Name: Marlon Forrest

Grade: 12

Subject: Applied Mathematics

Unit: one

Year submitted: 2013

17

Table of Content

Project title…………………………………………………………………………………..3

Purpose of project……………………………………………………………………………4

Method of data collection……………………………………………………………………5

Presentation of data………………………………………………………………………….6-11

Analysis of data……………………………………………………………………………...12-19

Discussion of findings……………………………………………………………………….20-23

Glossary ……………………………………………………………………………………..24

Reference…………………………………………………………………………………….25

Appendix……………………………………………………………………………………..26-29

17

PROJECT TITLE

To investigate and to find out the causes of student engaging in an extracurricular activity and how it affect their academic performance.

17

PURPOSE OF PROJECT

Extracurricular activities are activities performed by student that fall outside the realm of

the normal curriculum of school or university. Such activities are generally voluntary as opposed

to mandatory, non-paying, social, and philanthropic as opposed to scholastic and often involve

others of the same age group.

It has been observed that the time the student spend in extracurricular activity affect the

student overall school average. Therefore the researcher choose this topic to find out if the

number of hours spent in extracurricular activity affect their performance.

The benefits of doing this research is that data will be analyze on the student

extracurricular activity and the problem will be recognized. The source will be student from

various clubs. Another benefits is that alternative solution will be made for the student to the

problem they are facing.

17

METHOD OF DATA COLLECTION

The St. Mary High School has a population (N) of over fifteen hundred students. A

sampling frame of 275 students, consisting of only grade 8 students was chosen for the

observation due to the similarities in the subjects done by these students. A sample (n) of 30

students was selected to carry out this investigation. Data was collected by the use of

questionnaire and observation.Questionnaire allows for firsthand information, they are easily

administered and they are less time consuming. A random sample of 30 students was taken

which consist of 5 students from each class. On the other hand, observation gives the researcher

the ability to gather extra information with persons knowing.

The method of data collection was judged to be appropriate due to the fact that the

questions can be structured to gather only the information necessary for the investigation. There

were no flaws because the questionnaires were given to randomly chosen respondents so as to

prevent bias. In addition, the questions were clearly stated to prevent confusion so that they

could be easily answered.

The researcher was carried out on the January 15, 2013. Thirty (30) questionnaires were

given out to the students that were randomly chosen for the investigation and all were completed

and returned.

17

17

Figure1: Table showing number of respondents and their gender.

Sex Number of RespondentsMale 12Female 18

The table above shows the gender of the respondents who were chosen for the investigation.

17

The above bar graph shows the number of students which is in a extracurricular activity. There

were twenty (20) student who engage in track and field, eight (8)student who engage in cadet

and two (2) student who engage in quiz.

track&field cadet quiz0

5

10

15

20

25

20

8

2

Figure 2: Bar graph showing the number of students who engage in the various club

quizcadettrack&field

Types of Social Networks

Number of

students

17

The above diagram shows the average number of hours spent students on the various clubs.The

average number hours spent in track and field by students weekly is eight (8) hours, cadet

accounted for five (5) hours while only three (3) hours was spent in quiz.

track&fieldcadet

quiz

0

1

2

3

4

5

6

7

88

5

3

Figure 3: Bar graph showing the average number of hours spent in each club weekly

track&fieldcadetquiz

Social Networks

Hour

s

17

50%

20%

20%

10%

Figure 4: Pie chart showing reasons of students for using social networks

CommunicationLeisureTrendpersonal benefits

The above diagram shows the percentage of students who chose the various reasons for them

engaging in extracurricular activity. Fifty percent (50%) said that they engage in the club for

communication, twenty percent (20%) said leisure and trend while ten percent (10%) replied

personal benefits.

17

The figure above shows the average number of hours spent studying based on the type of

extracurricular activity the student engage in frequently. The students who engage in track and

field spend an average of four(4) hours studying, students who engage in cadet spend an average

of six (6) hours studying and those who engage in quiz spend an average of nine (9) hours

studying.

track&fieldcadet

quiz

0123456789

track&field

cadet

quiz

4

6

9

Figure 5: Conical graph showing the number of hours spent studying

track&fieldcadetquiz

social networks

Numberof

hoursspent

studying

17

17

CENTRAL TENDENCY

The figures below show the average grade for the students during the End of Term Exams 2011. They are as follows:

38% 50% 52% 55% 56% 57% 58% 60% 62% 63% 65% 66%68% 70% 72% 74% 75% 80% 80% 80% 80% 81% 82% 83%84% 84% 85% 86% 87% 93%

Mean

X=x1+¿ x2+x

3+… xn

n¿

=2126/30

=70.87%

Mean average of students in Term Exams 2011 = 70.87%

Mode

Mode= 80%

The most frequent average grade scored in exams = 80%.

