addmath+two+of+the+test

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ADDITIONAL MATHEMATICS

PROJECT WORK 1/2014

NAME: ANDY YANTO

SCHOOL: SMK SAINT COLUMBA MIRI

CLASS: 5 BENEVOLENCE

I.C. NUMBER: 970930-13-5970

ANGKA GILIRAN:

TEACHER`S NAME: MDM.PUI HUI FOUNG


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TITLE:


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CONTENT


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NUM

BER

ELEMENT PAGE

1. CONTENT 3-4

2. INTRODUCTION 5-6

3. APPRECIATION 7-8

4. BRIEF HISTORY OF DATA ANALYSIS 9-11

5. PART 1 12-19

6. PART 2 20-27

7. PART 3 28-32

8. PART 4 33-40

9. FURTHER EXPLORATION 41-

10. CONCLUSION

11. REFLECTION


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INTRODUCTION


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Student who taking Additional Mathematics subject in SPM are required to

carry out a project work while they are in Form 5 . The Curriculum

Management Sector,Sarawak Education Department has prepared the task for

us . We are expected to submit the project work within three weeks from the

first day the task is being administrated to us . This project must be done

individually . Upon completion of the Additional Mathematics Project Work,I

am able to gain valuable experiences and able to :

Apply and adapt a variety of problem solving strategies to solve routineand non-routine problems.

Experience classroom environments which are challenging,interesting andmeaningful.

Experience classroom environments where knowledge and skills areapplied in meaningful ways in solving real-life problems.

Experience classroom environments where expressing ones mathematicalthinking, reasoning and communication are highly encourage and

expected.

Experience classroom environments that stimulate and enhance effectivelearning.

Acquire effective mathematical communication through oral , writing anduse the language of mathematics to express mathematical ideas correctly

and precisely.

Enhance acquisition of mathematical knowledge and skills throughproblem solving in ways that increase interest and confidence. Prepare myself for the demand of my future undertakings and in

workplace.

Realize that additional mathematics is an important and powerful tool insolving real-life problems and hence develop positive attitude towards

additional mathematics.

Train myself not only to be independent learner but also tocollaborate,cooperate and share knowledge in an engaging and healthy

environment. Use technology especially the ICT appropriately and effectively. Train myself to appreciate the intrinsic values of additional mathematicsand to become more creative and innovative.


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APPRECIATION


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First and foremost, I would like to thank my Additional Mathematics

teacher,Mdm. Pui Hui Foung as she had gave me important guidance

and commitment during this project work . She had try her best to

teach me patiently until I had finished this project work when I faced

some difficulties on doing task.

I would also like to give thanks to all my friends for helping me and

always supporting me to complete this project work. They had shared

their ideas and provided me some help on solving problems . We

helped each other until we had finished this project work. This project

work would never have its conclusion without their help.

Furthermore, I would like to express my gratitude to my beloved

parents who provided everything needed in this project work such as

money. They contribute their time and spirit on sharing their

experience with me. Their support may raise the spirit in me to do this

project work smoothly. They had also always been my side and I hoped

they would still be there in the future.

In a nutshell, I would like to thank God for giving me energy,strength and healthy to carry out this project work.


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BRIEF HISTORY OF

DATA ANALYSIS


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Data 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 a variety of ways in which people can approach data analysis,

and it is notoriously easy to manipulate data during the analysis phase to push certain conclusions 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 observations.

In its 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, 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 the 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 of 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.

Bar graph


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Pie graph

Line graph

Favorite Foods

Pizza

33%

Hot Dogs

34%

Hamburgers33%

Pizza

Hot Dogs

Hamburgers

Price Per Barrel of Light Crude Oil Leaving Saudi

Arabia on Jan. 1

$0.00

$2.00

$4.00

$6.00

$8.00

$10.00

$12.00$14.00

$16.00

1973 1974 1975 1976 1977 1978 1979

Years

PricesPerBarrel


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PART 1


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Data analysis is important to businesses will be an understatement.In fact,no business can survive

without analyzing available data.There are many benefits of data analysis.However,the most important

ones are data analysis helps in structuring the findings from different sources of data collection like

survey research.It is again very helpful in breaking a macro problem into micro parts.Data analysis acts

like a filter when it comes to acquiring meaningful insights out of huge data-set.Every researcher has

sort out huge pile of data that he or she has collected,before reaching to a conclusion of the research

question.Mere data collection is of no use to the researcher.Data analysis proves to be crucial in this

process.It provides a meaningful base to critical decisions.It helps to create a complete dissertation

