SEKOLAH SEKOLAH BERASRAMA BERASRA MA PENUH INTEGRASI TUN TUN ABDUL AB DUL RAZAK PULAU SERAI, 26600 PEKAN PAHANG
ADDITIONAL MATHEMATICS PROJECT WORK 2/2013 Index Number in Our Daily Life
NAME MUHAMAD NAJMIL HAQIM BIN MUSTAFAR
I/C No. 960111 - 06 – 5543
CLASS 5 ABU QATADAH
TEACHER EN. NOR AZIZI FAIN
CONTENT CONTENTS
PAGES
OBJECTIVE
2
FOREWARD
3
INTRODUCTION INTRODUCTION
4-5
PART PART 1
6 - 12
PART PART 2
13 - 16
PART PART 3
17 - 18
FUTHER EXPLORATI EXPLORATION ON
19 - 25
REFLECTION
26
1
OBJECTIVES We students taking Additional Mathematics are required to carry out a project work while we are in Form Form 5. This year the Curricul Curriculum um Development De velopment Divisi Divi sion, on, Ministry of Education Educati on has has prepared four f our tasks for us. We are to choose choose and complete complete only ONE task based on our area of interest. This project can be done in groups or individually, but each of us are expected to submit an individually written report. Upon completion of the Additional Mathematics Project Work, we are to gain valuable experiences and able to:
Apply and adapt a variety of problem problem solving sol ving strategie strategi e s to solve sol ve routine routine and nonroutine problems;
Experience clas cl assroom sroom environments environments which are challengi chall enging, ng, interesting interesti ng and meaning meaningful ful and hence improve their thinking skills.
Experience clas cl assroom sroom environments environments where knowledge knowledge and s kills kill s are applied applie d in meaningful meaningful ways in s olving real-life real-li fe problem problemss
Experience clas cl assroom sroom environments environments where expressing express ing ones ones mathematical mathematical thinking,reas oning and communication communication are highly highl y encouraged encouraged and a nd expected
Experience Experience clas c lassroo sroom m environm environments ents that that s timulates timulates and enhances effective effe ctive learning.
Acquire effective eff ective mathematical mathematical communication communication through through oral and writing,and writing,a nd 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 increase interest and confidence
Prepare ourselves for the demand of our future undertakings and in workplace
Realise Reali se that mathematics athematics is an im i mportant portant and power powerful ful tool tool in solving s olving real real -life problems and hence develop positive attitude towards mathematics.
Train ourselves not only to be independent l earners but also to collabor colla borate, ate, to cooperate, and to share knowledge in an engaging and healthy environment
Use technology technology especially especial ly the the ICT appropr appropriately iately and effectively
Train ourselves to appreciate the intrinsic values of mathematics and to become more creative and innovative
Realize Real ize the import importance ance and the beauty beauty of mathematics
2
FOREWARD First of all, I would like to say Alhamdulillah, for giving me the strength and health to do this project work. Not forgotten my parents for providing everything, such as money, to buy anything that are related to this project work and their advice, which is the most needed for this project. Internet, books, computers, and etc. 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 my teacher, En. Nor Azizi Bin Fain for guiding me and my friends throughout this project. We had some difficulties in doing this task, but she taught us patiently until we knew what to do. She tried and tried to teach us until we understand what we supposed to do with the project work. Last but not least, my friends who were doing this project with me and sharing our ideas. They were helpful that when we combined combined and discusse discus sed d together, together, we had this this task ta sk done.
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INTRODUCTION HISTORY OF INDEX NUMBER
Index numbers are meant to study the change in the effects of such factors which cannot be
measured directly. According to Bowley, “Index numbers are u sed to measure the changes in some quantity which we cannot observe directly”. For example, changes in business activity in a country are not capable of direct meas measurem urement ent but it is poss possible ible to study relative relati ve changes in i n business busines s activity by studying studying the variation va riationss in the the values of s ome ome s uch factors factors which which affect af fect busines businesss activity, and which are capable of direct measurement.
