project work additional mathematics by nks
DESCRIPTION
akhirnye siap jgk... ni untk pnduan korg sume je yupp....sharing is caring.... hahaTRANSCRIPT
ADDITIONAL MATHEMATICS PROJECT WORK 2010
Work 4
Name : Norkamilah Binti ShahariI/C Number : 930826-11-5834Class : 5 Nilam 1Teacher : Mrs. Fazilah Binti RafieeDate :
Acknowledgement..................................................
Objectives...............................................................
Introduction ...........................................................
Part 1......................................................................
Part 2......................................................................
Part 3......................................................................
Further explorations...............................................
Reflections............................................................
Conclusion..............................................................
First of all, I would like to say Alhamdulillah, for giving me the strength and health
to do this project work and finish it on time.
Not forgotten to my parents for providing everything, such as money, to buy
anything that are related to this project work, their advise, which is the most needed for
this project and facilities such as internet, books, computers and all that. They also
supported me and encouraged me to complete this task so that I will not procrastinate in
doing it.
Then I would like to thank to my teacher, Mdm Fazilah for guiding me throughout
this project. Even I had some difficulties in doing this task, but she taught me patiently
until we knew what to do. She tried and tried to teach me until I understand what I’m
supposed to do with the project work.
Besides that, my friends who always supporting me. Even this project is
individually but we are cooperated doing this project especially in disscussion and
sharing ideas to ensure our task will finish completely.
Last but not least, any party which involved either directly or indirect in
completing this project work. Thank you everyone.
The aims of carrying out this project work are:
i. To apply and adapt a variety of problem-solving strategies to solve
problems.
ii. To improve thinking skills.
iii. To promote effective mathematical communication.
iv. To develop mathematical knowledge through problem solving
in a way that increases students’ interest and confidence.
v. To use the language of mathematics to express mathematical
ideas precisely.
vi. To provide learning environment that stimulates and enhances
effective learning.
vii. To develop positive attitude towards mathematics.
A Brief History Of Statistic
By the 18th century, the term " statistics" designated the systematic
collection of demographic and economic data by states. In the early 19th
century, the meaning of "statistics" broadened, then including the discipline
concerned with the collection, summary, and analysis of data. Today statistics is
widely employed in government, business, and all the sciences. Electronic
computers have expedited statistical computation, and have allowed statisticians
to develop "computer -intensive" methods.
The term "mathematical statistics" designates the mathematical theories
of probability and statistical inference, which are used in statistical practice. The
relation between statistics and probability theory developed rather late, however.
In the 19th century, statistics increasingly used probability theory, whose initial
results were found in the17th 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, which was invented
by Legendre and Gauss. Early probability theory and statistics was systematized
and extended by Laplace; following Laplace, probability and statistics have been
in continual development.
In the 19th century, social scientists used statistical r easoning and
probability models to advance the new sciences of experimental psychology and
sociology; physical scientists used statistical reasoning and probability models to
advance the new sciences of thermodynamics and statistical mechanics.
The development of statistical reasoning was closely associated with the
development of inductive logic and the scientific method. Statistics is not a field
of mathematics but an autonomous mathematical science , like computer science
or operations research. Unlike mathematics, statistics had its origins in public
administration and maintains a special concern with demography and economics.
Being concerned with the scientific method and inductive logic, statistical theory
has close association with the philosophy of science ; with its emphasis on
learning from data and making best predictions, statistics has great overlap with
the decision science and microeconomics. With its concerns with data, statistics
has overlap with information science and computer science .
Statistics Today
During the 20th century, the creation of precise instruments for
agricultural research, public health concerns (epidemiology, biostatistics,
etc.),industrial quality control, and economic and social purposes (unemployment
rate, econometry, etc.) necessitated substantial advances in statistical practices.
Today the use of statistics has broadened far beyond its origins.
Individuals and organizations use statistics to understand data and make
informed decisions throughout the natural and social sciences, medicine,
business, and other areas. Statistics is generally regarded not as a subfield of
mathematics but rather as a distinct, albeit allied, field. Many universities
maintain separate mathematics and stati stics departments. Statistics is also
taught in departments as diverse as psychology, education, and public health.
Index Number
Index numbers are today one of the most widely used statistical indicators.
Generally used to indicate the state of the economy, index numbers are aptly
called ‘barometers of economic activity’. Index numbers are used in comparing
production, sales or changes exports or imports over a certain period of time.