proposal.One of the most important uses of data analysis is that it helps in keeping human bias away

from research conclusion with the help of proper statistical treatment.With the help of data analysis,a

researcher can filter both qualitative and quantitative data for an assignment writing projects.Thus,it

can be said that data analysis is of utmost important for both the research and the researcher. In

another words ,data analysis is important for a doctor to diagnose the problem of the patient before

giving him any treatment. For example, if we can analyze the previous weather data, we can predict

future temperature. On the other hand, many considerations will be made for those who invested much

money in the Stock Market in Hong Kong. And these considerations also included the prediction of the

future trend by analyzing the previous data. In this project, a software package will be developed for

time series data prediction, based on Fuzzy system algorithms to data mining. This system predicts the

future trend of a set of data, based on the previous data. Two kinds of fuzzy models, Nearest

Neighborhood Clustering and Table Look up Scheme, are used to develop this system. Other

components of this system included inference engine, fuzzifier and defuzzifier. Our system accepts

multiple inputs and has single output (MISO). This software is developed by Visual Basic, which is a kind

of computer programming language. A graphical user interface (GUI) is designed with functions on

graphical plotting. The accuracy of prediction is represented by Mean Square Error (MSE) and Mean

Absolute Performance Error (MAPE).


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Collecting data can be easy and fun. But sometimes it can be hard to tell other people aboutwhat you have found. Thats why we use statistics. Two kinds of statistics are frequently used to

describe data. They are measures of central tendency and dispersion.

Mean,median and mode are measures of central tendency. They help summarize a bunch of

scores with a single number. Suppose you want to describe a bunch of data that you collected to a

friend for a particular variable like height of students in your class. One way would be to read eachheight you recorded to your friend. Your friend would listen to all of the heights and then come to a

conclusion about how tall students generally are in your class But this would take too much time.

Especially if you are in a class of 200 or 300 students! Another way to communicate with your

friend would be to use measures of central tendency like the mean, median and mode. They helpyou summarize bunches of numbers with one or just a few numbers. They make telling people

about your data easy.

Range, variance and standard deviation are measures of dispersion. These help you to know

the spread of scores within a bunch of scores. For example, if you were describing the heights ofstudents in your class to a friend, they might want to know how much the heights vary. Are all the

men about 5 feet 11 inches within a few centimeters or so? Or is there a lot of variation where somemen are 5 feet and others are 6 foot 5 inches? Measures of dispersion like the range, variance and

standard deviation tell you about the spread of scores in a data set. Like central tendency, they helpyou summarize a bunch of numbers with one or just a few numbers.

Types of measures of central tendency

A. MEAN

- commonly referred to as the average or arithmetic mean.

- most widely used measure of central location.

-mean can measure by group or ungroup method.

Ungroup :

23,20,17,18,15,17,16,20

Mean=

=

=18.25


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Group :

Mass (kg) 31-35 36-40 41-45 46-50 51-55 56-60

Number of students 3 8 10 18 9 2

Median ,m = L+(

=45.5 +(

= 46.6 kg

C. MODE

- is the value in the data set that occurs most frequently.

-mode can measure by group or ungroup method.

Ungroup :

2,5,7,6,10,7,9,8,4 2,8,11,9,4,5,13,9

Mode = 7 , Mode = 9

Group :

Mass (kg) Frequency Cumulative frequency Upper boundary

31-35 3 3 35.5

36-40 8 11 40.5

41-45 10 21 45.5

46-50 18 39 50.5

51-55 9 48 55.5

56-60 2 50 60.5

Mass (kg) 30-39 40-49 50-59 60-69 70-79

Frequency 8 11 14 7 5


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Modal class = 50-59 kg

Mode = 52.5 kg

Types of measures of dispersion

A. RANGE

-the difference between lowest and highest values

42 , 40 , 45 , 32 ,28

Range = 45 28

=17

B. VARIANCE

-the average of the squared differences from the mean.

-can measure by group or ungroup method

Ungroup :

5 , 6 , 7 , 2 , 3

Variance =

= 3.44


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Group :

-

Pocket money (RM) 2 3 4 5 6 7


x f fx 2 12 24 48

3 16 48 144

4 15 60 240

5 14 70 350

6 12 72 432

7 11 77 539

Variance , = -

=

-

= 2.658

C . STANDARD DEVIATION

-the Standard Deviation is a measure of how spread out numbers are.