Index numbers numbers are commonly commonly used statis sta tistica ticall devic device e for measuring the com c ombined bined fluctuations i n a group related variables varia bles.. If we wish wis h to compare compare the price price level l evel of consumer consumer items i tems today with that prevalent ten years ago, we are not interested in comparing the prices of only one item, but in comparing some sort of average price levels. We may wish to compare the present agricultural production or industrial production with that at the time of independence. Here again, we have to consider all items i tems of production production and each item may have undergone undergone a different fractional increase (or even a decrease). How do we obtain a composite measure? This composite measure is provided by index numbers numbers which may be defined as a device for f or combining combining the variations that have come in group of related variables over a period of time, with a view to obtain
a figure that represents the ‘net’ result of the change in the constitute constitute variables.
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Index numbers numbers may be be clas cl assi sifie fied d in terms terms of of the variables va riables that they are intended to measure. In business, busines s, different diffe rent groups groups of variables variabl es in the the measurement of which index number number techniques techniques are a re comm commonly used are (i) (i ) price, (ii) (i i) quantity, quantity, (iii) (i ii) value and (iv) business activity. ac tivity. Thus, we have index of wholesale prices, index of consumer prices, index of industrial output, index of value of exports and index of business activity, etc. Here we shall be mainly interested in index numbers of prices showing changes with respect to time, although methods described can be be applied applie d to other other case ca ses. s. In general, general , the present prese nt level of price pricess is compared compared with the the level leve l of prices in the past. The present period is called the current period and some period in the past is called ca lled the base period. period.
Index Numbers: Index numbers are statistical measures designed to show changes in a variable or group of related variables with respect to time, geographic location or other characteristics such as income, profession, etc. A collection of index numbers for different years, locations, etc., is sometimes called an index series.
Simple Index Number : A sim si mple index number number is a number number that that measures a relative change in a single si ngle variable with respect to a base.
Composite Composite Index N umber : A composite index number is a number that measures an average relative changes in a group of relative variables with respect to a base.
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PART 1 The price of goods sold in i n shop vary from one one shop to another. another. Shoppers Shoppers tend to buy goods which are not only reasonably price but also give value for their money. You are required required to carry carry out a survey on four different diffe rent items based bas ed on the following categories: food, detergent and stationery. The survey should be done in three different shop.
Part 1(a) Collect picture, newspaper cuttings or photos on item that you have chosen. Design a collage to illustrate the chosen item.
FOOD
6
DETERGENT
7
STATIONERY
8
Part 1(b) Record the item and their prices p rices systematically systematically as such such in Table 1. Since item may be differently packed, be sure to u se consistent consistent measurements for each item selected so that comparison can be done do ne easily easily and accu rately. rately.
The data in the table below i s only serve as a REFERENCE to you: you:
Category Categ ory Food
Detergent
Stationery
Item
Tesco Tes co
Giant
The Store Store
Self-risi Self- rising ng flour
2.70
3.70
3.30
Sugar
1.80
1.60
1.35
Butter
3.60
3.80
4.50
Eggs
3.60
2.90
3.00
Total Price Pric e
11.70
12.00
12.15
Washing Washi ng Powder Powder
19.00
21.00
20.50
Dish Dis h Washer
4.00
3.20
3.10
Liquid Bleach
6.00
5.50
4.90
Tile Cleaner
10.20
9.80
9.50
Total Price Pric e
39.20
39.50
38.00
Pencil (Shaker)
8.90
9.20
8.20
Highlighter Highlig hter
3.50
3.40
3.10
Permanent Permanent Marker Marker
3.50
2.90
3.80
Card Indexing
14.70
15.00
16.00
Grand Total
81.50
82.00
82.15
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Part 1(c) Create at least two suitable graphical representations (the use of ICT is encouraged) to compare contrast the price of the item chosen.
