Addmath Project Work Form5 2014 ( Official )

8/12/2019 Addmath Project Work Form5 2014 ( Official )

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NAME: DANIEL SOH KUNG MIN

CLASS: 5 ALLAMANDA

I/C NO: 970510-13-5245

TEACHERS NAME: MR HII HIONG CHEONG


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CONTENT


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CONTENT

CHAPTERS TITLES PAGES

1 CONTENT

2 INTRODUCTION

3 APPRECIATION

4 A BRIEF HISTORY OF

STATISTICS

5 PART A

6 PART B7 PART C

8 FURTHER EXPLORATION

9 CONCLUSION

10 REFLECTION


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INTRODUCTION


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INTRODUCTIONWe students 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

prepared two tasks for us. We are to choose and complete only

ONE task based on our area of interest. Upon completion of the

Additional Mathematics Project Work, it is hoped that students

will gain valuable experiences and able to:

Apply 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 their 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 encouraged and expected.


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Experience classroom environments that stimulates and

enhances effective learning.

Acquire effective mathematical communication through oral

and writing, and to use the language of mathematics to

express mathematical ideas correctly and precisely.

Enhance acquisition of mathematical knowledge and skills

through problem-solving in ways that increases interest and

confidence.

Prepare ourselves for the demands of our future

undertakings and in workplace.

Realise 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 independent learners but also

to collaborate, to cooperate, and to share knowledge in an

engaging and healthy environment.

Use technology especially the ICT appropriately and

effectively.

Train ourselves to appreciate the intrinsic values of

mathematics and to become more creative and innovative.

Realise the importance and beauty of mathematics.


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APPRECIATION


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APPRECIATION

First and foremost, I would like to thank my Additional

Mathematics teacher, Mr Hii Hiong Cheong as he gives us

important guidance and commitment during this project work. He

has been a very supportive figure throughout the whole project.

Next, we would like to thank our school for giving us the

chance to create this project work. School also provides us space

to discuss and carry out this project work.

Not forgetting our beloved parents who provided everything

needed in this project work, such as money, Internet, books,

computer and so on. They contribute their time and spirit on

sharing their experience with us. Their support may raise the spirit

in us to do this project work smoothly.

Last but not least, I would also like to thank all the teacher

and my friend for helping me collect the much needed data and

statistics for this. Not forgetting too all the other people who

were involved directly or indirectly towards making this project a

reality.

I thank you all


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A BRIEF HISTORY OFSTATISTICS


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A BRIEF HISTORY OF STATISTICS

The History of statistics can be said to start around 1749although, over time, there have been changes to theinterpretation of the word statistics . In early times, the meaningwas restricted to information about states. This was laterextended to include all collections of information of all types, andlater still it was extended to include the analysis andinterpretation of such data. In modern terms, "statistics" meansboth sets of collected information, as in national accounts and

temperature records, and analytical work whichrequires statistical inference.

Statistical activities are often associated with modelsexpressed using probabilities, and require probability theory forthem to be put on a firm theoretical basis: see History ofprobability.

A number of statistical concepts have had an importantimpact on a wide range of sciences. These include the design ofexperiments and approaches to statistical inference suchas Bayesian inference, each of which can be considered to havetheir own sequence in the development of the ideas underlyingmodern statistics.

By the 18th century, the term " statistics " designatedthe systematic collection of demographic and economic data bystates. In the early 19th century, the meaning of "statistics"

broadened to include the discipline concerned with the collection,summary, and analysis of data. Today statistics is widelyemployed in government, business, and all the sciences.Electronic computer s have expedited statistical computation, andhave allowed statisticians to develop "computer-intensive"methods.
http://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Sovereign_statehttp://en.wikipedia.org/wiki/National_accountshttp://en.wikipedia.org/wiki/Temperature_recordhttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Theory_(mathematical_logic)http://en.wikipedia.org/wiki/History_of_probabilityhttp://en.wikipedia.org/wiki/History_of_probabilityhttp://en.wikipedia.org/wiki/Design_of_experimentshttp://en.wikipedia.org/wiki/Design_of_experimentshttp://en.wikipedia.org/wiki/Bayesian_inferencehttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Official_statisticshttp://en.wikipedia.org/wiki/Demographichttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Computerhttp://en.wikipedia.org/wiki/Computational_statisticshttp://en.wikipedia.org/wiki/Computational_statisticshttp://en.wikipedia.org/wiki/Computerhttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Demographichttp://en.wikipedia.org/wiki/Official_statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Bayesian_inferencehttp://en.wikipedia.org/wiki/Design_of_experimentshttp://en.wikipedia.org/wiki/Design_of_experimentshttp://en.wikipedia.org/wiki/History_of_probabilityhttp://en.wikipedia.org/wiki/History_of_probabilityhttp://en.wikipedia.org/wiki/Theory_(mathematical_logic)http://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Temperature_recordhttp://en.wikipedia.org/wiki/National_accountshttp://en.wikipedia.org/wiki/Sovereign_statehttp://en.wikipedia.org/wiki/Statistics