- can measure by group or ungroup method

Ungroup :

5 , 6 , 7 , 2 , 3

Variance,= = 3.44

Standard deviaton , Q = = 1.855


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Group :

Pocket money (RM) 2 3 4 5 6 7


x f fx 2 12 24 48

3 16 48 144

4 15 60 240

5 14 70 350

6 12 72 432

7 11 77 539

Variance , = -

=

-

= 2.658

Standard deviation , Q = = 1.63


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PART 2


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Additional mathematics first test score for 5 Benevolence

Marks Number of students

1-5 2

6-10 3

11-15 516-20 6

21-25 5

26-30 3

31-35 3

36-40 3

41-45 1

46-50 1

51-55 1

56-60 0

61-65 066-70 1

71-75 3

76-80 0

81-85 1

Marks Frequency ,

f

Midpoint ,

x

fx Cumulative

frequency

Upper

boundary

1-5 2 3 6 2 5.5

6-10 3 8 24 5 10.5

11-15 5 13 65 10 15.5

16-20 6 18 108 16 20.5

21-25 5 23 115 21 25.5

26-30 3 28 84 24 30.5

31-35 3 33 99 27 35.5

36-40 3 38 114 30 40.5

41-45 1 43 43 31 45.5

46-50 1 48 48 32 50.5

51-55 1 53 53 33 55.5

56-60 0 58 0 33 60.5

61-65 0 63 0 33 65.5

66-70 1 68 68 34 70.5

71-75 3 73 219 37 75.5

76-80 0 78 0 37 80.5

81-85 1 83 83 38 85.5


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(a) Instead , the table is set up , calculate

(i) the mean

(ii) the mode

(iii) the median

(b) From your results , what kind of measure of central

tendency best to represent your class additional

mathematics performance scores and explain why .


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ANSWER :

Method 1 : ( Calculate by using formula)

(a)(i) Mean , = =

= 29.71 marks

(ii) Mode = 16-20 marks

(iii)Marks Frequency , f Cumulative

frequency

Upper boundary

1-5 2 2 5.5

6-10 3 5 10.5

11-15 5 10 15.5

16-20 6 16 20.5

21-25 5 21 25.526-30 3 24 30.5

31-35 3 27 35.5

36-40 3 30 40.5

41-45 1 31 45.5

46-50 1 32 50.5

51-55 1 33 55.5

56-60 0 33 60.5

61-65 0 33 65.5

66-70 1 34 70.5

71-75 3 37 75.5

76-80 0 37 80.5

81-85 1 38 85.5


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(iii) Median =

= 19.5Thus , median = 24 marks


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(b) Type of measure central tendency have mode , mean and median.

Median is best to represent my class additional mathematics

performance scores.This is because the data of 5 Benevolence

additional mathematics first test score are very skew and there

are a huge number of outliers. It is more widely known than

the trimmed mean, it may be good when your audience is not

statistically sophisticated. The classic example is income. In

most populations, incomes will be highly right skewed. That

is, there will be some people whose incomes are much, much

higher than all the others. When the data are right skewed,

the mean will be higher than the median. When they are left

skewed (much less common) the mean will be lower than the

median.


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PART 3


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Measure of dispersion of data is the

method to show the deviation from the

mean of data. From the table that has been

built, calculate

(i)The inter-quartile range

(ii)The standard deviation

Explain the advantages of using standard

deviation as compared with interquartile

range in representing the data.


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(i)the interquartile range

Q1= L1+(

= 10.5 +( = 15 marks

Q3 = L3+(

=35.5 +(

= 38 marks

Interquartile range = Q3 Q1

= 38 - 15

= 23 marks

Marks Frequency ,

f

Cumulative

frequency

Upper

boundary

1-5 2 2 5.5

6-10 3 5 10.5

11-15 5 10 15.5

16-20 6 16 20.5

21-25 5 21 25.5

26-30 3 24 30.5

31-35 3 27 35.5

36-40 3 30 40.5

41-45 1 31 45.5

46-50 1 32 50.5

51-55 1 33 55.5

56-60 0 33 60.5

61-65 0 33 65.5

66-70 1 34 70.5

71-75 3 37 75.5

76-80 0 37 80.5

81-85 1 38 85.5


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(ii) standard deviation

Mean ,

=

=

= 29.71 marks

Variance , = -

=

= 434.61 marks

Standard deviation , Q = = 20.85 marks

Marks Frequency , f Midpoint , x fx 1-5 2 3 6 18

6-10 3 8 24 192

11-15 5 13 65 845

16-20 6 18 108 1944

21-25 5 23 115 2645

26-30 3 28 84 2352

31-35 3 33 99 3267

36-40 3 38 114 4332

41-45 1 43 43 1849

46-50 1 48 48 2304

51-55 1 53 53 2809

56-60 0 58 0 061-65 0 63 0 0

66-70 1 68 68 4624

71-75 3 73 219 15987

76-80 0 78 0 0

81-85 1 83 83 6889

= 50057


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Standard deviation makes use of all data to calculate

