

Presentation of Data…………………………………………………………………$

Mathematical %no&ledge' nalysis of Data………………………………………!

Discussion of *indings………………………………………………………………#+

"onclusion……………………………………………………………………………$!

Bibliography…………………………………………………………………………$#

ppendix……………………………………………………………………………$$


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Purpose of Proect

n in,estigation to examine the academic performance of -th form students of .arrison "ollege

in the subjects/ Mathematics and 0nglish 1iterature and the relationship this academic

performance had &ith their BMI

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Method of !ata Collection

2he mar3s obtained by fifty selected - th year students at .arrison "ollege in the #4!- 0nglish

1iterature and Mathematics promotion exam &ere pro,ided by the school 2he &eights of fifty

selected students &ere measured using a scale and the heights of the same selected students using

a measuring tape 2he &eights and heights &ere tabulated and used to calculate the Body Mass

Index (BMI) using the formula5BMI= weight in kilograms ÷ height in meters #

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Presentation of !ata

Students

Weight(kg)

Height(m2)

BMI=weight(kg)/height(m2)

Boy 1 54.4 2.8 19.5Boy 2 49.94 2.9 17.2

Boy 3 61.2 2.8 21.9

Boy 4 79.8 3.2 24.9

Boy 5 63.5 3.2 19.8

Boy 6 57.1 2.7 21.1

Boy 7 83.9 3.1 27.1

Boy 8 59 3.5 16.9

Boy 9 52.1 3.1 16.9

Boy 10 77.5 3.2 24.2

Boy 11 51.2 3.2 16

Boy 12 58.5 2.9 20.2

Boy 13 73.4 2.9 25.3

Boy 14 48.5 2.7 18

Boy 15 53.5 2.9 18.4

Boy 16 55.3 3.2 17.3

Boy 17 68.9 3.1 22.2

Boy 18 73 3.4 21.5

Boy 19 61.2 2.9 21.1

Boy 20 77.1 3.4 22.7

Boy 21 63.1 3 21.3

Boy 23 52.1 3.2 16.3

Boy 24 59 3.2 18.4

Boy 25 64.9 3.2 20.3

Boy 26 72.7 3.2 20.3

3


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Marks (%)Students

Underweight/healthy/oerweight/o!ese

"nglish#iterature

Mathemati$s

Boy 1 Healthy 63 70

Boy 2 Healthy 79 56

Boy 3 Healthy 64 65Boy 4 Overweight 66 82

Boy 5 Healthy 85 80

Boy 6 Healthy 72 65

Boy 7 Overweight 62 57

Boy 8 Healthy 74 78

Boy 9 Healthy 70 81

Boy 10 Overweight 78 30

Boy 11 Underweight 60 43

Boy 12 Healthy 73 70

Boy 13 Overweight 66 54Boy 14 Healthy 67 76








Boy 22 Underweight 67 48




4


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Students

Weight(kg)

Height(m2)

BMI=weight(kg)/height(m2)

irl 1 49.9 2.6 19.2

irl 2 56.7 3.1 18.3

irl 3 54.4 2.6 21

irl 4 61.2 2.4 25.5

irl 5 59 2.7 22

irl 6 41.7 2.5 16.7

irl 7 54 2.9 18.6

irl 8 52.1 2.9 18

irl 9 41.3 2.5 16.5

irl 10 52.6 2.8 18.8

irl 11 54.4 2.7 20.1

irl 12 62.6 2.7 23.2

irl 13 50.8 2.8 18.1

irl 14 47.2 2.6 18.2

irl 15 70.8 2.4 29.5

irl 16 47.2 2.4 20

irl 17 54.9 2.6 21.1

irl 18 45.8 2.6 17.6

irl 19 55.3 2.5 22.1

irl 20 43.5 2.3 18.9

irl 21 42.2 2.6 16.2

irl 22 67.6 3.2 21.1irl 23 57.2 2.7 21.2

irl 24 68 2.3 29.6

irl 25 81.8 2.8 29.2

5


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Marks (%)