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The term " mathematical statistics " designates the mathematicaltheories of probability and statistical inference, which are usedin statistical practice. The relation between statistics andprobability theory developed rather late, however. In the 19thcentury, statistics increasingly used probability theory, whoseinitial results were found in the 17th and 18th centuries,particularly in the analysis of games of chance (gambling). By 1800,astronomy used probability models and statistical theories,particularly the method of least squares. Early probability theoryand statistics was systematized in the 19th century and statisticalreasoning and probability models were used by social scientists toadvance the new sciences of experimentalpsychology and sociology, and by physical scientistsin thermodynamics and statistical mechanics. The development ofstatistical reasoning was closely associated with the developmentof inductive logic and the scientific method.

Statistics can be regarded as not a field of mathematics butan autonomous mathematical science, like computer science andoperations research. Unlike mathematics, statistics had its origins

in public administration. It is used in demography and economics. With its emphasis on learning from data and making bestpredictions, statistics has a considerable overlap with decisionscience and microeconomics. With its concerns with data, statistics has overlap with information science and computerscience.
http://en.wikipedia.org/wiki/Mathematical_statisticshttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Applied_statisticshttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Games_of_chancehttp://en.wikipedia.org/wiki/Method_of_least_squareshttp://en.wikipedia.org/wiki/Experimental_psychologyhttp://en.wikipedia.org/wiki/Experimental_psychologyhttp://en.wikipedia.org/wiki/Sociologyhttp://en.wikipedia.org/wiki/Thermodynamicshttp://en.wikipedia.org/wiki/Statistical_mechanicshttp://en.wikipedia.org/wiki/Inductive_logichttp://en.wikipedia.org/wiki/Scientific_methodhttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Mathematical_sciencehttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Operations_researchhttp://en.wikipedia.org/wiki/Public_administrationhttp://en.wikipedia.org/wiki/Demographyhttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Decision_sciencehttp://en.wikipedia.org/wiki/Decision_sciencehttp://en.wikipedia.org/wiki/Microeconomicshttp://en.wikipedia.org/wiki/Datahttp://en.wikipedia.org/wiki/Information_sciencehttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Information_sciencehttp://en.wikipedia.org/wiki/Datahttp://en.wikipedia.org/wiki/Microeconomicshttp://en.wikipedia.org/wiki/Decision_sciencehttp://en.wikipedia.org/wiki/Decision_sciencehttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Demographyhttp://en.wikipedia.org/wiki/Public_administrationhttp://en.wikipedia.org/wiki/Operations_researchhttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Mathematical_sciencehttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Scientific_methodhttp://en.wikipedia.org/wiki/Inductive_logichttp://en.wikipedia.org/wiki/Statistical_mechanicshttp://en.wikipedia.org/wiki/Thermodynamicshttp://en.wikipedia.org/wiki/Sociologyhttp://en.wikipedia.org/wiki/Experimental_psychologyhttp://en.wikipedia.org/wiki/Experimental_psychologyhttp://en.wikipedia.org/wiki/Method_of_least_squareshttp://en.wikipedia.org/wiki/Games_of_chancehttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Applied_statisticshttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Mathematical_statistics


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PART A


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PART AThe importance of the data representation and data analysis in

our daily life.

What is Data representation?

There are two types of data, one type is the Qualitative and

the other is the Quantitative data. Qualitative data uses words such

as favourite cars like BMW while Quantitative data uses numbers

such as number of uncles like 4.

To expand on those two types of data weve seen above;

there are two types of quantitative data, discrete and continuousdata. Discrete data can be counted for example number of cars and

continuous data is measured for example the height of someone

170cm, which can only be found by carrying out measurements.

Data can be categorized depending on how it has been collected;Primary data us data collected by you while secondary data is data

collected by someone else, this is usually data which has been

provided to work from for example in experiments or exams.


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The advantages of primary data is that youre satisfied with

the data, you have a good and confident understanding of the dataaccuracy since you collected it, and you re very aware of how the

data was collected. The disadvantages are data collection can take

a very long time and it can also be very expensive.

