ADDITIONAL MATHEMATICS PROJECT WORK FORM 5 2014

Name :Andy Yanto I.C Number :970406-13-6053Class :5 BENEVOLENCE School :SMK ST. COLUMBA, MIRIAngka Giliran:Teacher Name:Mdm Pui Hui Foung

Title: Content:

Number Element Page1 Content2 Introduction3 Appreciation4 Brief history of data analysis5 Part 16 Part 27 Part 3

8 Part 49 Further Exploration10 Conclusion11 Reflection

Introduction We, as a form 5 student taking Additional Mathematics are required to carry out a project work while we are in form 5. This year, the Curriculum Development

Division, Ministry of Education has prepare a task for us. We are to complete one task that have been given by us from our teacher. This project must be done individually and must be completed within the time period given. During the period while I am doing this project and after completion of this Additional Mathematics project, I am able to gain valuable experience that cannot be bought and also able to:

-Apple and adapt a variety of problem solving strategies to solve routine and non-routine problems.-Experience classroom environments which are challenging, interesting and meaningful and hence improve our knowledge and also thinking skills.-Experience classroom environments where knowledge and skills are applied in meaningful ways in solving real-life problems.-Experience classroom environments where expressing ones mathematical thinking, reasoning and communication are highly recommended and encouraged.-Experience classroom environments that stimulates and enhances effective learning and help to focus in class.-Acquire effective mathematical communication through oral and writing, and able to use the language of mathematics to express mathematical ideas correctly and with precise.-Enhance acquisition of mathematical knowledge and skills through problem solving in ways that helps to increase the interest and also the confidence when solving problems.-Prepare ourselves for the demand of our future undertaking and in workplace.-Realize that mathematics is an important and powerful tool in solving real-life problems and hence develop positive attitude towards mathematics.-Train ourselves not only to be an independent learners but also to learn how to collaborate, to cooperate, and to share knowledge in a healthy environment.-Use technology especially the ICT in an effectively and also appropriate way.-Train ourselves in learning how to appreciate the intrinsic values of mathematics and to become more creative and innovative.-Help us to realize the importance and the beauty of mathematics no only in solving problems but also in our daily life.

Appreciation

First and foremost, I would like to express my gratitude and my thanks to my Additional Mathematics teacher, Madam Pui Hui Foung as she had given us countless important guidance and commitment during this project work. She has been a very supportive figure to us throughout the whole project.

Next, I would like to express my thank to my school for giving us this chance to do this Additional Mathematics project work.

Not forgetting our beloved parents who provided everything in this project work, suck as money, internet, reference books, computer and so on. They contribute their golden time and spirit on sharing their experience with us. Their support raise the spirit hidden in me to do this project smoothly and successfully.

Last but no least, I would like to express my thankfulness to my teacher and friend again for helping me throughout this project work. Without their help, I may not done this project smoothly.

A brief history of data analysisData analysis is a practice in which raw data is ordered and organized so that useful information can be extracted from it. The process of organizing and thinking about data is key to understanding what the data does and does not contain. There are variety of ways in which people can approach data analysis , and its notoriously easy to manipulate data

during the analysis phase to push certain conclusion or agendas. For this reason, it is important to pay attention when data analysis is presented , and to think critically about the data and the conclusions which were drawn. Raw data can take a variety of forms, including measurements, survey responses, and observation. In this raw form, this information can be incredibly useful, but also overwhelming. Over the course of the data analysis process, the raw data is ordered in a way which will be useful. For example, survey results may be tallied, so that people can see at a glance how many people answered the survey, and how people responded to specific questions. In the course of organizing the data, the trends often emerge, and these trends can be highlighted in the write-up of the data to ensure that readers take note. In a casual survey of ice cream preferences, for example, more women than men might express a fondness for chocolate, and this could be a point of interest for the researcher. Modeling the data with the use of mathematics and other tools can sometimes exaggerate such points of interest in the data, making them easier for the researcher to see. Charts, graphs, and textual write-ups of data are all forms of data analysis. These methods are designed to refine and distill the data so that readers can glean interesting information without needing to sort through all of the data on their own.summarizing data is often critical to supporting arguments made with that data, as is presenting the data in a clear and understandable way. The raw data may also be included in the form of an appendix so that people can look up specifics for themselves. When people encounter summarized data and conclusions, they should view them critically. Asking where the data is from is important, as is asking about the sampling method used to collect the data, and the size of sample. If the source of the data appears to have a conflict of interest with the type of data being gathered this can call the results into question. Likewise data gathered from a small sample or a sample which is not truly random may be questionable utility. Reputable researchers will always provide information about the data gathering techniques used, the source of funding, and the point of the data collection in the beginning of the analysis so that readers can think about this information while they review the analysis.