Stude

nts

Underweight/healthy/oerwei

ght/o!ese

"nglish

#iterature

Mathemati

$s

irl 1 Healthy 77 93

irl 2 Healthy 79 40

irl 3 Healthy 81 45

irl 4 Overweight 86 43

irl 5 Healthy 70 29

irl 6 Underweight 75 75

irl 7 Healthy 79 76

irl 8 Healthy 81 93

irl 9 Healthy 78 50

irl 10 Healthy 51 67irl 11 Healthy 78 82

irl 12 Healthy 73 70



irl 15 O!e"e 76 71





irl 20 Healthy 74 49irl 21 Underweight 84 74



irl 24 O!e"e 70 42

irl 25 O!e"e 62 29

6


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!iagram ": Steam and #eaf !iagram Sho$ing the Body Mass %ndex for &emales

#tea$

%ea&

1 6 7 7 8 8 8 8 8 9 9 9 9

2 0 0 1 1 1 1 2 2 3 6 9

3 0 0

"&' 3'0 $ean" 30

!iagram ': Stem and #eaf !iagram Sho$ing the Body Mass %ndex for Males

#tea$

%ea&

1 6 6 7 7 7 7 8 8 8

2 0 0 0 0 0 1 1 1 2 2 2 3 4 5 5 7

"&' 2'0 $ean" 20

!iagram (: Box and )his*ers Plots of +,erall Body Mass %ndex for &emales and Males

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1

2

0 5 10 15 20 25 30 35

B( &or (ale" B( &or *e$ale"

Pie Chart ": The Percentage of Body Mass %ndex -an*ing for &emales

8+

77+

4+

12+

Underweight

Healthy

Overweight

O!e"e

8


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Pie Chart ': The Percentage of Body Mass %ndex -an*ing for Males

8+

75+

17+

Underweight

Healthy

Overweight

O!e"e

Bar Chart ": Sho$ing the Most Common Mar* -anges for &emales in English #iterature

75,100 60,74 59,50 49,40 Under 400

2

4

6

8

10

12

14

12

10

2

1

0

Marks (%)

reuen$y

9


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Bar Chart ': Sho$ing the Most Common Mar* -anges for &emales in Mathematics

75,100 60,74 59,50 49,40 Under 400

1

2

3

4

5

6

7

8

8

4

3

8

2

Marks (%)

reuen$y

Bar Chart (: Sho$ing the Most Common Mar* -anges for Males in English #iterature

75,100 60,74 59,50 49,40 Under 40

0

2

4

6

8

10

12

14

16

18

7

18

0 0 0

Marks(%)

reuen$y

10


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Bar Chart .: Sho$ing the Most Common Mar* -anges for Males in Mathematics

75,100 60,74 59,50 49,40 Under 40

0

1

2

3

4

5

6

7

8

9

9

65

23

Marks(%)

reuen$y

Pie Chart (: Sho$ing the Performances for &emales in English #iterature

48+

40+

8+4+

rade - 75+,100+)

rade B 60+,74+)

rade / 59+,50+)

rade 49+,40+)

11


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Pie Chart .: Sho$ing the Performances for &emales in Mathematics

32+

16+12+

32+

8+rade - 75+,100+) rade B 60+,74+) rade / 59+,50+)

rade 49+,40+) rade Under 40+)

Pie Chart /: Sho$ing the Performances for Males in English #iterature

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28+

72+

rade - 75+,100+)rade B 60+,74+)

rade / 59+,50+)

rade 49+,40+)

rade Under 40+)

Pie Chart 0: Sho$ing the Performances for Males in Mathematics

36+

24+

20+

8+

12+

rade - 75+,100+)

rade B 60+,74+)

rade / 59+,50+)

rade 49+,40+)

rade Under 49+)

Bar Chart /: Sho$ing the A,erage Mar*s in English #iterature for &emales and Males

categorised in their Body Mass %ndex -an*ing

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(ale"

*e$ale"

0 10 20 30 40 50 60 70 80 90

64

80

73

71

68

86

Underweight

Healthy

Overweight

"nglish #iterature marks (%)

*ender

Bar Chart 0: Sho$ing the A,erage Mar*s in Mathematics for &emales and Males

categorised in their Body Mass %ndex -an*ing

(ale"

*e$ale"

