ADDITIONAL MATHS SBA.docx

8/16/2019 ADDITIONAL MATHS SBA.docx

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Caribbean Examination Council

Caribbean Secondary Education Certificate

School Based Assessment

Additional Mathematics – Project B

Does good physical health and fitness as indicated by Body Mass Index influence

the academic performance of adolescents?

Name of student: Jamila Williams

Candidate number:

School code: 03001

Name of Centre: !arrison "ollege

Year of examination: #01$


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able of Contents

itle Pa!e

%urpose of %ro&ect''''''''''''''''''''''''''(1

Method of Data "ollection'''''''''''''''''''''''#

%resentation of Data'''''''''''''''''''''''''((3

Mathematical )no*ledge+ ,nalysis of Data'''''''''''''''(((1

Discussion of -indings''''''''''''''''''''''''(#.

"onclusion'''''''''''''''''''''''''''''31

Bibliography''''''''''''''''''''''''''''(3#

,ppendix'''''''''''''''''''''''''''''((33


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Pur"ose of Project

/he Body Mass Index BMI of a person is defined as a measure of body fat *hich is the ratio of

the *eight of the body measured in 2ilograms to the suare of the height measured in meters

suared(

BMI *as used as a measure of the student4s physical features and health as it is the most suitable

measure( 5ot only is it non6in7asi7e8 it is also inexpensi7e8 simple and non6time consuming and

it gi7es a measure of the indi7idual4s body fat based on their *eight in relation to height( /he

BMI scale is then used to categori9e indi7iduals into either under*eight8 healthy8 o7er*eight or

obese(

/he purpose of this pro&ect is to examine the relationship bet*een the health and fitness of

secondary students and their academic performance in :nglish ;iterature and Mathematics(

/he 7ariables being considered are<

1 the health status of the students as indicated by Body Mass Index !ealthy normal BMI

and =nhealthy under*eight8 o7er*eight or obese BMI

# academic performance in t*o selected sub&ects :nglish ;iterature and Mathematics

3 >ender Male and -emale


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Method of #ata Collection

/he heights and *eights of students in a sample of 0 students consisting of # females and #

males *ere measured(

!eights in meters *ere measured using a measuring tape( @tudents *ere as2ed to stand against

a 7ertical *all in their bare feet and the le7el of the top of the s2ull *as mar2ed on the *all( /he

height *as the distance bet*een the floor and this mar2(

Weights in 2ilograms *ere measured using a *eighing scale( @tudents *ere as2ed to stand on

the scale in their bare feet and *ith their poc2ets empty(

/he Body Mass Index BMI of each student *as calculated using the formula

BMI = weight

(height )2

/he health status of each student *as classified using the age referenced Body Mass Index

>raphs gi7e reference as sho*n in the appendix(

/he #01 -orm %romotion :xamination mar2s as a percentage for :nglish ;iterature and

Mathematics *ere pro7ided by the school *ith the consent of the students( @tudent pri7acy *as

maintained as no names *ere recorded(


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Presentation of #ata

AB$E %: able sho&in! the B'M'() *ealth Status and +,%- Mathematics and En!lish $iterature

"romotion mar.s /01 for +- male students at *arrison Colle!e'


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AB$E +: able sho&in! the B'M'(') *ealth Status and +,%- Math and En!lish $iterature

Promotion Examination mar.s /01 for +- female students at *arrison Colle!e'


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8%

77%

4%

12%

Underweight

Healthy

Overweight

Obese

2i!ure 3: he Percenta!e of Body Mass (ndex 4an.in! for 2emales

8%

75%

17%

Underweight

Healthy

Overweight

Obese

2i!ure -: he Percenta!e of Body Mass (ndex 4an.in! for Males


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0

2

4

6

8

10

12

1210

21

0

No. o st!dents

Marks (%)

Frequency

2i!ure 5: #istribution of Promotion Examination Mar.s for 2emales in En!lish $iterature

0

1

2

"

4

5

6

7

8

8

4"

8

2

No. o st!dents

Marks (%)