PART 1

Part 1:The importance of data analysis in everyday life

The importance of data analysis is the lifeline of any business. Whether one wants to arrive at some marketing decisions or fine-tune new product launch strategy, data analysis is the key to all the problems.

Data analysis can offer the following benefits:-Structuring the findings from survey research or other means of data collection-Acquiring meaningful insights from the dataset-Basing critical decisions from the findings-Ruling out human bias through proper statistical treatment

Example of data analysis:

This is an example of data analysis of loan balance

Mean

Mean is define as sum of all values of data divided by the number of data.

Meanwhile for mean of grouped data, the mean can be find in this following formula.

Mode

Mode is the value that occurs the most often in a set of data or with the highest frequency.

We can determine the modal class from a histogram graph to find the mode of the grouped data. The mode of the class can be represent by the tallest bar in the graph.

Median

Median is the centre value of a set of data after the data are arranged in ascending or descending order.

Median can be obtain through the this formula.

M=L+( N2 −F

f m )C

RangeRange can be find through the differences of largest value of data and the smallest value of data.

Range = Largest value of data – smallest value of data

Inter-quartile range

The inter-quartile range could be determine by the difference of third quartile and the first quartile. The inter-quartile range could be found by an ungrouped data in arrange order.The first quartile, Q1 , is a value that divides the values of data that are less than the median into two equal parts.The second quartile, Q2 , is a value that divides the set of data into two equal parts. The third quartile, Q3 , is the value that divides the values of data that are greater than the median into two equal parts.

Q1=L+( 14 N−F

f m )C

Q3=L+( 34 N−F

f m )C

INTER-QUARTILE RANGE = Q3 – Q1

Standard DeviationStandard deviation can be define by a quantity expressing by how much the members of a group differ from the mean value for the group.

The standard deviation can be obtain through this formula

σ=√(∑ fx2

∑ f )− x̄2

PART 2

NO NAME OF STUDENT MARKS1 AFRANSELL VLARIE 202 AINAA DIYANA BT SHAPHERI 133 AMIRUL AZIZI BIN ABDUL TAIB 324 ANDREA BAI DADIOS JALLONG 135 ANDY YANTO BIN MOHAMMAD ALI 306 APRIL LING 527 ARMAND ZAIN BIN MOHD ANTHONY 148 AYYBRENDA EDDA JOHN MUDA 39 BARRY NGUMBANG ANAK LLOYD 29

10 CALVIN MELUDA AK KENNETH 1711 CATHERINE LAURA KING 1312 CHIN KIAN YU 3013 CHRISTINE PHANG SYN YOUNG 7514 DYLAN LIM WEE LEE 10

15 ERICSON MAHESH LUSUI A/L RAKESH 1916 FILADELFIA ANAK JOSALI 417 GEOFFEREY TANG CHOK CHUONG 4218 GEORGE WONG SIN HONG 3619 GIBSON PANYAU AK JACKSON RODI 2120 HENG YI ZHI 7121 HWONG HARN HYEE 1822 JACKY ONG CHEN YONG 3223 JESSICA KHOO SIOK LIN 3224 LEE KAH YII 2125 LIM XIN YING 5026 LING FUNG PING 8527 MACWALLACE ANAK MARKUS JUTI 3628 MAY LING 6829 MICHELLE KANG SIAW HANG 7330 MOHAMAD SHAFIQ BIN MOHAMAD ADNAN 831 MOHAMMAD IZZUANDY BIN YUSOP 832 MUHAMMAD ZUIDIQAR BIN ARUN 2333 NUR ATHILAH BINTI USOP 2534 PHILIP ANAK PATRICK 1635 SAMATHA LIGENG KATO 1136 TCHONG JEAN 4037 VANESSA AK ROY WILSON 2338 VANNYLISSA URAI 20

2(A)Mark Frequency , f Cumulative

frequency ,fcMidpoint ,x Fx

1-5 2 2 3 66-10 3 5 8 24

11-15 5 10 13 6516-20 6 16 18 10821-25 5 21 23 11526-30 3 24 28 8431-35 3 27 33 9936-40 3 30 38 11441-45 1 31 43 4346-50 1 32 48 4851-55 1 33 53 5356-60 0 33 58 0