45 40 35 30 25
Tesco Giant
20
The Store 15 10 5 0 Fo o d
De te r gent
St ati oner y
45 40 35 30 25
Tesco Giant
20
The Store 15 10 5 0 Fo o d
De te r gent
St ati oner y
10
Part 1 (d):
Based Based on the th e graphical repr esentatio esentations ns that you h ave constructed constructed in part 1(c), interpret, discuss and d raw consclusion. Comment Comment on your findings.
Based on the graphical representations that I have constructed in Part 1(c), it is shown that there are large and small differences dif ferences among the the prices of items in i n each category ca tegory between the shops. In the food category, the smallest price difference are of those of sugar, while the highest is i s the price price of eggs. Besides Besi des food, deter detergent gent als o shows shows a large price price difference difference between between its items. Among them is the price of liquid dishwasher and clothes detergent. On the other hand,
stationery items doesn’t have any obvious price difference. The graph also show that most of the items that are high priced comes from the Boulevard Supermarket, while the lowest price items come from the Discount Store. The graph 1(d) will show the conclusion of the difference among the shops based upon the shops grand total.
45 40 35 30 25
Tesco Giant
20
The Store 15 10 5 0 Fo o d
De te r gent
St ati oner y Graph 1(d)
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Part 1(e)
The item that has a large price difference = washing powder
∑ = 19+21+20.5 = 121 = 20.20 (2dp) 3 6 ∑ Standard Standar d deviation deviation = √ ()2 19 −21 +20.5 (121 )2 = √ 3 6 1222.25 (121 )2 =√ 3 6
Mean , X =
= 0.8498
Reason Reason of d ifference ifference in price pr ice :
Bulk buying from the retailer gives the lower cost resulted in lower relling price.
Hypermarket own brands are much cheaper than the expansive brand-don’t involve in advertiving resulted in lower – selling price
Sales and discount offer by the supermarket.
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PART 2 Every year SBP Integrasi Tun Abdul Razak organises a carnival to raise funds for the school. This year the school plans to install CCTV in order to enchance its security. Last year, during the nasi lemak l emak . Due to the popularity of this local food, your carnival, your your clas s made and and sold nasi
class has decided to carry out the same project for this ye ar’s carnival.
Part 2(a)
I. Complete Table 2 with the prices of the given items for the year 2013
13
Part 2(b)
Calculate the price index for each of the items in Table 2 for the year 2013 based on the year 2012.
14
Part 2(c)
Calculate the composite index for the cost of a packet of nasi lemak in the year2013 based on the year 2012. Dis cuss how you obtained your answer. a nswer.
15
Part 2(d)
In the year 2012, the nasi lemak was sold at RM2.00 each. Suggest a suitable selli s elling ng price price for a packet of the nasi lemak in the year 2013. Give reasons for your answer.
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PART 3 In order order to upgrade the security, my school has decided to ins tall closed-ci clos ed-circuit rcuit TV (CCTV).
Part 3(a) Suggest a suitable nu mber of cameras to be installed and t heir placement. placement. Give you r reasons. reasons. Illustrate Illustrate with a p lan.
I sugges s uggestt 4 cameras cameras to be installed ins talled at my my school. The cameras will be install ed at the s taff room roomss and the offi office. ce. This Thi s action will be done to avoid avoi d any robbery robbery cas c ase e from from happen.
Part 3(b) Find out the cost of installation of the CCTV. CCTV. A set of CCTV with 4 cameras : RM2100
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Part 3(c) If your class intends to sponsor 10% of the th e cost, how many packets of nasi lemak lemak must your class sell?
