add math project 10

8/3/2019 Add Math Project 10

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SMK (P) ST. GEORGE

ADDITIONAL MATHEMATICS WORK 4 / 2010INDEX NUMBER IN OUR DAILY LIFE

NAME : ROSLIZA BINTI ABDUL RAHIM

CLASS : 5 JED

TEACHER : PUAN LEONG


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Introduction

A price index (plural: price indices or price indexes) is a normalized average

(typically a weightedaverage) ofprices for a given class ofgoods or services in a

given region, during a given interval of time. It is a statistic designed to help to

compare how these prices, taken as a whole, differ between time periods or

geographical locations.

Price indices have several potential uses. For particularly broad indices, the index can

be said to measure the economy's price level or a cost of living. More narrow price

indices can help producers with business plans and pricing. Sometimes, they can be

useful in helping to guide investment.

Some notable price indices include:

Consumer price index Producer price index

GDP deflator

No clear consensus has emerged on who created the first price index. The earliest

reported research in this area came from Welshman Rice Vaughan who examined

price level change in his 1675 bookA Discourse of Coin and Coinage. Vaughan

wanted to separate the inflationary impact of the influx of precious metals brought by

Spain from the New World from the effect due to currency debasement. Vaughan

compared labor statutes from his own time to similar statutes dating back to Edward

III. These statutes set wages for certain tasks and provided a good record of thechange in wage levels. Vaughan reasoned that the market for basic labor did not

fluctuate much with time and that a basic laborers salary would probably buy the

same amount of goods in different time periods, so that a laborer's salary acted as a

basket of goods. Vaughan's analysis indicated that price levels in England had risen

six to eightfold over the preceding century.[1]

While Vaughan can be considered a forerunner of price index research, his analysis

did not actually involve calculating an index.[1] In 1707 Englishman William

Fleetwood created perhaps the first true price index. An Oxford student asked

Fleetwood to help show how prices had changed. The student stood to lose his

fellowship since a fifteenth century stipulation barred students with annual incomes

over five pounds from receiving a fellowship. Fleetwood, who already had an interest

in price change, had collected a large amount of price data going back hundreds of

years. Fleetwood proposed an index consisting of averaged price relatives and used

his methods to show that the value of five pounds had changed greatly over the course

of 260 years. He argued on behalf of the Oxford students and published his findings

anonymously in a volume entitled Chronicon Preciosum.[2]
http://en.wikipedia.org/wiki/Averagehttp://en.wikipedia.org/wiki/Weighted_meanhttp://en.wikipedia.org/wiki/Weighted_meanhttp://en.wikipedia.org/wiki/Pricehttp://en.wikipedia.org/wiki/Good_(economics)http://en.wikipedia.org/wiki/Service_(economics)http://en.wikipedia.org/wiki/Statistichttp://en.wikipedia.org/wiki/Price_levelhttp://en.wikipedia.org/wiki/Cost_of_livinghttp://en.wikipedia.org/wiki/Consumer_price_indexhttp://en.wikipedia.org/wiki/Producer_price_indexhttp://en.wikipedia.org/wiki/GDP_deflatorhttp://en.wikipedia.org/wiki/Waleshttp://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/vaughan/coinhttp://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/vaughan/coinhttp://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/vaughan/coinhttp://en.wikipedia.org/wiki/Spainhttp://en.wikipedia.org/wiki/New_Worldhttp://en.wikipedia.org/wiki/Debasementhttp://en.wikipedia.org/wiki/Statute_of_Labourers_of_1351http://en.wikipedia.org/wiki/Edward_IIIhttp://en.wikipedia.org/wiki/Edward_IIIhttp://en.wikipedia.org/wiki/Price_index#cite_note-Chance.2C_108-0http://en.wikipedia.org/wiki/Price_index#cite_note-Chance.2C_108-0http://en.wikipedia.org/wiki/William_Fleetwoodhttp://en.wikipedia.org/wiki/William_Fleetwoodhttp://en.wikipedia.org/wiki/Price_index#cite_note-1http://en.wikipedia.org/wiki/Averagehttp://en.wikipedia.org/wiki/Weighted_meanhttp://en.wikipedia.org/wiki/Pricehttp://en.wikipedia.org/wiki/Good_(economics)http://en.wikipedia.org/wiki/Service_(economics)http://en.wikipedia.org/wiki/Statistichttp://en.wikipedia.org/wiki/Price_levelhttp://en.wikipedia.org/wiki/Cost_of_livinghttp://en.wikipedia.org/wiki/Consumer_price_indexhttp://en.wikipedia.org/wiki/Producer_price_indexhttp://en.wikipedia.org/wiki/GDP_deflatorhttp://en.wikipedia.org/wiki/Waleshttp://socserv2.socsci.mcmaster.ca/~econ/ugcm/3ll3/vaughan/coinhttp://en.wikipedia.org/wiki/Spainhttp://en.wikipedia.org/wiki/New_Worldhttp://en.wikipedia.org/wiki/Debasementhttp://en.wikipedia.org/wiki/Statute_of_Labourers_of_1351http://en.wikipedia.org/wiki/Edward_IIIhttp://en.wikipedia.org/wiki/Edward_IIIhttp://en.wikipedia.org/wiki/Price_index#cite_note-Chance.2C_108-0http://en.wikipedia.org/wiki/Price_index#cite_note-Chance.2C_108-0http://en.wikipedia.org/wiki/William_Fleetwoodhttp://en.wikipedia.org/wiki/William_Fleetwoodhttp://en.wikipedia.org/wiki/Price_index#cite_note-1