The advantages of secondary data it is quicker and easier toget the data in large amounts and its also cheap since the data is

often available. The disadvantages are; youre not aware of the

data accuracy or how the data was collected and it might be out of

date.

Ways of collecting data are using questionnaires, counting,

measurements, or data logging; Data logging refers to a machine

used to record results at set intervals. You can use books to up data,

you can also use magazines, newspapers and the internet


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What is Data Analysis?

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. Analysis of data is a process of

inspecting, cleaning, transforming, and modelling data with the

goal of discovering useful information, suggesting conclusions,

and supporting decision making. Data analysis has multiple facets

and approaches, encompassing diverse techniques under a variety

of names, in different business, science, and social science

domains.

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


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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.

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.


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What is the importance of Data Representation and Data

Analysis in our daily life?

It is necessary for us to know about the importance of data

analysis in our daily life. 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. How to predict the future trend ofstock market or weather temperature by using computers? In this

project, a software package will be developed for time series data

prediction, based on Fuzzy system algorithms to data mining.

Data Analysis provides important info. There are some

people who absolutely live for numbers and information and just

about anything else that can be compiled and analyzed, and that

makes data analysis a good occupation. More than just numbers

data can be collected to provide important statistics to support

many decisions.

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


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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/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 ithelps 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 importance for both the research and the

researcher. Or to put it in another words data analysis is as

important to a researcher as it is important for a doctor to diagnose

the problem of the patient before giving him any treatment.


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Type of data representation and data analysis

Frequency histogram

Pie Chart Ogive

Box Plot

Example 1 ( Histogram )

Survey results of the ages of students in the Adult Basic Education maths classes areshown in this frequency table.

AgeInterval(yrs) Frequency

15-19 13

20-24 15

25-29 20

30-34 10

35-39 8

40-44 4

Frequency Histogram for the data above


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Example 2 ( box- plot )

Use the chart above and include a cumulative frequency column. From this draw anogive graph. Use the graph to find the median, lower quartile, upper quartile andlowest and highest value.

Draw a box-plot.Age Interval(yrs) Frequency Cumulative frequency

15-19 13 13

20-24 15 28

25-29 20 48

30-34 10 58

35-39 8 66

40-44 4 70

Lowest Value: 15

Highest Value: 44

Five-number summaryLowest value: 1525% Quartile: 2150% Quartile(median) 2675% Quartile: 36Highest value: 44

Box Plot


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Example 4 ( Ogive )

Lowest value: 10 yearsHighest value: 19 years

Age of students(years)

attending zoo

Tally Cumulative

Frequency

Total number

of students 10 3 3 3 x 10 = 30

11 5 8 5 x 11 = 55

12 5 13 5 x 12 = 60

13 1 14 1 x 13 = 13

14 1 15 1 x 14 = 14

15 1 16 1 x 15 = 15

16 1 17 1 x 16 = 16

17 1 18 1 x 17 = 17

18 1 19 1 x 18 = 18

19 1 20 1 x 19 = 19

Total = 20 Total =237


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PART BFormula of mean ( Ungrouped data )

= Sum of all the data values

= Number of data values

=

= 66.45

Median class = and Median class =

=20 th value = 21 th value

35, 40, 43, 44, 45, 50, 52, 52, 54, 55, 57, 58, 60, 60, 62,63, 65, 65,

65, 66, 68, 68

Median=

= 67


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PART C


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PART Ca.

Class Tally Frequency

30-38 | 1

39-47 |||| 4

48-56 |||| 5

57-65 |||| |||| 9

66-74 |||| |||| 9

75-83 |||| | 6

84-92 |||| | 6

b.Refer the graph on Page

Modal classes mark =

c.Refer the graph on Page

d. Formula of mean ( Grouped data )


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Formula of median ( Grouped data )

Class Midpoint, x Frequency, f fx Cumulative

frequency, cf

30-38 34 1 34 1

39-47 43 4 172 5

48-56 52 5 260 10

57-65 61 9 549 19

66-74 70 9 630 28

75-83 79 6 474 34

84-92 88 6 528 40

TOTAL 40 2,647

=

= 66.18


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Median class= th observation

= 20 th observation

= 66-74

Median = 9

= 66.5

The conjecture about the mean and median is ungrouped dataand grouped data for the Mid-year Examination of the Additional

Mathematics is almost the same which is 66.18 and 66.5 for

ungrouped data and 66.45 and 66.7 for the grouped data. The

conjecture is proved.