The role-played by index numbers in Indian trade and industry is impossible to
ignore. It is a very well known fact that the wage contracts of workers in our
country are tied to the cost of living index numbers.
By definition, an index number is a statistical measure designed to show
changes in a variable or a group or related variables with respect to time,
geographic location or other characteristics such as income, profession, etc.
Characteristics of an Index Numbers
1. These are expressed as a percentage: Index number is calculated as a ratio
of the current value to a base value and expressed as a percentage. It must be
clearly understood that the index number for the base year is always 100. An
index number is commonly referred to as an index.
2. Index numbers are specialized averages: An index number is an average
with a difference. An index number is used for purposes of comparison in cases
where the series being compared could be expressed in different units i.e. a
manufactured products index (a part of the whole sale price index) is constructed
using items like Dairy Products, Sugar, Edible Oils, Tea and Coffee, etc. These
items naturally are expressed in different units like sugar in kgs, milk in liters, etc.
The index number is obtained as a result of an average of all these items, which
are expressed in different units. On the other hand, average is a single figure
representing a group expressed in the same units.
3. Index numbers measures changes that are not directly measurable: An
index number is used for measuring the magnitude of changes in such
phenomenon, which are not capable of direct measurement. Index numbers
essentially capture the changes in the group of related variables over a period of
time. For example, if the index of industrial production is 215.1 in 1992-93 (base
year 1980-81) it means that the industrial production in that year was up by 2.15
times compared to 1980-81. But it does not, however, mean that the net increase
in the index reflects an equivalent increase in industrial production in all sectors
of the industry. Some sectors might have increased their production more than
2.15 times while other sectors may have increased their production only
marginally.
Uses of index numbers
1. Establishes trends
Index numbers when analyzed reveal a general trend of the phenomenon under
study. For eg. Index numbers of unemployment of the country not only reflects
the trends in the phenomenon but are useful in determining factors leading to
unemployment.
2. Helps in policy making
It is widely known that the dearness allowances paid to the employees is linked
to the cost of living index, generally the consumer price index. From time to time
it is the cost of living index, which forms the basis of many a wages agreement
between the employees union and the employer. Thus index numbers guide
policy making.
3. Determines purchasing power of the rupee
Usually index numbers are used to determine the purchasing power of the rupee.
Suppose the consumers price index for urban non-manual employees increased
from 100 in 1984 to 202 in 1992, the real purchasing power of the rupee can be
found out as follows: 100/202=0.495 It indicates that if rupee was worth 100
paise in 1984 its purchasing power is 49.5 paise in 1992.
4. Deflates time series data
Index numbers play a vital role in adjusting the original data to reflect reality. For
example, nominal income(income at current prices) can be transformed into real
income(reflecting the actual purchasing power) by using income deflators.
Similarly, assume that industrial production is represented in value terms as a
product of volume of production and price. If the subsequent year’s industrial
production were to be higher by 20% in value, the increase may not be as a
result of increase in the volume of production as one would have it but because
of increase in the price. The inflation which has caused the increase in the series
can be eliminated by the usage of an appropriate price index and thus making
the series real.
Types of index numbers
Three are three types of principal indices. They are:
1. Price Index
The most frequently used form of index numbers is the price index. A price
index compares charges in price of edible oils. If an attempt is being made to
compare the prices of edible oils this year to the prices of edible oils last year, it
involves, firstly, a comparison of two price situations over time and secondly, the
heterogeneity of the edible oils given the various varieties of oils. By constructing
a price index number, we are summarizing the price movements of each type of
oil in this group of edible oils into a single number called the price index. The
Whole Price Index (WPI). Consumer Price Index (CPI) are some of the popularly
used price indices.
2. Quantity Index
A quantity index measures the changes in quantity from one period to
another. If in the above example, instead of the price of edible oils, we are
interested in the quantum of production of edible oils in those years, then we are
comparing quantities in two different years or over a period of time. It is the
quantity index that needs to be constructed here. The popular quantity index
used in this country and elsewhere is the index of industrial production (HP). The
index of industrial production measures the increase or decrease in the level of
industrial production in a given period compared to some base period.
3. Value Index
The value index is a combination index. It combines price and quantity
changes to present a more spatial comparison. The value index as such
measures changes in net monetary worth. Though the value index enables
comparison of value of a commodity in a year to the value of that commodity in a
base year, it has limited use. Usually value index is used in sales, inventories,
foreign trade, etc. Its limited use is owing to the inability of the value index to
distinguish the effects of price and quantity separately.