0 10 20 30 40 50 60 70 80

46

75

69

62

56

43

Underweight

Healthy

Overweight

Mathemati$s Marks (%)

*ender

1rade A 1rade B 1rade C 1rade ! 1rade E

6-78!447 947867 -478-:7 478:7 ;nder 47

Mathematical 2no$ledge3 Analysis of !ata

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2he test &as conducted in order to in,estigate if health (indicated by Body Mass Index)

influence academic performance 2he test &as di,ided into gender< males and females and t&o

subjects 0nglish 1iterature and Mathematics

*irst/ &e must find the a,erage Body Mass Index obtained by females and males using the

results from the =tem and 1eaf Diagrams/ in Diagrams ! and # 2he a,erage or mean is a number

expressing the central or ,alue in a set of data 2he formula is5 Mean> Σ x

n < &here x

represents the sum of the data ,alues and n represents the number of data ,alues

2he a,erage Body Mass Index for *emales rounded off >

16+17+17+18+18+18+18+18+19+19+19+19+20+20+21+21+21+21+22+22+23+26+29+30+3¿

)÷ 25

>522

25

> #!

2he a,erage Body Mass Index for Males rounded off >

(16+16+17+17+17+17+18+18+18+20+20+20+20+20+21+21+21+22+22+22+23+24+25+25+

>507

25

15


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>#4

Bar Chart 4: Sho$ing the A,erage BM% for &emales and Males

*e$ale"

(ale"

19.4 19.6 19.8 20 20.2 20.4 20.6 20.8 21

21

20

Body Mass Inde+ (kg/m2)

;sing the =tem and 1eaf Diagrams/ in Diagrams ! and # (see page 6)/ &e can find the lo&er and

upper uartiles/ mode/ maximum and minimum ,alues for the Body Mass Index for *emales and

Males

@! represents the lo&er uartile

@# represents the median

@$ represents the upper uartile

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BM% for &emales

The lo$er 5uartile > @!>n+1

4

> 25+14

>26

4

> 9- > 6th

@! > !+

The median > @#>n+1

2

>25+12

>26

2

> !$th

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@# > #4

The upper 5uartile> @$>3 (n+1)

4

>3 (25+1)

4

>78

4

>!:- > #4th

@$ > ##

The minimum ,alue > !9

The maximum ,alue > $4

Mode > !+

BM% for Males

The lo$er 5uartile > @!>n+1

4

18


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>78

4

>!:- > #4th

@$> ##

The minimum ,alue > !9

The maximum ,alue > #6

Mode > #4

Box and Ahis3ers Plot is a graph displaying the lo&er uartile/ median/ upper uartile and

minimum and maximum ,alues 2his is done by ordering the data/ identifying the fi,e ,alues

necessary and plotting the graph ;sing the data that &as calculated and determined abo,e/ Box

and Ahis3ers Plots &ere plotted and dra&n for the BMI for both *emale and Male (see Diagram

$)

=tandard de,iation is a measure of ho& data is spread out relati,e to the mean of the data Ae

can find the standard de,iation of mar3s in 0nglish 1iterature for males and females and

standard de,iation of mar3s in Mathematics for males and females using the euation of standard

de,iation5

σ >

xi−´ x¿2

¿ Σ ¿¿√ ¿

20


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9+ 8$$9 !!#:

69 9 #!-$

6# 49 4!

6+ 99 4:

6! 4$9 4!$

6$ !9 #9:96 8$9 !:4!

+! :9 :#:$

+$ !!9 !$-:

6# 49 4!

> !6+ !!444+

Cumber of mar3s> #-

´ x 6

Σ xi

n

>1784

25

> 6!$9

x i−´ x¿2

¿ Σ ¿¿

σ =√ ¿

>1100.08

25

> √ 44.00

> 99$

22


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Standard !e,iation of mar*s in Mathematics for Males

xi

xi

¿ −´ x )