the spread of data from average while range only uses two

data , that is the largest value data and the smallest valuedata, so standard deviation is a more accurate measure.If a

single value changes , then the standard deviation will also

change. Hence the standard deviation is a more powerful

summary measure as it makes more comprehensive use of

the entire dataset. However,situations when the mean might

not be an appropriate measure of centre were

discussed previously. If the mean is not a meaningfulsummary of the centre of the data, then it follows that the

standard deviation, which is calculated from distances

around the mean, will not be a useful summary of the spread

of the values.Therefore, if distributional assumptions can be

made and there are adequate numbers in the sample to

check those assumptions , then the mean and standard

deviation should be used to quantify the centre and spreadof the measurements.


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PART 4


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Additional mathematics first trial score for 5 Benevolence

Marks Number of students

15-19 1

20-24 1

25-29 230-34 2

35-39 2

40-44 9

45-49 6

50-54 6

55-59 2

60-64 2

65-69 2

70-74 0

75-79 180-84 0

85-89 1

90-94 1

Marks Frequency ,

f

Midpoint ,

x

fx Cumulative

frequency

Upper

boundary

15-19 1 17 17 1 19.5

20-24 1 22 22 2 24.5

25-29 2 27 54 4 29.5

30-34 2 32 64 6 34.5

35-39 2 37 74 8 39.5

40-44 9 42 378 17 44.5

45-49 6 47 282 23 49.5

50-54 6 52 312 29 54.5

55-59 2 57 114 31 59.5

60-64 2 62 124 33 64.5

65-69 2 67 134 35 69.5

70-74 0 72 0 35 74.5

75-79 1 77 77 36 79.5

80-84 0 82 0 36 84.5

85-89 1 87 87 37 89.5

90-94 1 92 92 38 94.5


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(a) From the information obtained, calculate

(i) the mean

(ii) the mode

(iii) the median

(iv) the interquartile range

(v) the standard deviation

Make a comparison of the data analysis for First Test and First

Trial Examination.


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ANSWER :

(a)(i) Mean , = =

= 48.18 marks

(ii) Mode class = 40-44 marks

Mode = 42.5 marks


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(iv) the interquartile range

Q1= L1+(

= 39.5 +( = 40.33 marks

Q3 = L3+(

=49.5 +(

= 54.08 marks

Interquartile range = Q3 Q1

= 54.08 40.33

= 13.75 marks

Marks Frequency , f Cumulative

frequency

Upper boundary

15-19 1 1 19.5

20-24 1 2 24.5

25-29 2 4 29.5

30-34 2 6 34.5

35-39 2 8 39.5

40-44 9 17 44.5

45-49 6 23 49.5

50-54 6 29 54.5

55-59 2 31 59.5

60-64 2 33 64.5

65-69 2 35 69.5

70-74 0 35 74.5

75-79 1 36 79.5

80-84 0 36 84.5

85-89 1 37 89.5

90-94 1 38 94.5


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(v) standard deviation

Mean , =

=

= 48.18 marks

Variance , = -

=

= 244.4 marks

Standard deviation , Q = = 15.63 marks

Marks Frequency , f Midpoint , x fx

15-19 1 17 17 289

20-24 1 22 22 484

25-29 2 27 54 1458

30-34 2 32 64 2048

35-39 2 37 74 2738

40-44 9 42 378 15876

45-49 6 47 282 13254

50-54 6 52 312 16224

55-59 2 57 114 6498

60-64 2 62 124 7688

65-69 2 67 134 8978

70-74 0 72 0 0

75-79 1 77 77 5929

80-84 0 82 0 0

85-89 1 87 87 7569

90-94 1 92 92 8464

= 97497


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FURTHER

EXPLORATION


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CONCLUSION


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In the process of conducting this project, I have

learnt that perseverance pays off, especially when I

obtain just a small reward for all my hard work. For

me, succeeding in completing this project work has

been reward enough. I have also learnt that additional

mathematics is used everywhere in our real life from

the most simple things. Besides, I have also learnt

many moral values from this project work. This

project work had taught me to be more confidentwhen doing something especially the homework given

by teachers. I also learnt to become a more disciplined

student who is punctual and independent after

completed my project work.


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REFLECTION


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