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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
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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 15 Healthy 64 39
Boy 16 Healthy 68 63
Boy 17 Healthy 76 92
Boy 18 Healthy 72 56
Boy 19 Healthy 78 81
Boy 20 Healthy 71 53
Boy 21 Healthy 73 68
Boy 22 Underweight 67 48
Boy 23 Healthy 81 84
Boy 24 Healthy 83 38
Boy 25 Healthy 72 91
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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
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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 13 Healthy 74 46
irl 14 Healthy 74 43
irl 15 O!e"e 76 71
irl 16 Healthy 83 77
irl 17 Healthy 64 53
irl 18 Healthy 54 45
irl 19 Healthy 72 52
irl 20 Healthy 74 49irl 21 Underweight 84 74
irl 22 Healthy 44 85
irl 23 Healthy 62 91
irl 24 O!e"e 70 42
irl 25 O!e"e 62 29
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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+)
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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
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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
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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 ¿¿√ ¿
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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!$9
x i−´ x¿2
¿ Σ ¿¿
σ =√ ¿
>1100.08
25
> √ 44.00
> 99$
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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
!
#
$
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-
9
6
+
:!4
!!
!#
!$
!
!-
!9
!6
!+
!:
#4
#!
##
#$
#
#-
Males
Student 8eight 9m' )eight 9*g
!
#
$
-
9
6
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+
:
!4
!!
!#
!$!
!-
!9
!6
!+
!:
#4
#!
##
#$
#
#-
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