Calculating index number
Index number Is a measure used to show the change of a certain quantity for a
stated period of time by choosing a specific time as the base year. In general an
index number is the comparison of a quantity at two different times and is
expressed as a percentage.
I=Q1Q0
×100
I = index number
Q1 = quantity at specific time
Qo = quantity at base time
The composite index is the weighted mean for all the items in a certain situation.
Ī =∑ Wᵢ Iᵢ
∑Wᵢ
Ī = Composite index
W = weightage
I= index number
The prices of good sold in shops are vary from one shop to another. Shoppers
tend to buy goods which are not only reasonably priced but also give value for their
money. I had carried out a survey on four different items based on the following
categories which is food, detergent and stationery. The survey was done in three
different shops. Informations below shows the results from my research.
Question (a) Picture
Stationery
Food
Detergent
Question (b) Data
Category ItemPrice (RM)
Mydin Mall Embat Shop Si Comel
Food
1.Self raising flour(500g) 2.00 2.50 2.102. Sugar(1000g) 1.80 1.90 1.853. Butter (250g) 3.50 3.60 3.604. Eggs (Grade A) 8.20 8.50 8.40Total price 15.50 16.50 15.95
Detergent1. Dishwash 1.80 2.00 1.952. Softener 3.90 4.20 4.003. Floor cleaner 10.90 11.00 11.304. Powder D/gent 9.50 9.50 9.60Total price 26.10 26.70 26.85
Stationery1. Eraser 0.80 0.80 0.702. Marker 3.00 3.60 3.903. Pencil colour 5.50 5.40 5.304. Scissor 2.30 2.30 2.40Total price 11.60 12.10 12.30
Grand total 53.20 55.30 55.10
Question (c)
Mydin Mall Embat Shop Si Comel0123456789
Food
Self Raising FlourSugarButterEggs
Mydin Mall Embat Shop Si Comel0
2
4
6
8
10
12
Detergent
Dishwash SoftenerFloor CleanerPowder D/gent
Mydin Mall Embat Shop Si Comel0
1
2
3
4
5
6
Stationery
EraserMarkerPencil ColourScissor
Question (D)
Based on all the graph in question 1(C) , we can conclude that Mydin Mall offers
the lowest price for their customers. Then followed by Si Comel and Embat Shop. This
is because the supplier of the Mydin Mall gives the special price for it as it buy by bulk.
Si comel offer the normal price for their customer as it does not get special price from
the supplier. While, Embat Shop have to sold the items at the higher price because the
shop buy the items by bulk from Mydin Mall.
Other factors that influenced the prices of goods in the shops is such as the
location of the shop, the population of the customers, the status of the shop, the size of
the shop, and the rent for the shop.
Mydin Mall can offer the lowest price because it is situated at stratergic place so
indirectly this factor can attract customer buy at the mall. When there are many
customers, the demand of the items will be high and the mall can buy by bulk directly
with the supplier to get the special price. The status of the shop also influenced the
price of the goods sold. As example the shop with status mall will offer the lowest price
than the shop with status mini market. The size of the shop also will influenced the
price. When the size of the shop is bigger its mean it can sell many different items in the
shop. Indirectly the shop will known as one stop center and it will attract many
customers as the people nowadays are very busy. Mydin Mall is a bigmall and it
provides many items that we need in our life. Eventhough Mydin Mall have to pay rent
for the place, but it not gives too much effects to the price of goods sold as it has many
buyers.
Si Comel and Embat Shop cannot offer the prices as Mydin Mall because they
are situated outside the urban area like Mydin Mall. So the population of the customer
will not be as many as customer in Mydin Mall. These shops get the supply for their
goods from Mydin Mall. Even they buy by bulk with Mydin Mall but their prices still will
be higher than Mydin Mall. The size of these shop also small and cannot provide too
much goods for their customers. They just sold basic needed for their customers. As
they not have too much customers, so the rent that they have to pay will influenced the
price of the goods sold.
As a conclusion, there are many factors that affect the price of the goods solds in
a shop. So, we must be a smart customer to ensure we can get the lowest price. The
graph below will show the conclusion of the difference among the shops based upon
the shops grand total.
Grand Total50
51
52
53
54
55
56
57
58
Mydin MallSi ComelEmbat Shop
Question (e) The item that has large price different among the shops is marker. Mydin Mall
sold it at RM 3.00, Si Comel sold it at RM3.90 while Embat Shop sold it at RM 3.60.