10% X RM2100 = RM210
RM13.22 10 = RM1.40
Cost for a packet of nasi lemak = Selling price = RM2.10 RM2.10 Profit = RM2.10 – RM1.40 = RM0.70
Packets of nasi lemak must must be sell sel l
RM210 = RM0.70 = 300 packets
Part 3(d) Can your class achieve the 10% 10% target? Do you t hink your yo ur class class should carry ou t a different project instead? Yes because many visitors from Pekan will come and visit our school during the carnival.This phenom phenomenon enon will increase the selling sel ling of our our nasi lemak. Last year, we we had sold s old about 400 packets of nasi lemak. So, this year our target is 600 packets of nasi lemak will besold. From the sel ling, li ng, we we can sponsor 10% for the cost of install ation of the CCTV andwe andwe will get profit of about RM210. I think my class should not carry out different projectas we can get a lot of profit from the selling of nasi lemak. We need to focus on sellingnasi lemak only so we can achieve our target. Great efforts will led to great outcomes
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FUTHER EXPLORATION Index numb numbers ers are being used in many different dail da ily y situations, si tuations, for example air pollution index, stock market index, gold index and property index. Obtain information from the internet or other reliable sources on the importance of two different types of index number number of your your choice. choice . Elabor Ela borate ate the use and the impor importance tance of these index numbers in daily life.
Air Pollution Index Air pollution is the introduction introduction of chemicals, of chemicals, particulate matter, or biological materials that cause harm or discomfort to humans or other living organisms, or damages the the natural environment into the atmosphere. The atmosphere atmosphere is i s a complex complex dynamic dynamic natural natural gaseou gas eouss system s ystem that is essential es sential 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) (als o know known n as the Air Pollution Index (API ) or or Pollutant
Standard Index (PSI ) is a number number used by government government agencies age ncies to characterize characteri ze the quality of the the air at a t a given gi ven location. location. As the AQI increases , an increasi increasingly ngly large percentage percentage of the populatio population n is likely l ikely to experience experience incr i ncreasi easingly ngly severe adverse health effects. To comput compute e the AQI requires an air pollutant concentration from a monitor or model. The function used to convert from air ai r pollutant concentration to AQI varies by pollutant, and is different diff erent in diff different erent countr countries ies.. Air quali quality ty index index values are divided divided into ranges, ranges, and each range is ass igned a descriptor descri ptor and a color code. Standardized Standardized public health advis ories are associated ass ociated with with each AQI range. An agency mig might ht also al so encourage encourage members members of the public public to take public transpor trans portation tation or work work from home home when AQI levels level s are high.
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Limitations of the AQI Most air contaminants do not have an associated AQI. Many countries monitor groundlevel ozone, particulates, sulphur dioxide, carbon monoxide and nitrogen dioxide and calculate air quality indices i ndices for these pollutants. pollutants.
Causes 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 of winds lets air pollution remain remain in a local area.
Indices by location
South Korea The Ministry of Environment Environment of South South Korea uses the Comprehensic Comprehensice e Air-qual Ai r-quality ity Index (CAI) to describe the ambient air quality based on health risk of air pollution. The index aims to help the public public eas e asil ily y understand understand air quality quali ty level and prot protect ect the health heal th of of people from ai r pollution. - The T he CAI has values of 0 through through 500, which are divided into i nto six si x categories. categ ories. The higher the the CAI value, the greater the the level of ai r pollution pollution.. - Of O f values of the five air pollutants, pollutants, the the highest hig hest is the CAI value.
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CAI
Description Description
0-50
Good
51-100
Moderate
101-150
Unhealthy for sensitive sensi tive groups groups
A level that may have harmful impacts on patients and members of sensitive sensi tive groups. groups.
151-250
Unhealthy
A level that may have harmful impacts on patients and members of sensitive sensi tive group groupss (children, (children, aged a ged or weak people), and a nd also als o cause the the general public public unpleas unpleasant ant feelings .
251-350
Very unheal unhealthy thy
351-500
Hazardous
Health Health Implications
A level that will not impact impact patients patients suffering from diseas es related to air pollution.
A level which may have a meager impact on patients in case of chronic exposure.
A level which may have a serious impact on patients and members of sensitive sensi tive groups groups in case of acute exposure. exposure.
A level which may need to take emergency measures for patients and members of sensitive groups and have harmful impacts on the general public.