Frequency

2i!ure 6: #istribution of Promotion Examination Mar.s for 2emales in Mathematics


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75#100 60#74 5$#50 4$#40 Under 40

0

2

4

6

810

12

14

16

18

7

18

0 0 0

No. o st!dents

Marks(%)

Frequency

2i!ure 7: #istribution of Promotion Examination Mar.s for Males in En!lish $iterature

75#100 60#74 5$#50 4$#40 Under 40

0

1

2

"

4

5

6

7

8

$

$

65

2"

No. o st!dents

Marks(%)

Frequency

2i!ure 8: #istribution of Promotion Examination Mar.s for Males in Mathematics


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48%

40%

8% 4%

rade & '75%#100%(

rade ) '60%#74%(

rade * '5$%#50%(

rade + '4$%#40%(

2i!ure %,: Academic Performances for 2emales in En!lish $iterature


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"2%

16%12%

"2%

8%rade & '75%#100%( rade ) '60%#74%( rade * '5$%#50%(

rade + '4$%#40%( rade , 'Under 40%(

2i!ure %%: Academic Performances for 2emales in Mathematics

28%

72%

rade & '75%#100%(

rade ) '60%#74%(

rade * '5$%#50%(

rade + '4$%#40%(

rade , 'Under 40%(

2i!ure %+: Academic Performances for Males in En!lish $iterature


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"6%

24%

20%

8%

12%

rade & '75%#100%(

rade ) '60%#74%(

rade * '5$%#50%(

rade + '4$%#40%(

rade , 'Under 4$%(

2i!ure %9: Academic Performances for Males in Mathematics

!ealthy =nhealthy

0

#

$

.

10

1#

$0A6$A

C0A6CA

.0A6.A

State of Students

No' of Students

2i!ure 6: Bar chart sho&in! the distribution of the +,%- Promotion Examination Mar.s /01 in

En!lish $iterature for *ealthy and nhealthy Male Students


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!ealthy =nhealthy

0

#

$

.

10

1#

0A6A

0A6A

$0A6$A

C0A6CA

.0A6.A

State of Students

No' of Students

2i!ure 7: Bar chart sho&in! the distribution of the +,%- Promotion Examination Mar.s /01 in

En!lish $iterature for *ealthy and nhealthy 2emale Students'

!ealthy =nhealthy

0

0(

1

1(

##(

3

3(

(

30A63A

0A6A 0A6A

$0A6$A

C0A6CA

.0A6.A

0A6A

State of Students

No' of Students

2i!ure %,: Bar chart sho&in! the distribution of the +,%- Promotion Examination Mar.s /01 in

Mathematics for *ealthy and nhealthy Male Students


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!ealthy =nhealthy

0

1

#

3

$

C

#0A6#A 30A63A

0A6A

0A6A

$0A6$A

C0A6CA

.0A6.A

0A6A

State of Students

No' of Students

2i!ure %%: Bar chart sho&in! the distribution of the +,%- Promotion Examination Mar.s /01 in

Mathematics for *ealthy and nhealthy 2emale Students

@te

m ;eaf

$ 3 3 $ C

C 0 1 1 # # 3 $ C .. 0 3

$ 3

Means $3

-igure 1$< , stem and leaf diagram sho*ing the :nglish ;iterature mar2s of healthy males

@tem ;eaf

$ 0 1 $ C

C .

$

Means $


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-igure 1C< , stem and leaf diagram sho*ing the :nglish ;iterature mar2s of unhealthy males

@tem ;eaf

3 . .

3 $

$ # .

C 0 0 .

. 0 0 1

0 1

Means

-igure 1.< , stem and leaf diagram sho*ing the Mathematics mar2s of healthy males

@tem ;eaf 3 0

3 .