x

¿¿¿

−´ x ¿2

64 -# #64

-9 8++ 66

9- 4# 44

+# !6# #:-+

+4 !-# #$!4

9- 4# 44

-6 86+ 94+

6+ !$# !6#

+! !9# #9#

$4 8$+ !#!!4

$ 8#!+ 6-#

64 -# #64

- 8!4+ !!99

69 !!# !#-

$: 8#-+ 99-9

9$ 8!+ $#

:# #6# 6$:+

-9 8++ 66+! !9# #9#

-$ 8!!+ !$:#

9+ $# !4#

+ 8!9+ #+##

+ !:# $9+9

$+ 8#9+ 6!+#

:! #9# 9+9

> !9#4 64$6#

Cumber of mar3s> #-

´ x 6

Σ xi

n

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>1620

25

> 9+

x i−´ x¿2

¿ Σ ¿¿

σ =√ ¿

>

√

7037.2

25

6 √ 281.5

> !9+

Standard !e,iation of mar*s in English #iterature for &emales

xi

xi

¿ −´ x )

x

¿

¿¿

−´ x ¿2

66 :9 #94

6: 9:9 +

+! +9: +4#+

+9 !$:9 !:++64 8#4 !9

6- #:9 +69

6: 9:9 +

+! +:9 +4#+

6+ -:9 $--#

-! 8#!4 #9+

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6+ -:9 $--#

6$ 4:9 4:#

6 !:9 $+

6 !:9 $+

69 $:9 !-9+

+$ !4:9 !#4!#9 8+4 99

- 8!+4 $#-

6# 844 444#

6 !:9 $+

+ !!:9 !$4

8#+4 6+9#

9# 8!44 !44+4

64 8#'4 !9

9# 8!44 !44+4

> !+4! #969:#

Cumber of mar3s> #-

´ x 6

Σ xi

n

61801

25

6 6#4

x i−´ x¿2

¿ Σ ¿¿

σ =√ ¿

> √2676.92

25

> √ 107.08

25


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> !4$-

Standard !e,iation of mar*s in Mathematics for &emales

xi

xi

¿ −´ x )

x

¿¿¿

−´ x ¿2

:$ $## !4$9+

4 8#4+ $#9

- 8!-+ #:9

$ 8!6+ $!9+

#: 8$!+ !4!!#

6- !# #4!9

69 !-# #$!4

:$ $## !4$9+

-4 8!4+ !!99

96 9# $+

+# #!# :64 :# +9

9 8!+ #!:4

$ 8!6+ $!9+

6! !4# !44

66 !9# #9#

-$ 86+ 94+

- 8!-+ #:9

-# 8++ 66

: 8!!+ !$:#

6 !$# !6#

+- ## -+-9

:! $4# :!#4

# 8!++ $-$

#: 8$!+ !4!!#

> !-#4

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Cumber of mar3s> #-

´ x 6

Σ xi

n

61520

25

6 94+

x i−´ x¿2

¿ Σ ¿¿

σ =√ ¿

6 √9671

25

6 √ 386

>!:9

!iscussion of &indings

&EMA#ES 7S MA#ES

s sho&n in Pie "hart ! and #/ majority of female and male students are healthy lso

it is e,ident that majority of females obtained a grade in 0nglish 1iterature but the mar3s

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,aried from grades to D as sho&n in Pie "hart $ n the other hand/ males performed

exceptionally &ell recei,ing only grades and B in 0nglish 1iterature as sho&n in Pie "hart -

In Pie "hart / it is sho&n that the same number of female students obtained a

grade and D in Mathematics .o&e,er/ in Pie "hart 9 it is sho&n that the mar3s ,aried from

grades to 0 but majority of the males obtained a grade

*or females/ the a,erage 0nglish 1iterature mar3 &as 6#7 and the standard de,iation

&as !4$- &hich is not much de,iation 2his indicates that the mar3s &ere some&hat close to the

mean and consistent lso it sho&s that the females performed &ell because the a,erage 0nglish

1iterature mar3 &as ran3ed to be a grade B 2he standard de,iation for males in 0nglish

1iterature &as found to be 99$ &hich is small de,iation of the mar3s 2his indicated that the

males performed &ell because the a,erage mar3 for 0nglish 1iterature &as 6!7 &hich is ran3ed

to be a Erade B Both 0nglish 1iterature a,erages for males and females &ere ran3ed to be a

grade B but the femaleFs a,erage &as higher than the maleFs by !7

2he a,erage Mathematics mar3 for females &as 9!7 and the standard de,iation &as

!:9/ indicating that there &as a &ide de,iation of the mar3s *urthermore/ the a,erage