61-65 0 33 63 066-70 1 34 68 6871-75 3 37 73 21976-80 0 37 78 081-85 1 38 83 83

38 ∑fx 1129

(I)The Mean

x̄=∑ fx

∑ f

=112938 =29.71

(II)The ModeMethod 1: The modal cass=16-20

Method 2:by using graph

(III)The MedianMethod 1:By using formula

M=L+( N2 −F

f m )C

=19 .5+(12

(38)−14

22 )(10 )

=21 .77

Method 2:by graph

0 10 20 30 40 50 60 70 80 900

5

10

15

20

25

30

35

40

Y-Values

Y-Values

2(B)The best to represent measure of central tendency for the class mathematics performance

score is MEAN. This is because It can be used with both discrete and continuous data, although its use is most often with continuous data. The mean is equal to the sum of all the values in the data set divided by the number of values in the data set.

PART 3

Part 3

(I)The inter-quartile range

Mark Frequency , f Cumulative frequency ,fc

Midpoint ,x Fx Upper boundary

1-5 2 2 3 6 5.56-10 3 5 8 24 10.5

11-15 5 10 13 65 15.516-20 6 16 18 108 20.521-25 5 21 23 115 25.526-30 3 24 28 84 30.531-35 3 27 33 99 35.536-40 3 30 38 114 40.541-45 1 31 43 43 45.546-50 1 32 48 48 50.551-55 1 33 53 53 55.556-60 0 33 58 0 60.561-65 0 33 63 0 65.566-70 1 34 68 68 70.571-75 3 37 73 219 75.576-80 0 37 78 0 80.581-85 1 38 83 83 85.5

∑fx 1129

Q1= L1+(N4– F1

f 1¿c

= 10.5 +(9.5−55

¿5

= 15 marks

Q3 = L3+(3N4– F3

f 3¿ c

=35.5 +(28.5−273

¿5

= 38 marksInterquartile range = Q3 – Q1 = 38 - 15 = 23 marks

(II) The standard deviation

Mean , ~x = ∑ fx

∑ f

= 112938

= 29.71 marks

Variance , Q2= ∑fx

2

∑ f - ~x2

= 5005738 – 29.712

= 434.61 marks

Standard deviation , Q = √434.61

= 20.85 marks

Mark Frequency , f Midpoint ,x Fx Fx2

1-5 2 3 6 186-10 3 8 24 192

11-15 5 13 65 84516-20 6 18 108 194421-25 5 23 115 264526-30 3 28 84 235231-35 3 33 99 326736-40 3 38 114 433241-45 1 43 43 184946-50 1 48 48 230451-55 1 53 53 280956-60 0 58 0 061-65 0 63 0 066-70 1 68 68 462471-75 3 73 219 1598776-80 0 78 0 081-85 1 83 83 6889

Fx=1129 Fx2=50057

The advantages of using standard deviation as compared with inter-quartile in representing the data is that :

Standard deviation makes use of all data to calculate the spread of data from average while range only uses two data which is the largest value data and the smallest value data, so standard deviation is a more accurate measure.

In addition, standard deviation measures the spread of data from the MEAN while range measures only the two extreme values which is the difference between the largest value and smallest value data.

Meanwhile for  the inter-quartile range are much less sensitive to changes in the data than the standard deviation. If a single value changes then the standard deviation, by definition, will also change.

Hence the standard deviation is a more powerful summary measure as it makes more comprehensive use of the entire dataset.

PART 4

Part 4(A)

NO CLASS NAME OF STUDENT MARK

[ FIRST

TRIAL ]

