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# Applied math sba

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# Applied math sba

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### Applied math sba

1. 1. Name: Marlon Forrest Grade: 12 Subject: Applied Mathematics Unit: one Year submitted: 2013
2. 2. 2 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
3. 3. 3 PROJECT TITLE To investigate and to find out the causes of student engaging in an extracurricular activity and how it affect their academic performance.
4. 4. 4 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.
5. 5. 5 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.
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7. 7. 7 Figure1: Table showing number of respondents and their gender. Sex Number of Respondents Male 12 Female 18 The table above shows the gender of the respondents who were chosen for the investigation.
8. 8. 8 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. 20 8 2 0 5 10 15 20 25 track&field cadet quiz Number of students Types of Social Networks Figure 2: Bar graph showing the number of students who engage in the various club quiz cadet track&field
9. 9. 9 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. 0 1 2 3 4 5 6 7 8 track&field cadet quiz 8 5 3 Hours Social Networks Figure 3: Bar graph showing the average number of hours spent in each club weekly track&field cadet quiz
10. 10. 10 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. 50% 20% 20% 10% Figure 4: Pie chart showing reasons of students for using social networks Communication Leisure Trend personal benefits
11. 11. 11 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&field cadet quiz 0 1 2 3 4 5 6 7 8 9 track&field cadet quiz 4 6 9 Number of hours spent studying social networks Figure 5: Conical graph showing the number of hours spent studying track&field cadet quiz
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13. 13. 13 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 = =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%
14. 14. 14 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
15. 15. 15 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 Total Low 0 1 1 2 Medium 0 3 12 15 High 2 4 7 13 Total 2 8 20 30 Table showing the hours spentin an extracurricular activity by students and their average grades. Time (avg.) 2 5 8 Total Low 0.133 0.533 1.333 2 Medium 1 4 10 15 High 0.867 3.467 8.667 13 Total 2 8 20 30 Contingency table
16. 16. 16 Expected 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 ᵡ2 5% (4) = 9.488 O E (O-E)2 E 0 0.133 0.133 0 1 1 2 0.867 1.481 1 0.533 0.409 3 4 0.25 4 3.467 0.082 1 1.333 0.083 12 10 0.4 7 8.667 0.321 ∑O=30 ∑E=30 ∑(O-E)2 = 4.159 E
17. 17. 17 Since x2 = 4.159 <ᵡ2 5% (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. . y = -1.714x + 82.52 R² = 0.056 0 10 20 30 40 50 60 70 80 90 100 0 2 4 6 8 10 averagegradeinexam(%) time spent in extra curicular activity (hrs) Average grade Average grade Linear (Average grade)
18. 18. 18 Average number of hours spent in extracurricular activity Average xy x2 y2 8 38% 304 64 1444 5 50% 250 25 2500 8 52% 416 64 2704 8 55% 440 64 3025 8 56% 448 64 3136 8 57% 456 64 3249 5 58% 464 25 3364 8 60% 480 64 3600 8 62% 496 64 3844 8 63% 504 64 3969 8 65% 520 64 4225 8 66% 528 64 4356 5 68% 340 25 4624 8 70% 560 64 4900 8 72% 576 64 5184 5 74% 370 25 5476 8 75% 600 64 5625 8 80% 640 64 6400 5 80% 400 25 6400 8 80% 640 64+ 6400 5 80% 400 25 6400 2 81% 162 4 6561 5 82% 410 25 6724 8 83% 664 64 6889 5 84% 420 25 7056 8 84% 672 64 7056 2 85% 170 4 7225 8 86% 688 64 7396 8 87% 696 64 7569 8 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)]
19. 19. 19 = -1514664 =-1514664 =-1514664 √-1203840*-2732138280 √3.289057347*1015 57350303.81 = -0.0264
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22. 22. 22 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
23. 23. 23 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.
24. 24. 24 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.
25. 25. 25 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 coefficient N Population size. n Sample size.
26. 26. 26 Reference Fligner, M A. (2006). Introduction to the practice of statistics, New York, W. H. Freeman and company.
27. 27. 27
28. 28. 28 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) yes b) Sometimes c) No 3. If yes, which type ofextra-curricular activity? a) Track and Field b) Cadet c) Quiz 4. How long do you spend at the club weekly? a) 0-2hrs b) 3-4hrs c) 5-6hrs d) 7-8hrs 5. What is your reason for taking part in aextra-curricular activity? a) Communication b) Leisure
29. 29. 29 c) trend d) Personal benefit 6. How many hours do you spend studying? a) 0-2hrs b) 3-5hrs c) 6-7hrs d) 8-9hrs 7. What was your average grade for the End of Term Exams 2011? a) 90% and over b) 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) Yes b) 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? ……………………………………………………………………………………………… ………………………………………………………………………………………………