Calculate the mean
x=∑ x
N
¿3+3.6+3.9
3
¿3.5
Calculate the standard deviation
σ=√σ2 Or
σ=√∑ ¿¿¿¿
¿√ (3−3.5 )2+(3.6−3.5)2+(3.9−3.5)2
3
¿0.3742
The difference of the price of the marker in these three shops is maybe due to the
price given by the supplier to the shops. Mydin Mall can sold it at lowest prices because the
demand of the buyers for the the item is high so it can buy by bulk with the supplier. So the
shop can get the special price. The demand of the item in Embat Shop and Si Comel are low.
This is because the customers are more interested to buy the stationery items in mall or
stationery shops as there are more options to choose. So Embat Shop and Si Comel cannot
buy by bulk the stationery items with their supplier.
Every year my school organises a carnival to raise funds for the school. This year
my school plans to install air conditioners in the school library. Last year, during the
carnival, my class made and sold butter cakes. Because of the popularity of butter
cakes, my class has decided to carry out the same project for this year’s carnival.
Question (a)
From the data in Part 1, I would go to Mydin Mall to purchase the ingredients for the
butter cakes. This is because Mydin Mall offers the lowest price among the shops for
the items I want to buy. So my class will able to sold the butter cakes at the low price
and get some profits form the sale. Futhermore, Mydin Mall is located not far from my
school. So it is easier to my friends and I to go there.
Question (b)
Ingredient Quantity per cakePrice in the year
2009 (RM)Price in the year
2010 (RM)Self-raising flour 250 g 0.90 1.00
Sugar 200 g 0.35 0.36Butter 250 g 3.30 3.50
Eggs (Grade A) 5 eggs (300 g) 1.25 1.37
(i) Calculate Price Index
I= P1P 0
×100
Self raising-four
¿ 1.000.90
× 100
¿111.11
Sugar
¿0.360.35
× 100
=102.86
Butter
¿ 3.503.30
×100
=106.06
Eggs (Grade A)
¿ 1.371.25
×100
=109.60
(ii) Composite index
Ī =∑ Wᵢ Iᵢ
∑Wᵢ
¿(5× 111.11)+(4 ×102.86 )+(5×106.06 )+(6× 109.60)
5+4+5+6
=107.74
To calculate composite index firstly use the formula of composite index. Get the
value for the formula. Lets quantity per cake be as weightage, W. Obtain the price index
from the calculation in question (i). Then, calculate by using the calculator.
(iii)
On 2009, RM 15.00On 2010, suitable price is :
x15
×100=107.74 %
x× 100=107.74 ×15
x=1616.10100
x=16.20
Thus, the suitable price for the butter cake for the year 2010 is RM 16.20. The
increase in price is also suitable because of the rise in the price of the ingredients.
Question (c)
(i) To determine suitable capacity of air conditioner to be installed based on volume/ size of a room
For common usage, air conditioner is rated according to horse power (1HP),
which is approximately 700W to 1000W of electrical power. It is suitable for a
room size 1000ft which is around 27m of volume. If we buy an air conditioner
with 3HP, it is suitable for a room around 81m.
(ii) Estimate the volume of school library By using a measuring tape, the dimension for the library is:
Height=3.6m
Width=9.0m
Length=20.12m
Volume of the room=3.6 x 9.0 x 20.12
=651.90m3 One unit of air conditioner with 3HP is for 81 m3
For 651.90 m3=651.9081
¿ 8.048
This means our school library needs 8 unit of air conditioner.
(iii) My class intends to sponsor one air conditioner for the school library. The
calculation below is to find how many butter cakes we must sell in order to
buy the air conditioner.
1 unit of 3 HP air conditioner = RM 1800Cost for a cake = RM 6.23Selling price = RM 16.20Profit =RM 16.20- RM6.23
= RM 9.97
Number of cakes to buy 1 unit of air conditioner =
18009.97
=180.54=181 cakes
As a committee member for the carnival, I am required to prepare an estimated
budget to organise this year’s carnival. I has taken into consideration the increases in
expenditur from the previous year due to inflation The price of food, transportation and
tents has increased by 15%. The cost of games, prizes and decorations remains the
same,whereas the cost of miscellaneous items has increase by 30%.
(a)Table 3 has been completed based on the above information.