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Part 1

Category ItemPrice ( RM)

Tesco Econsave Jusco

Food 1. Self-Raising Flour ( 1kg) 3.65 3.95 4.052. Sugar ( Prai coarse sugar1kg)

1.65 1.65 1.65

3. Butter ( Buttercup DairySpread 500g)

8.49 8.90 8.90

4. Eggs(grade A) ( Seri Murnivit E 10s)

3.59 3.99 4.00

Total Price 17.38 18.49 18.60

Detergent

1. Softlan (3L) 6.99 6.95 6.992. TOP Liquid Blue Oceania

(5L)

21.99 22.90 24.90

3. ABC Detergent Powder(1kg)

17.90 17.90 17.90

4. Dynamo Regular (3kg) 18.25 12.50 12.99Total Price 65.13 60.25 62.78

Stationery

1.Faber Castel Trip Grib 2BPencil ( Box of 12 pcs)

9.20 7.20 9.60

2. Faber Castel click Ballpens 4 pcs

2.39 3.20 3.50

3. Unicon Ruler 15cm HalfWhite-2pcs

1.00 1.00 1.20

4. Papermate Liquid Paper7ml-2 pcs

10.40 10.70 12.40

Total Price 22.99 22.10 26.70

Grand Total 105.5 100.84 108.08


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c)

For the food category Tesco has the cheapest price. This is because for every item

Tesco sells them at a cheaper price compared to Econsave and Jusco.

Self-RaisingFlour(

1kg)

Sugar(Praicoarsesu

gar

1kg)

Butter(ButtercupDairy

Spread500g)

Eggs(gradeA)(Seri

MurnivitE10s)

Tesco

Econsave

Jusco

0

1

2

3

4

5

6

7

8

9

Price (RM)

Shops

Food Comparison


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For Soflan detergent Econsave is the cheapest, TOP Liquid Blue Oceania Tesco is thecheapest, ABC Detergent powder is the same at all the shops and for DynamoEconsave has the cheapest price.

Softlan(3L)

TOPLi

quidBlue

Oceania(5L)

ABCDetergent

Powder

(1kg)

DynamoRegular(3kg)

Tesco

Econsave

Jusco

0

5

10

15

20

25

Price (RM)

Shops

Detergent Comparison

Comparing the price of Detergent among Tesco, Econsave and Jusco

0

5

10

15

20

25

30

Softlan (3L) TOP Liquid Blue Oceania

(5L)

ABC Detergent Powder

(1kg)

Dynamo Regular (3kg)

Price(RM)

Tesco

Econsave

Jusco


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Econsave sells Faber castel Trip Grib 2B at the cheapest price. Faber Castel click Ballpens is cheaper at Tesco. The price for Unicorn Ruler at Tesco and Econsave is thesame price which is also cheaper than Jusco. Tesco sells Papermate Liquid Paper at acheaper price compared to Jusco and Econsave.