3 $

$

C

. #

Means

-igure 1< , stem and leaf diagram sho*ing the Mathematics mar2s of unhealthy males

@te

m ;eaf


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@tem ;eaf

#

3

1 3

$

C 1

Means

-igure #3< , stem and leaf diagram sho*ing the Mathematics mar2s of unhealthy females

Mathematical ;no&led!e< Analysis of #ata

-or each of the . groups being considered i(e( !ealthy Males :nglish literature8 =nhealthy

Males :nglish ;iterature8 !ealthy Males Mathematics8 =nhealthy Males Mathematics8

!ealthy -emales :nglish ;iterature8 =nhealthy -emales :nglish ;iterature8 !ealthy -emales

Mathematics and =nhealthy -emales Mathematics a Box6and6Whis2er plot *as dra*n( /hese

sho* for each specified group8 the lo*est promotion examination mar28 the highest promotion

examination mar28 the lo*er uartile8 the median and the upper uartile for each group( /he

median mar2 # is the 7alue that di7ides the data for a specific group into t*o eual parts( /he


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data is arranged in ascending order( /he median is that 7alue *hich occurs in the ( n+12 )th

position of the data *here n E number of students in the group( Where this position is not a

*hole number8 then the median is the mean of the mar2 immediately before and the mar2 after

the determined position( /he lo*er uartile 1 is the median of the lo*er half of the data set(

/he upper uartile 3 is the median of the upper half of the data set( /he interuartile range is

the difference bet*een the upper uartile and the lo*er uartile(

-igures #8 #8 #$ and #C sho* the Box6and6Whis2er plots for each of the . groups being

considered(


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0 10 20 "0 40 50 60 70 80 $0 100

English Literature marks : Healthy vs Unhealthy males

Healthy

Unhealthy

Marks

2i!ure +3: A box and &his.er "lot sho&in! the En!lish $iterature mar.s of healthy andunhealthy males

0 10 20 "0 40 50 60 70 80 $0 100

Mathematics marks: Healthy vs Unhealthy males

Healthy

Unhealthy

Marks

2i!ure +-: A box and &his.er "lot sho&in! the Mathematics mar.s of healthy and

unhealthy males


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0 10 20 "0 40 50 60 70 80 $0 100

English Literature marks: Healthy vs Unhealthy females

Healthy

Unhealthy

Marks

2i!ure +5: A box and &his.er "lot sho&in! the En!lish $iterature mar.s of healthy and

unhealthy females

0 10 20 "0 40 50 60 70 80 $0 100

Mathematics marks: Healthy vs Unhealthy females

Healthy

Unhealthy

Marks

2i!ure +6: A box and &his.er "lot sho&in! the Mathematics mar.s of healthy and

unhealthy females


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/he mean and standard de7iation for each of the eight specified groups *ere calculated( /he

follo*ing formulas *ere used<

Mean=∑ X

i

n

Standard deviation=√∑ ( X i−mean )

2

n

∑ X i represents the sum of all the mar2s for a specified group(

Fn4 represents the number of students in a specified group(

/ables 38 8 8 $8 C8 .8 and 10 sho* the results of these calculations for the eight specified

groups being considered(

/he statistics for the eight specified groups are summari9ed in /able 11(


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= /=>Mean1 /=>Mean1+

$3 6(3# .$(.$#

$3 6(3# .$(.$#

$ $ 0$$$ $$ 3$

$C $C .

$ $ C$1

C0 C0 00

C1 C1 01

C1 C1 01

C# C# 1.

C# C# 1.

C3 C3 3#

C C C$

C$ C$ CC$CC CC #

C. C. $0.

.0 .0 $00

.3 .3 $..

. . C##

G 13C #333(C#.

5umber of

students 1

meanE

@tandard de7iationE

meanE 13C

1

@tandard de7iationE $(3

meanE C#(3#

able 9: A table sho&in! the calculation of the mean and standard de?iation of a set of

mar.s obtained in En!lish $iterature for healthy males


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$0 6$(1$$$$$$$C 3.(0#CCCCC.

$1 6(1$$$$$$$C #$($

$ 61(1$$$$$$$C 1(3$1111111$$ 60(1$$$$$$$C 0(0#CCCCCC.