Expenditure Amount in 2009 (RM) Amount in 2010 (RM)Food 1200.00 1380.00
Games 500.00 500.00Transportation 300.00 345.00Decorations 200.00 200.00
Prizes 600.00 600.00Tents 800.00 920.00
Miscellaneous 400.00 520.00
Table 3
(b) Calculation to find the composite index
ExpenditureAmount in 2009 (RM)
Amount in 2010 (RM)
Price Index,
I=p1
p0
×100
Weightage,W
Food 1200.00 1380.00 115 12Games 500.00 500.00 100 5
Transportation 300.00 345.00 115 3Decorations 200.00 200.00 100 2
Prizes 600.00 600.00 100 6Tents 800.00 920.00 115 8
Miscellaneous 400.00 520.00 130 4
Composite Index
Ī =∑ Wᵢ Iᵢ
∑Wᵢ
= 115 (12 )+100 (5 )+115 (3 )+100 (2 )+100 (6 )+115 (8 )+130(4)
(12+5+3+2+6+8+4)
¿ 446540
=111.625
The total price for the year 2010 increase by 111.625%. This is because some price in
the year 2009 increased in the year 2010.
(c) The change in the composite index for the estimate budget for the carnival
from the year 2009 to the year 2010 is the same as the change from the year
2010 to the year 2011. Below are the calculation to determine the composite
index of the budget for the year 2011 based on the year 2009.
Composite index for the year 2009 to the year 2010
=111.625
Composite index for the year 2010 to the year 2011
=111.625
I 20112009
× 100=I 20102009
× I 20112010
I 20112009
=111.625 ×111.625 ×1
100
I 20112009
=124.60
AIR POLLUTION INDEX
Air pollution is the introduction of chemicals, particulate matter, or biological
materials that cause harm or discomfort to humans or other living organisms, or
damages the natural environment into the atmosphere. The atmosphere is a complex
dynamic natural gaseous system that is essential to support life on planet Earth.
Stratospheric ozone depletion due to air pollution has long been recognized as a threat
to human health as well as to the Earth's ecosystems.
The Air Quality Index (AQI) (also known as the Air Pollution Index (API) or
Pollutant Standard Index (PSI) is a number used by government agencies to
characterize the quality of the air at a given location. As the AQI increases, an
increasingly large percentage of the population is likely to experience increasingly
severe adverse health effects. To compute the AQI requires an air pollutant
concentration from a monitor or model. The function used to convert from air pollutant
concentration to AQI varies by pollutant, and is different in different countries. Air
quality index values are divided into ranges, and each range is assigned a descriptor
and a color code. Standardized public health advisories are associated with each AQI
range. An agency might also encourage members of the public to take public
transportation or work from home when AQI levels are high.
Limitations of the AQI
Most air contaminants do not have an associated AQI. Many countries monitor
ground-level ozone, particulates, sulphur dioxide, carbon monoxide and nitrogen
dioxide and calculate air quality indices for these pollutants.
Causes of Poor Air Quality
The AQI can worsen (go up) due to lack of dilution of air emissions by fresh air.
Stagnant air, often caused by an anticyclone or temperature inversion, or other lack of
winds lets air pollution remain in a local area.
Indices by location
South Korea
The Ministry of Environment of South Korea uses the Comprehensice Air-quality
Index (CAI) to describe the ambient air quality based on health risk of air
pollution. The index aims to help the public easily understand air quality level and
protect the health of people from air pollution. - The CAI has values of 0 through
500, which are divided into six categories. The higher the CAI value, the greater
the level of air pollution. - Of values of the five air pollutants, the highest is the
CAI value.
CAI Description Health Implications
0-50 GoodA level that will not impact patients suffering from diseases related to air pollution.
51-100
ModerateA level which may have a meager impact on patients in case of chronic exposure.
101-150
Unhealthy for sensitive groups
A level that may have harmful impacts on patients and members of sensitive groups.
151-250
Unhealthy
A level that may have harmful impacts on patients and members of sensitive groups (children, aged or weak people), and also cause the general public unpleasant feelings.
251-350
Very unhealthyA level which may have a serious impact on patients and members of sensitive groups in case of acute exposure.
351-500
Hazardous
A level which may need to take emergency measures for patients and members of sensitive groups and have harmful impacts on the general public.
Malaysia
The air quality in Malaysia is reported as the API or Air Pollution Index. Four of
the index's pollutant components (i.e., carbon monoxide, ozone, nitrogen dioxide
and sulfur dioxide) are reported in ppmv but PM10 particulate matter is reported
in μg/m³.