FaberCastel Trip

Grib 2B

Pencil (

Box of 12

pcs)

Faber

Castel

click Ball

pens 4 pcs

Unicon

Ruler

15cm Half

White-

2pcs

Papermate

Liquid

Paper

7ml-2 pcs

Tesco

Econsave

Jusco

0

2

4

6

8

10

12

14

Price (RM)

Shops

Stationary Comparison


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Conclusion:

Comparing the total price of selected items of food, detergent and stationary

among Tesco, Econsave and Jusco

0

10

20

30

40

50

60

70

Food Detergent Stationary

Tesco

Econsave

Jusco

FoodDetergent

Stationary

Tesco

Econsave

Jusco

0

10

20

30

40

50

60

70

Price (RM)

Comparing the total price of selcted items of food, detergent and

stationary among Tesco, Econsave and Jusco

Tesco

Econsave

Jusco


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The price at Tesco are competitive for most items. However, shoppers are advised tocompare prices between Tesco and Econsave, especially the high price item such asdetergent. This is because, at Tesco, sometime the price for certain items isabnormally higher than Econsave.

The price are less competitive at Jaya Jusco (especially stationary). However, fordetergent and food, the price difference is not obvious. Therefore, shoppers areadvised to consider other factors such as parking fee, transportation, time consumingand etc. before making decision.


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e) From the table above, the item that has large price difference is Dynamo Regular

(3kg) Detergent.

The mean of the price,

Mean = 18.25+12.50+12.99= 14.48

3

The standard Deviation = 2.60

The price difference is possibly due to Jusco and Econsave are doing promotion for

this item.


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Part 2

a) I would go to Tesco to purchase the ingredients fo the butter cakes. This is

because all the items there are cheaper compared to Econsave and Jusco.

When the price of the raw materials are cheaper, there are better chances of

the sale to be better as we will be able to sell them at a cheaper price. This will

then give us a higher chance of getting a good profit out of the sale of butter

cakes.

b) I

b) II

Price index Weightage Price index weightage101.4 0.9 10=9 912.694.3 0.35 10=3.5 330.05

128.6 3.30 10=33 4243.8143.6 1.25 10=12.5 1795

W= 58 IW = 7281.45

Composite Index

= IW

W

= 7281.45

58

Ingredients Quantity per cake

Price in theyear 2009(RM)

Price in theyear 2010(RM)

Price Index

Self-raisingflour

250g 0.90 0.9125 101.4

Sugar 200g 0.35 0.33 94.3Butter 250g 3.30 4.245 128.6Eggs (Grade A) 5 eggs 1.25 1.795 143.6


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= 125.54


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c) I

Capacity of any cooling machine is known in 'ton'. Ton here means One ton ofwater(1,000kg).If we take water which already cool at 0 degree centigrade and switchon the machine, then quantity of ice produced in 24 hours(one day) will determine its

capacity. If it produces one ton of ice then capacity of machine is one ton.If itproduces 100 kg of ice(solid) in 24 hrs then the capacity is 0.1 ton.

(Source of information: http://sawaal.ibibo.com/physics/how-cal ... 13215.html)

The capacity of air conditioner is given in BTU (British Thermal Unit) or HP (HorsePower). The British thermal unit (BTU or Btu) is a traditional unit of energy equal toabout 1.06 kilojoules. It is approximately the amount of energy needed to heat 1

pound (0.454 kg) of water 1 F (0.556 C). It is used in the power, steam generation,heating and air conditioning industries. In scientific contexts the BTU has largely

been replaced by the SI unit of energy, the joule, though it may be used as a measure

of agricultural energy production (BTU/kg). It is still used unofficially in metricEnglish-speaking countries (such as Canada and the United Kingdom), and remainsthe standard unit of classification for air conditioning units manufactured and sold inmany non-English-speaking metric countries.

(Sources of information: http://en.wikipedia.org/wiki/British_thermal_unit )
http://sawaal.ibibo.com/physics/how-calculate-capacity-airconditioner-813215.htmlhttp://en.wikipedia.org/wiki/British_thermal_unithttp://sawaal.ibibo.com/physics/how-calculate-capacity-airconditioner-813215.htmlhttp://en.wikipedia.org/wiki/British_thermal_unit


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To determine the BTUs needed to cool a given space follow this procedure:

1. Calculate the total square feet to be cooled: Measure the size of the room (orrooms) to be cooled, to obtain total square feet. Multiply room length by widthfor each room and if there are multiple rooms, add the room areas together to

get a single number.2. Read the Base BTUs needed from Table below.The table below gives

recommended air conditioning BTU's necessary to cool a single room. Thedata in the table assumes that the ceiling over the room is insulated and thatthe room is not over or is not itself a special heat-producing area such as akitchen or boiler room.

Table 1: Base BTUs - Recommended Air Conditioner BTUs

Number ofRoomsCooled

Room AreaMINimumsq.ft.

Room AreaMAXimumsq.ft.