$C 0(.33333333 0($

C. 11(.3333333 10(0#CCCC.

G 3C #0$(.333333

5umber of

students $

meanE

meanE 3C@tandard

de7iationE

$

mean $$(1$$$$$$C

@tandard

de7iationE $(31$


mar.s obtained in En!lish $iterature for unhealthy males


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3. 630(31C.C 1(0C01

3. 630(31C.C 1(0C01

3 61(31C.C #3(C30C# 613(31C.C 1CC(310#3

$ 61#(31C.C 11($C.$C0

$# 6$(31C.C 3(..1$$.

$ 6(31C.C 1.($#$03.C.

$ 63(31C.C 10(.3

$. 60(31C.C 0(0C###

C0 1($.#10#$ #(.3$$0C

C0 1($.#10#$ #(.3$$0C

C $($.#10#$ ($C.$C03$

C. ($.#10#$ 3(C.333#.0 11($.#103 13$(#0CC$

.0 11($.#103 13$(#0CC$

.1 1#($.#103 1$0(..1$C

. 1($.#103 #(.

0 #1($.#103 C0(#0.$1

1 ##($.#103 1(C30C#

G 1#. #.0(10#$3

5umber of

students 1

meanE

@tandard

de7iationE

meanE 1#.

1

@tandardde7iationE 1(#0#3

meanE $.(31C

able -: A table sho&in! the calculation of the mean and standard de?iation of a set of

mar.s obtained in Mathematics for healthy males


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30 6## .

3 6 .1

. 6 1$

3 1 1

$ 1$

.# 30 00

G 31# 1.

5umber of

students $

meanE

meanE 31#

@tandard

de7iationE

$

meanE #@tandard

de7iationE 1C(30.$


mar.s obtained in Mathematics for unhealthy males



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1 6#0(#$31C #1(3#$3

3 61.(#$31C 33(##3C$C

$1 610(#$31C 110(.033#1

$3 6.(#$31C. C#($.0$0

$ 6$(#$31C. #(#CCC.

$ 6#(#$31C. $(3.##C1$.C1 60(#$31C. 0(#CC00.31

C# 0(C3$.#11 0(##3C$C31

C3 1(C3$.#11 #(1C1C1#

C #(C3$.#11 $(11113C3

C #(C3$.#11 $(11113C3

CC (C3$.#11 #($1#1..

CC (C3$.#11 #($1#1..

C. $(C3$.#11 1(0..C#$

C C(C3$.#11 (.$.

C C(C3$.#11 (.$..0 .(C3$.#11 C1(.033#1

.1 (C3$.#11 .(C0$##

.# 10(C3$.#1 10($.0$0

G 13

5umber of

students 1

meanE

@tandard de7iationE

meanE 13

1

@tandard de7iationE (11.CC

meanE C1(#$31C


mar.s obtained in En!lish $iterature for healthy females


$# 613(1$$$$$$C 1C3(3$11111


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$ 6$(1$$$$$$$C 3.(0#CCCCC.

C 61(1$$$$$$$C 1(3$1111111

C$ 0(.33333333 0($

. .(.33333333 C.(0#CCCCC.

.$ 10(.3333333 11C(3$11111

G 1 0.(.333333

5umber of

students $

meanE

meanE 1 @tandard de7iationE

$

meanE C(1$$$C @tandard de7iationE (0#


mar.s obtained in En!lish $iterature for unhealthy females


# 631 $1


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3 6#1 1

# 61. 3#

61 ##

61 ##

$ 61 1$

C 613 1$. 61# 1

0 610 100

# 6. $

# 6. $

$C C

$ .1

C 1 ##

CC 1C #.

.1 #1 1

0 30 003 33 10.

3 33 10.