Mathematics mar3 for males &as 9-7 and the standard de,iation &as found to be !9+ &hich is

a fairly &ide spread of the mar3s to the a,erage 2his implies that for both male and females the

mar3s of Mathematics ,aried across the grade range/ implying that a fe& students did &ell/ a fe&

students performed a,erage and a fe& students failed

s sho&n in Diagram $/ for both female and male the minimum point BMI &as !9

and the lo&er uartile &as !+ lso/ the median BMI of both genders &as !+ and the upper

uartiles &ere the same as &ell/ &hich &as ## In spite of the similar results obtained by males a

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females/ the maximum ,alues &ere different 2he maximum BMI ,alue for females &as $4 and

the maximum BMI ,alue &as #6 2his indicates that the BMI ,alues for the girls ,aried across

the range of BMIs ha,ing a &ider de,iation that the males

;sing Bar "hart -/ the highest a,erage mar3 in 0nglish 1iterature for females &as a

grade categorised in their BMI &as o,er&eight/ the healthy category obtained a Erade B and

the under&eight category obtained a grade 2he highest a,erage mar3 in 0nglish 1iterature for

males &as a grade B categorised in their BMI &as healthy/ the o,er&eight category obtained a

grade B and the under&eight category obtained a grade B 2his signifies that in both male and

female in all the BMI categories/ good a,erages &ere recei,ed but the female o,er&eight

category recei,ed +97 &hich is the highest a,erage o,erall

In Bar "hart 9/ the highest a,erage Mathematics mar3 for females &as a grade

categorised in their BMI is under&eight/ the healthy category obtained a Erade B and the

o,er&eight category obtained a Erade D In Mathematics/ the highest a,erage mar3 for males

&as obtained by the healthy category &hich &as a grade B/ the o,er&eight category obtained a

grade " and the under&eight category obtained a grade D 2his implies that under&eight females

recei,ed the highest a,erage o,erall although both male and female obtained generally fair

a,erages

In sum/ by studying the data abo,e/ females obtained the highest a,erages o,erall in

both 0nglish 1iterature and Mathematics .o&e,er/ the healthy category recei,ed the highest

a,erages in 0nglish 1iterature and Mathematics for males/ &hich indicates that being healthy

could ha,e influenced the academic performance of males

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Conclusion

In conclusion/ from examining the data obtained through this study/ it can be said that good

health influences academic performance lthough females performed better than the males in

both subjects/ students that are considered healthy regardless of gender performed the best

o,erall

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It is suggested that students should include healthy foods in their diets and the school should

facilitate a fruit day e,ery &ee3 It is also suggested that students should study more in

preparation for their promotion exams to recei,e better results

In this experiment/ participants &ere all ta3en from the same school so that the en,ironment

&ould not influence their results lso/ this conclusion only pertains to 0nglish 1iterature and

Mathematics and may not be true for other subjects ther factors that should be considered for

the further e,aluation of this study include personFs social and economic en,ironment/ the

personFs education le,el or the genetics of the indi,idual

Bibliography

http5''studycom'academy'lesson'&hat8is8bmi8definition8formula8calculationhtml

http5''&&&&hoint'hia'e,idence'doh'en'

31

http://study.com/academy/lesson/what-is-bmi-definition-formula-calculation.htmlhttp://www.who.int/hia/evidence/doh/en/http://www.who.int/hia/evidence/doh/en/http://study.com/academy/lesson/what-is-bmi-definition-formula-calculation.html


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Appendix

&emales

Student 8eight 9m' )eight 9*g

!

#

$

32


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-

9

6

+

:!4

!!

!#

!$

!

!-

!9

!6

!+

!:

#4

#!

##

#$

#

#-

Males

Student 8eight 9m' )eight 9*g

!

#

$

-

9

6

33


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+

:

!4

!!

!#

!$!

!-

!9

!6

!+

!:

#4

#!

##

#$

#

#-

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ADD Maths Sba Draft 1