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e. Formula of standard deviation

Method 1 :

Class Midpoint, x Frequency,f fx

30-38 34 1 34 1,156

39-47 43 4 172 7,396

48-56 52 5 260 13,52057-65 61 9 549 33,489

66-74 70 9 630 44,100

75-83 79 6 474 37,446

84-92 88 6 528 46,464

TOTAL 40 2,647 183,571

= = 14.47


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Method 2:

Class Midpoint,x Frequency,f (x- ) (x- )2

f(x- )2

30-38 34 1 -32.18 1,035.55 1,035.55

39-47 43 4 -23.18 537.31 2,149.24

48-56 52 5 -14.18 201.07 1,005.35

57-62 61 9 -5.18 26.83 241.47

66-74 70 9 3.82 14.59 131.3175-83 79 6 12.82 164.35 986.10

84-92 88 6 21.82 476.11 2,856.66

TOTAL 8,405.68

= = 14.50


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Formula of interquartile range

Method 1 : Using formula

Interquartile range = Q3-Q1

Class of Q1 = th observation

= 10 th observation

= 48-56

Class Midpoint, x Frequency, f fx Cumulative

frequency, cf

30-38 34 1 34 139-47 43 4 172 5

48-56 52 5 260 10

57-65 61 9 549 19

66-74 70 9 630 28

75-83 79 6 474 3484-92 88 6 528 40

TOTAL 40 2,647


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Q1= )9

= 56.5

Class of Q3 = th observation

= 30 th observation

= 75-83

Q3=

= 77.5

Interquartile range = 77.5-56.5

= 21

Method 2: Using ogive


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Advantages of using standard deviation

The standard deviation gives a measure of dispersion of the

data about the mean. A direct analogy would be that of theinterquartile range, which gives a measure of dispersion about the

median. However, the standard deviation is generally more useful

than the interquartile range as it includes all data in its

calculation. The interquartile range is totally dependent on just

two values and ignores all the other observations in the data. This

reduces the accuracy it extreme value is present in the data. Since

the marks does not contain any extreme value, standard

deviation give a better measures compared to interquartile range.


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FURTHEREXPLORATION


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FURTHER EXPLORATION

a. Mean

=

= 49.43

Formula of Standard deviation

x2 = 50 2+41 2+61 2+28 2+48 2+62 2+60 2+15 2+62 2+67 2+56 2+50 2+

44 2+32 2+27 2+36 2+46 2+22 2+36 2+68 2+53 2+36 2+70 2+46 2+

38 2+75 2+80 2+75 2+56 2+43 2+73 2+61 2+40 2+28 2+43 2+52 2+

33 2+45 2+59 2+60 2

= 107,515

= = 15.64


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b. The mean and standard deviation from Mid-year

Examination is 66.18 and 14.50 while the mean and

standard deviation from Final Year Examination is 49.43 and

15.64. The students achieve a higher marks in Mid-year

Examination than Final Year Examination because the mean

and the standard deviations from Mid-year Examination is

much better than then Final Year Examination collected data.


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CONCLUSION


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CONCLUSIONAfter I accomplished the project, I have found that the

Additional Mathematics is fun and very useful in our daily life to

make our life easier. I also have learnt the important of

perseverance as time will be inverted to ensure the completion

and excellence of this project. On the other hands, I have learnt

the virtue to make together as I have helped and received help

from my fellow peers in the completion of this project. Besides, I

can adapt with everyday problems by applying the mathematics

thinking skills that Ive had. I realized the importance to be

thankful and appreciative during completing this task. This is

because I able to apply my mathematical knowledge in daily life

and appreciate the beauty of Additional Mathematics. This project

is a several training stage for me to prepare myself for the

demands of my future undertaking in the university and work life.


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REFLECTION


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RELECTIONWhile I conducting this project, a lot of information that I

found. I have learnt how data appear in our life.

Apart from that, this project encourages the student to work

together and share their knowledge. It is also encourage student

to gather information from the internet, improve thinking skills

and promote effective mathematical communication.

Not only that, I had learned some moral values that I

practice. This project had taught me to responsible on the works

that are given to me to be completed. This project also had made

me felt more confidence to do works and not to give easily when

we could not find the solution for the question. I also learned to

be more discipline on time, which I was given about a month to

complete this project and pass up to my teacher just in time. I

also enjoy doing this project. I spend my time with friends to

complete this project and it had tighten our friendship.

Last but no least, I proposed this project should be continue

because it brings a lot of moral value to the student and also test

Addmath Project Work Form5 2014 ( Official )

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Transcript of Addmath Project Work Form5 2014 ( Official )