Median

Median position= ½(n+1)th

=1/2(30+1th

=1/2(31)th

=15.5

=16th

16th position = 74%

17

PROBABILITY

Conditional Probability

In order to ascertain the needed data about whether or not the number of hours spent in extracurricular activity affect the performance of the students in the exams, the researcher saw it necessary to conduct a probability test using conditionalprobability.

Let G be the event that a student obtained an average grade of below 60% in the exam.

Let H be the event that a student spent an average of 8 hours in an extracurricular activity.

P (G/H) = P (GnH) = (5/30)= 0.167 = 0.2503 = 167/667

P(H) (20/30) 0.667

Let G be the event that a student obtained an average grade of below 60% in the exam.

Let H be the event that a student spent an average of 8 hours in an extracurricular activity

P (G/H) = P (GnH) = (15/30) = 0.50 = 0.7463 = 50/67

P (H) (20/30) 0.67

17

Chi- Square Test

The grades used below are the average grades of the students observed. They are described as low (below 51%), medium (between 50% and 80%) and high (above 79%). The average number of hours spent in an extracurricular activity was also used.

Time (avg.) 2 5 8 TotalLow 0 1 1 2Medium 0 3 12 15High 2 4 7 13Total 2 8 20 30

Table showing the hours spentin an extracurricular activity by students and their average grades.

Time (avg.) 2 5 8 TotalLow 0.133 0.533 1.333 2Medium 1 4 10 15High 0.867 3.467 8.667 13Total 2 8 20 30

Contingency table

17

O E (O-E) 2 E

0 0.133 0.1330 1 12 0.867 1.4811 0.533 0.4093 4 0.254 3.467 0.0821 1.333 0.08312 10 0.47 8.667 0.321∑O=30 ∑E=30 ∑(O-E) 2 = 4.159

EExpected Frequency = Row total * Column total

Grand total

Ho: The average grades obtained by students in their end of term exams and the number of hours spent in extracurricular activity are independent variables.

H 1: The average grades obtained by students in their end of term exams and the number of hours spent in an extracurricular activity are not independent variables.

Row * Column

ν = (3-1) * (3-1)

= 2*2

= 22

= 4

x2= 4.159

ᵡ25% (4) = 9.488

17

Since x2 = 4.159 <ᵡ25% (4) = 9.488, we do not reject Ho and conclude that the average grade

obtained by students and the average number of hours spent in an extracurricular activity are independent.

Correlation and Linear regression graph

Y= average grade obtained in exam.

X=number of hours spent in an extracurricular activity.

1 2 3 4 5 6 7 8 90

10

20

30

40

50

60

70

80

90

100

f(x) = − 1.71428571428571 x + 82.5238095238095R² = 0.0560246692988271

Average grade

Average gradeLinear (Average grade)

time spent in extra curicular activity (hrs)

aver

age

grad

e in

exa

m (%

)

.

17

Average number of hours spent in extracurricular

activity

Average xy x2 y2

8 38% 304 64 14445 50% 250 25 25008 52% 416 64 27048 55% 440 64 30258 56% 448 64 31368 57% 456 64 32495 58% 464 25 33648 60% 480 64 36008 62% 496 64 38448 63% 504 64 39698 65% 520 64 42258 66% 528 64 43565 68% 340 25 46248 70% 560 64 49008 72% 576 64 51845 74% 370 25 54768 75% 600 64 56258 80% 640 64 64005 80% 400 25 64008 80% 640 64+ 64005 80% 400 25 64002 81% 162 4 65615 82% 410 25 67248 83% 664 64 68895 84% 420 25 70568 84% 672 64 70562 85% 170 4 72258 86% 688 64 73968 87% 696 64 75698 93% 744 64 8649∑x=204 ∑y=9551 ∑xy=14458 ∑x2=1488 ∑y2=150325

r=n ∑xy - ∑x∑y=30(14458) – (204) (9551)

√[n∑x2-(∑x)2]*[n ∑y2-(∑y)2] √[30(1488 – 41616] * [30(150325 – 91221601)]

17

= -1514664 =-1514664 =-1514664

√-1203840*-2732138280 √3.289057347*1015 57350303.81

= -0.0264

17

17

17

According to Fligner (2006) “Observation studies are investigations in which one simply

observes the state of some population, usually with data collected by sampling. Even with proper

sampling, data from observational studies are generally not appropriate for investigation cause-

and –effect relations between variables”.