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Malaysia The air quality in Malaysia is reported reported as a s the API or or Air Pollution Poll ution Index. Four of the index's pollutant components (i.e., carbon monoxide, ozone, nitrogen dioxide and sulfur dioxide) are reported in PM10 particulate matter is reported in μg/m³. Unlike the American AQI, AQ I, the index number number can exceed exce ed 500. Above 500, a state of emergency is declared in the reporting area. Usually, this means that non-essential government services are suspended, suspended, and all al l ports ports in the the affected area area closed. c losed. There There may also als o be be a prohibition prohibition on private sector sec tor commercial commercial and industria industriall activities acti vities in the the reporting reporting area excluding the food sector.
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Stock Market Index
A comparison of three major U.S. stock indices: the NASDAQ Composite, Dow Jones Industrial Industrial Average, Average, and S&P 500. All three have the same height at March 2007. Notice the large dot-com spike spi ke on on the NASDAQ, a result res ult of of the large l arge number number of tech. companies companies on that index.
A stock market index is a method of measuring a section of the stock market. Many indices are cited ci ted by news or fi nancial services fi rms rms and are used as benchmarks, to measure the performance of portfolios 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 (typical ly large) companies companies without without regard for where where they are domici domiciled led or traded. Two examples are MSCI World and S&P Global 100. A national index represents the perform performance ance of the stock market market of a given g iven nation 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 nation's largest larges t stock exchanges, s uch as the American American S&P 500, the Japanese Nikkei 225, and the the British Britis h FTSE 100.
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The concept may be extended well beyond an exchange. The Dow Jones Total Stock Market Index, as its name implies, 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 ADRs)) and most traded on the NASDAQ and NASDAQ and American Stock Exchange. Russell Investment Group added to the family of indices by launching the Russell Global Index. More More specialised special ised indices exis t tracking tracking the the perfo perform rmance ance of specific specif ic s ectors ectors of the the market. The Morgan Stanley Biotech Index, for example, example, consis ts of 36 American firms in the 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 Some indices, such s uch as the the S&P 500, have multiple versions versions..[1] 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 total retur return, n, full capitalization price, price, float-adjusted fl oat-adjusted total return return,, float-adjusted price, price, and equal weight. The difference between between the full capitalization, ca pitalization, float-adjusted, float -adjusted, and equal weight weig ht versi versions ons is in how how index components components are weighted.
Uses and importance of air pollution index and stock market index As everyone everyone can see,the ai r pollution index i ndex is use by the governm g overnment ent to meas measure ure the air
quality index and to detect any pollutants in our country’s air.This is to ensure the air is clean and safe for us to inhale.Besides inhale.Besi des that,an that,an early early warning warning can ca n be given to us if the air pollution is to high for us to get out of our homes. This warning is given based upon readings and interpretations of the air pollution index. As for the stock market market index, it is i s mai mainly nly for the busines s entrepreneur entrepreneurs. s. This type of index is used us ed to determine the outcome outcome of a stock s tock market market and a nd also als o the conclusion conclusi on of a stock
market. market. The stock market index is imp i mportant ortant because bec ause a country’s country’s economica economicall state sta te sometimes depend on it.
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CONCLUSION After doing research, answering questions, drawing graphs and some problem solving, I saw that the usage of index number 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 essecities. 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.
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REFLECTION After spending countless hours, days and night to finish this project and also sacrificing my time video games and mangas in this mid year holiday, there are several things that I can say...
Additional Additi onal Mathematics... Mathematics...
After sacrificing sacrifici ng my precious time just for you...
From the day I born... From the day I was able to holding holdi ng pencil... From the day I start start learning... le arning...
Sacrificing my Computer Games... Sacrificing my Video Games... Sacrificing my Facebook.. Facebook....
And... From the day I heard h eard your name... I always alw ays thought that you will be my greatest
Sacrificing my Internet... Sacrificing Sacrifici ng my Anime ... Sacrificing my Manga... Manga...
obstacle obstacle and rival i n excell ing
I real ized something really important in you...
in my life...
I really love you...
But after countless of hours... Countless of days... Countless Countless of nights...
You are my real friend... You my partner... You are my soul mate...
I LOVE U ADDITIONAL MATHEMATICS...
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