1 5 ATTENTIVENESS AGNES KONG EE FUI 64

2 ALDEN JONG SHI XIAN 50

3 ALICIA LIONG SHII YIE 93

4 AMELIA GOH SHEY NING 50

5 AMELIE PETER AFFERY 85

6 APPLE HII NING YUN 50

7 CALVIN KONG KAI WEN 50

8 CARMEN KRYSTER LIM CHIEN MIEN 46

9 CHEN EE XIN 83

10 CHIEW KIT YEE 55

11 CHONG PING SHENG 50

12 DARYLL LAI TAY MAY 67

13 EMILY WONG SIAO QING 56

14 GRACE WUI SIEW SAN 50

15 HIUNG CHIEN YU 71

16 HO YING SIEN 60

17 ILYAS BIN YUSNAWANNIE 50

18 JASMINE PUI EN HUI 61

19 JEREMIAH JONG 40

20 JONG CHAO YU 72

21 LAM SU ANN 47

22 LEE YIET YIEN 73

23 LING KWONG YAM 62

24 LOH JIEN HWA 60

25 MICHELLE WONG SIE PING 79

26 RACHAEL CHIN SUE MEI 50

27 RENEE CHIU ZHI XUAN 60

28 SHIRLEY LAU HUI NING 79

29 VALENTINE LING ANN 67

30 VALERIE SIM YEN ROU 94

31 WONG PIK SZE 93

32 YIP CHUN FAI 87

1 5 BENEVOLENCEAFRANSELL VLARIE

40

2AINAA DIYANA BT SHAPHERI

48

3AMIRUL AZIZI BIN ABDUL TAIB

40

4ANDREA BAI DADIOS JALLONG

45

5ANDY YANTO BIN MOHAMMAD ALI

50

6APRIL LING

50

7ARMAND ZAIN BIN MOHD ANTHONY

45

8AYYBRENDA EDDA JOHN MUDA

45

9BARRY NGUMBANG ANAK LLOYD

51

10CALVIN MELUDA AK KENNETH

50

11CATHERINE LAURA KING

30

12CHIN KIAN YU

60

13CHRISTINE PHANG SYN YOUNG

65

14DYLAN LIM WEE LEE

40

15ERICSON MAHESH LUSUI A/L

RAKESH 40

16FILADELFIA ANAK JOSALI

35

17GEOFFEREY TANG CHOK CHUONG

46

18GEORGE WONG SIN HONG

53

19GIBSON PANYAU AK JACKSON RODI

40

20HENG YI ZHI

56

21HWONG HARN HYEE

40

22JACKY ONG CHEN YONG

51

23JESSICA KHOO SIOK LIN

61

24LEE KAH YII

40

25LIM XIN YING

69

26LING FUNG PING

90

27MACWALLACE ANAK MARKUS JUTI

48

28MAY LING

75

29MICHELLE KANG SIAW HANG

85

30MOHAMAD SHAFIQ BIN MOHAMAD

ADNAN 24

31MOHAMMAD IZZUANDY BIN YUSOP

19

32MUHAMMAD ZUIDIQAR BIN ARUN

25

33NUR ATHILAH BINTI USOP

41

34PHILIP ANAK PATRICK

40

35SAMATHA LIGENG KATO

30

36TCHONG JEAN

58

37VANESSA AK ROY WILSON

38

38VANNYLISSA URAI

29

1 5 COMPASSION ALVIN SIM JIA LE 70

2 AMANDA LAU HUI SHEAN 57

3 AMELIA HO JIA LIN 60

4 AMMY NAWIE ANAK FRANCIS 22

5 AMY JANE ANAK BANSI 32

6 ANDY WONG SIEW TUANG 46

7 ANISAH ALIEA AKMAL BINTI ROSLI 32

8 BILLY AGGLAN ROBERT GALANG 14

9 CALVIN PANAI NUWEL 37

10 CHIA SHI TENG 60

11 CHONG YING QI 40

12 CLARINE WONG XIN JIE 18

13 FAM CHOON FATT 30

14 HAMILTON TAN YUNG FUI 40

15 IVIN THEN KAI XIN 12

16 JOSLYN SIEW ZI TONG 30

17 LABELLE ZEE YULO 15

18 MAYSILDA AK JALAN 50

19 NATALIE SINGA 30

20 NEENA BINTI MOHD QISTY 40

21 NICOLE GARNETTE PHILIP 20

22 NUR SHAFINAZ BINTI SEHAT 22

23 NURHAZIQAH AFFIFAH BINTI

HANAFIAH

39

24 RICHARD KONG CHEE WEI 4

25 SAMUEL DAVIES ANAK REBU 50

26 SHREEIN SEMUEL 40

27 WONG NGIE YEW 50

28 YVONNE LAU 56

1 5 DILIGENT ATHIRAH SYAHIRA BINTI JASNIE 13

2 AWG KU MOHD ARHAFIZ NIK

YNGWIE BIN MOHD ARAFAH

8

3 CALEB THO 4

4 GABRIEL ENGAN GAU 15

5 HIZSRIN BIN BUJANG 35

6 INTAN SHAFINAZ BINTI KARIM 20

7 JASMINE SIA YOE TUNG 35

8 LIEW JOON YEN 2

9 MARK VOON 15

10 MAURISA WINNNIE ANAK ALBERT

RENGGA

5

11 MOHD FIRDAUS BIN BUYONG 11

12 MOHD KHAIRUL HAFIZAN 16

13 NICHOLAS JAMBALAK WILSON

JANANG

12

14 NUR AZIRA BINTI ABD RAHMAN 8

15 NURRUL NAZURAH BINTI SOFPIAN 6

16 NURUL SHAHIERA BINTI ISMAIL 15