The investigation gave significant information about the relationship between the

performance of students and the average time spentin an extracurricular activity.

It was found out that the average grade the student observed was 70.87%. After

examining this data more closely, it was seen that 53.33% of the students observed scored above

the average grade. On further observation, the modal average was found to be 80% as it was the

average that was obtained the most. The central average amount was found to be 74%, this

revealed that 50% of the student observed scored 74% or below and also that 50% were scoring

74% or above.

A probability test was done to see if it was more likely for a student to spend greater

amount of hours in extracurricular activity and still obtain high grades or was it that students had

to spend less time in extracurricular activity to achieve these grade. After completing the test, it

was seen that the probability of a student scoring an average of 60% or above while spending an

average of 8 hours in extracurricular activity (0.7463 or 50/67) was significantly than the

probability of a student scoring an average of below 60% while spending an average of 8 hours

in an extracurricular activity (0.2503 or 167/667).

To test for the relationship/independence of the average grade and the average hours

spentin an extracurricular activity, a chi-squared test and correlation and linear regression graph

was done. The chi-squared test showed that at the 5% level of significance that the average grade

17

obtained in the exam and the average number of hours spent on social networks is independent.

This is because x2=4.159<ᵡ2=9.488, therefore x2 would fall below the rejection region and

conclude that both variables are independent.

On the other hand, the correlation and linear regression graph revealed that there was a

very low negative relationship between the average grade obtained and the hours spentin an

extracurricular activity. This was given by the correlation coefficient=0.0264. The regression

coefficient -1.7143 represents the decrease in y for each unit increase in x, that is for every 1

hour increase in time the average grade obtained will decrease by 1.7143%. The constant of

82.524 represents the theoretical value of y when x=0.

17

Conclusion

From the investigation it can be seen that there is a very low negative relationship between the

average grade obtained and the hours spentin an extracurricular activity. As was seen from the

calculations carried out, an increase in the hours spentin an extracurricular activity has a small

effect on the grades obtained as was shown by the regression coefficient of -1.7143.

Out of this investigation, it can be inferred that even though the students tend to score good

grades even though spending a large amount of time on social networks, the number of hours

spent in an extracurricular activity cause their grades to decrease slightly.

17

Glossary

Symbols Meanings

∑ The sum of any values.

µ The mean value.

ᵡ2 The chi-square test value.

P The probability of any event.O The observed frequency.E The expected frequency.

(O-E) 2 E

The test statistic.

ν The degrees of freedom of the test.X2 The critical value (rejection region) of the test.r The linear correlation coefficientN Population size.n Sample size.

17

Reference

Fligner, M A. (2006). Introduction to the practice of statistics, New York, W. H. Freeman and company.

17

17

QUESTIONNAIRE

Dear Student,

I am a sixth form student at the Saint Mary High School who is currently studying Applied Mathematics. This investigation is a requirement for a CAPE Applied Mathematics school based assessment (SBA). The main objective of this questionnaire is to gather information which is accurate and reliable. The researcher is asking for your cooperation in successfully completing this questionnaire as your confidentiality is guaranteed.

Please circle the appropriate response.

Gender………………………………………

1. State your age:

……………………………………...

2. Do you engage in a extra-curricular activity?

a) yesb) Sometimes c) No

3. If yes, which type ofextra-curricular activity?

a) Track and Field b) Cadetc) Quiz

4. How long do you spend at the club weekly?

a) 0-2hrsb) 3-4hrsc) 5-6hrsd) 7-8hrs

5. What is your reason for taking part in aextra-curricular activity?a) Communicationb) Leisure

17

c) trendd) Personal benefit

6. How many hours do you spend studying?a) 0-2hrsb) 3-5hrsc) 6-7hrsd) 8-9hrs

7. What was your average grade for the End of Term Exams 2011?a) 90% and overb) 80-89%c) 70-79%d) 69% and under

8. Do you think that the amount of hours spent in extra-curricular activity have any effect on your academic performance?a) Yesb) No

9. If yes, in what way?………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

10. What do you think can be done to curb this problem?………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

11. How do you think the action stated above will help to fix the problem?………………………………………………………………………………………………………………………………………………………………………………………………

17