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