Unlike the American AQI, the index number can exceed 500. Above 500, a state
of emergency is declared in the reporting area. Usually, this means that non-
essential government services are suspended, and all ports in the affected area
closed. There may also be a prohibition on private sector commercial and
industrial activities in the reporting area excluding the food sector.
Stock Market Index
A comparison of three major U.S. stock indices: the NASDAQ Composite, Dow Jones Industrial Average, and S&P 500. All three have the same height at March 2007. Notice the large dot-com spike on the NASDAQ, a result of the large number of tech. companies on that index.
A stock market index is a method of measuring a section of the stock
market. Many indices are cited by news or financial services firms and are used
as benchmarks, to measure the performance of portfolios such as mutual funds.
Types of indices
Stock market indices may be classed in many ways. A 'world' or 'global'
stock market index includes (typically large) companies without regard for where
they are domiciled or traded. Two examples are MSCI World and S&P Global
100.
A national index represents the performance of the stock market of a
given nation—and by proxy, reflects investor sentiment on the state of its
economy. The most regularly quoted market indices are national indices
composed of the stocks of large companies listed on a nation's largest stock
exchanges, such as the American S&P 500, the Japanese Nikkei 225, and the
British FTSE 100.
The concept may be extended well beyond an exchange. The Wilshire
5000 Index, the original total market index, represents the stocks of nearly every
publicly traded company in the United States, including all U.S. stocks traded on
the New York Stock Exchange (but not ADRs or Limited Partnerships), NASDAQ
and American Stock Exchange. Russell Investment Group added to the family of
indices by launching the Russell Global Index.
More specialised indices exist tracking the performance of specific sectors
of the market. Some examples include the Wilshire US REIT which tracks more
than 80 American Real Estate Investment Trusts and the Morgan Stanley
Biotech Index which consists of 36 American firms in the biotechnology industry.
Other indices may track companies of a certain size, a certain type of
management, or even more specialized criteria — one index published by Linux
Weekly News tracks stocks of companies that sell products and services based
on the Linux operating environment.
Index versions
Some indices, such as the S&P 500, have multiple versions. These
versions can differ based on how the index components are weighted and on
how dividends are accounted for. For example, there are three versions of the
S&P 500 index: price return, which only considers the price of the components,
total return, which accounts for dividend reinvestment, and net total return, which
accounts for dividend reinvestment after the deduction of a withholding tax. As
another example, the Wilshire 4500 and Wilshire 5000 indices have five versions
each: full capitalization total return, full capitalization price, float-adjusted total
return, float-adjusted price, and equal weight. The difference between the full
capitalization, float-adjusted, and equal weight versions is in how index
components are weighted.
USES AND IMPORTANCE OF AIR POLLUTION INDEX AND STOCK MARKET INDEX
As everyone can see,the air pollution index is use by the government to
measure the quality of air index and to detect any pollutants in our country’s
air.This is to ensure the air is clean and safe for us ti inhale.Besides that,an early
warning can be given to us if the air pollution is too high for us to get out of our
homes.This warning is given based upon readings and unterpretations of the air
index.
As for the stock market index, it is mainly for the business entrepreneurs.
This type of index is used to determine the outcome of a stock market and also
the conclusion of a stock market. The stock market index is important because a
country’s economical state sometimes depend on it.
After spending countless hours,days and night to finish this project and also sacrificing my time for chatting and movies in this mid year holiday,there are several things that I can say...
Additional Mathematics...From the day I born...From the day I was able to holding pencil...From the day I start learning...And...From the day I heard your name...
I always thought that you will be my greatest obstacle and rival in excelling in my life...But after countless of hours...Countless of days...Countless of nights...
After sacrificing my precious time just for you...Sacrificing my play Time..Sacrificing my Chatting...Sacrificing my Facebook...Sacrificing my internet...
Sacrifing my Anime... Sacrificing my Movies...I realized something really important in you...
I really love you...You are my real friend...You my partner...You are my soulmate...
I LOVE U ADDITIONAL MATHEMATICS…..
CONCLUSION
After doing research,answering questions,drawing graphs and
some problem solving, I saw that the usage of statistics is important
in daily life.It is not just widely used in markets but also in interpreting
the condition of the surrounding like the air or the water.Especially in
conducting an air-pollution survey.In conclusion,statistics is a daily life
nessecities.Without it,surveys can’t be conducted, the stock market
can’t be interpret and many more. So,we should be thankful of the
people who contribute in the idea of statistics.