17 OLOVIA NATASA DISMAS 14

18 POOK XIN YUAN 35

19 PRESLEY TINGGIE ANAK KENNEDY 13

20 PRISCA SANDU ANAK ANDEW UNAL 10

21 STANLEY TANG ENG KIET 23

22 VONG JIANG SIANG 4

Part 4(B)

B(I):The Mean

x̄=∑ fx

∑ f

= 183138

= 48.18

Marks Frequency , f

Midpoint , x

fx Cumulative frequency

Upper boundary

15-19 1 17 17 1 19.520-24 1 22 22 2 24.525-29 2 27 54 4 29.530-34 2 32 64 6 34.535-39 2 37 74 8 39.540-44 9 42 378 17 44.545-49 6 47 282 23 49.550-54 6 52 312 29 54.555-59 2 57 114 31 59.560-64 2 62 124 33 64.565-69 2 67 134 35 69.570-74 0 72 0 35 74.575-79 1 77 77 36 79.580-84 0 82 0 36 84.585-89 1 87 87 37 89.590-94 1 92 92 38 94.5

38 1831

B(II):The modeModal class = 40-44

B(III):The MedianMethod 1 : Formula

=39 . 5+(12

(120)−45

46 )(20 )

=46 . 02

B(IV):The inter-quartile range

Q1= L1+(N4– F1

f 1¿c

= 39.5 +(9.5−89

¿5

= 40.33

Q3 = L3+(3N4– F3

f 3¿ c

=49.5 +(28.5−236

¿5

= 54.08

Interquartile range = Q3 – Q1 = 54.08 – 40.33 = 13.75

B(V):The Standard Deviation

Mean , ~x = ∑ fx

∑ f

= 183138

= 48.18

Variance , Q2= ∑fx

2

∑ f - ~x2

= 97497

38 – 48.182

= 244.4

Marks Frequency , f Midpoint , x fx fx2

15-19 1 17 17 28920-24 1 22 22 48425-29 2 27 54 145830-34 2 32 64 204835-39 2 37 74 273840-44 9 42 378 1587645-49 6 47 282 1325450-54 6 52 312 1622455-59 2 57 114 649860-64 2 62 124 768865-69 2 67 134 897870-74 0 72 0 075-79 1 77 77 592980-84 0 82 0 085-89 1 87 87 756990-94 1 92 92 8464

38 1831 97497

Standard deviation , Q = √244.4

= 15.63

Based on the data that I have collected, I found out that the result in first trial examination is better than the first semester. Because of the mode ,the mean, the median, the inter-quartile range and the standard deviation for the first trial examination is higher than the first semester.

Further Exploration:

Based on the interview that I had made, there are few learning strategies that had been taken by my classmates and also my schoolmates in pursuit of excellence:(I)Make a timetable(II)Know how to use the time wisely(III)Do more exercise to improve skill(IV)Help each other because it help us to share knowledge(V)Ask around your classmate or teacher if we do not understand the question(VI)Focus in class

Conclusion:

After doing this Additional Mathematics project, I realize that Additional Mathematics is very important in daily life.About this project, overall, it’s quite joyful and interesting because I need to plan it carefully and with systematic because it is about my future. In fact, the further exploration is a good session because it can open my mind and know more about the importance of data analysis and statistic in daily life.

Reflections:

From this project, I learnt the importance of perseverance as time had been invested to ensure the completion and excellence of this project. Also, I learnt to be thankful and appreciative. This is because, I am able to apply my mathematical knowledge in daily life and appreciate the beauty of mathematics. All and all, I

have spent countless hours doing this project. I realize that this subject is a compulsory subject to me. Without it, I could not fulfill my big dreams and wishes.