G 110 C0C$

5umber of students 1

meanE@tandard de7iationE

meanE 110

1

@tandard de7iationE 1(.#C03

meanE $0


mar.s obtained in Mathematics for healthy females


# 6#$( C0#(#

1 61( #10(#


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3 61#( 1$(#

C1 1( #0(#

C 1.( 3#(#

C 1( 3.0(#

G 333 #031(

5umber of students $

meanE

meanE 333

@tandard

de7iationE

$

meanE (

@tandard

de7iationE #0(1$..

able %,: A table sho&in! the calculation of the mean and standard de?iation of a set of

mar.s obtained in Mathematics for unhealthy females

Column% N@

$o&est

Score

*i!hest

Score

Media

n

(nter

uartil

e ran!e Mean

Standar

d

#e?iatio

n

0"asse

s


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=nhealthyMales :(l $ $0 C. $( (C

$$(1$$$C $(31$ 100A

!ealthy

Males :(l 1 $3 . C# .( C#(3# $(3 100A=nhealthy

-emales :(l $ $# .$ C 11(C

C(1$$$

C (0# 100A!ealthy

-emales :(l 1 # .# C 11(C1(#$3

# (11.CC 100A

=nhealthy

Males M $ 30 .# 0( 11 # 1C(30.$ 0A

!ealthyMales M 1 3. 1 C0 #1

$.(31C 1(#0#3 .A

=nhealthy

-emales M $ # C C 31(C ( #0(1$.. 30A!ealthy

-emales M 1 # 3 # 30( $0 1(.#C03 #A

able %%: Summary of statistical results for 7 s"ecified !rou"s of -th 2orm students at

*arrison Colle!e

/&here M> Mathematics) E'l – En!lish $iterature1


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#iscussion of 2indin!s

/able 11 summari9ed the results of unhealthy and healthy males and females in :nglish

;iterature and Mathematics( =nhealthy boys performed better in :nglish ;iterature recei7ing

100A passes *ith a mean of $$(1$$$C and a small standard de7iation of $(31$8 implying that

the mar2s *ere consistent and close to the mean mar2( Hn the other hand8 in Mathematics there

*as a *ide 7ariability of mar2s across the mar2 range because of the large standard de7iation of

1C(30.$ recei7ing 0A passes( /he median and mean for unhealthy females in :nglish

;iterature *as determined to be the same8 this indicates that the dataset it e7enly distributed from

the lo*est to the highest 7alues *hile unhealthy females in Mathematics8 the data *as *idely

distributed because of a large standard de7iation of #0(1$..(

In Mathematics8 the healthy male4s mar2s had a large 7ariability to its mean of $.(31C *hile

healthy females also had a large de7iation to its mean of $0 but healthy males performed better

than healthy females recei7ing CA more passes than the females( In :nglish ;iterature8 healthy

males performed slightly better than healthy females( /he standard de7iation for healthy males

*as determined to be $(3 *hich is not much de7iation and the mar2s are close to the mean8

C3(3#( /his sho*s that healthy males performed *ell in :nglish ;iterature *hile healthy females

recei7ed a standard de7iation of (11.CC *hich is not much de7iation a*ay from the mean of

C1(#$3#8 indicating that healthy females also performed *ell in :nglish ;iterature(

In sum8 it can be said that students performed better in :nglish ;iterature than in Mathematics

despite of their health statuses and gender( ,lso8 in Mathematics males performed some*hat

better than females but considering both :nglish ;iterature and Mathematics8 males performed

better( -urthermore8 healthy males performed better than unhealthy males in both Mathematics

and :nglish ;iterature( Hn the other hand8 healthy females performed better than unhealthy


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females only in :nglish ;iterature *hile unhealthy females performed slightly better than

healthy females in Mathematics( It appears that healthy students perform better than unhealthy

students(


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Conclusion

In conclusion8 from examining the data obtained through this study8 it can be said that good

health influences academic performance( !ealthy students in both genders performed better than

unhealthy students( It *ould appear that fitness seems to be more critical *ith males than

females but females *ould do good or poorly academically regardless of their health status(

In this experiment8 participants *ere all ta2en from the same school so that the en7ironment

*ould not influence their results( ,lso8 this conclusion only pertains to :nglish ;iterature and

Mathematics and may not be true for other sub&ects( Hther factors that should be considered for

the further e7aluation of this study include person4s social and economic en7ironment8 the

person4s education le7el or the genetics of the indi7idual(


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Biblio!ra"hy

http


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A""endix


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ADDITIONAL MATHS SBA.docx

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