BTUsNeeded

One . 100 4,000 - 6,000

One 100 180 6,000 - 7,500

One 180 270 7,500 - 9,000

One 270 400 9,000 - 10,500

Several . 400 10,500 - 12,000

Several 400 500 12,000 - 13,500

Several 500 700 13,500 - 15,000

Several 700 800 15,000 - 16,500

Large Areas . 900 16,500 - 18,000

Large Areas 900 1000 18,000 - 19,500

Large Areas 1,000 1,100 19,500 - 21,000

Large Areas 1,000 1,100 19,500 - 21,000

Large Areas 1,100 1,200 12,000 - 22,500

Large Areas 1,200 1,500 22,500 - 24,000

Large Areas 1,500 1,700 24,000 - 25,500

Large Areas 1,700 1,900 25,500 - 27,000

Large Areas 1,900 2,200 27,000 - 28,500

3. Add additional BTUs for these factors:

a. + 4,000 BTUs for each room below a ceiling or roof which is not insulatedb. + 4,000 BTUs for a home or residential kitchen included in the cooled areac. + 1,500 BTUs for each window which receives significant daily sunshined. + 1,500 BTUs for a room over a kitchen or boiler room IF the kitchen or

boiler room is actively producing heat during the cooling period

e. + 600 BTUs per person over two, if more than two occupants will beoccupying the room during the cooling period


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4. Subtract BTUs from the total required if these factors are present:

- 1,000 BTUs if the room is on the shaded side of the building

5. Calculate the final total BTUh needed from the above steps. This should place you

in the right range of cooling capacity needed. Review the warning below aboutbuying an oversized air conditioner.

c) II

The volume of the school library is 12,000 cubic feet, and it has an averageinsulation ,the library has 4 windows receiving significant sunlight, and we expectthere are in average 30 students at all time using the library everyday, the calculationof the Capacity of the Air Conditioner is as below:

12,000 x 3 = 36,000 BTU/h (for a room of 12,000 cubic feet with average insulation)+ 4 x 1,500 BTU/h (for 4 windows receiving significant sunlight)

+ 30 x 600 BTU/h (for 30 students occupying the library)= 60,000 BTU/h

So, air conditioners needs to have a total capacity of 60,000 BTU/h for the library.The capacity and price of the air conditioners is obtain from this website HSL (HockSin Leong)'s official website. http://www.hslene.com.my/default_ca.htm

I have chosenAIR COND-WALL SPLIT TYPE 2HP.Cooling Capacity: 17,100 BTU/hPrice: RM 2,399

and

AIR COND-WALL SPLIT 1HP (Model SHP-AHAUP9LMV)

Cooling capacity: 9000 BTU/hPrice: RM1,199

In order to obtain cooling capacity of 60,000 BTU/h, you need 3 units ofAIRCOND-WALL SPLIT TYPE 2HP and 1 unit ofAIR COND-WALL SPLIT 1HP.

Therefore, the total price is RM 2,399 x 3 + RM 1,199 = RM 8,396c) IIIf the selling price of the cake is RM18,80, the profit you make for selling each cake= RM18.80 - (RM 0.9125 + RM0.33 + RM4.245 + RM1.795) = RM 11.5175 RM11.5

The price of the 4 units of air conditioner = RM 8,396. In order to buy the 4 units ofair conditioner, you need to sell8396 = 730 units of butter cake11.5
http://www.hslene.com.my/default_ca.htmhttp://www.hslene.com.my/default_ca.htmhttp://www.hslene.com.my/default_ca.htmhttp://www.hslene.com.my/default_ca.htmhttp://www.hslene.com.my/default_ca.htmhttp://www.hslene.com.my/default_ca.htmhttp://www.hslene.com.my/default_ca.htmhttp://www.hslene.com.my/default_ca.htmhttp://www.hslene.com.my/default_ca.htmhttp://www.hslene.com.my/default_ca.htmhttp://www.hslene.com.my/default_ca.htmhttp://www.hslene.com.my/default_ca.htm


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Part 3

a)

Expenditure Amount in 2009 (RM) Amount in 2010 (RM)

Food 1200.00 1380.00

Games 500.00 500.00

Transportation 300.00 345.00

Decorations 200.00 200.00

Prizes 600.00 600.00

Tents 800.00 920.00

Miscellaneous 400.00 520.00

b)

Weightage Price Index Price index weightage12 115 1380

5 100 500

3 115 345

2 100 200

6 100 600

8 115 920

4 130 520

W = 40 IW = 4465Composite index

IW 4465= W = 40 = 111.625

Conclusion:The overall budget for year 2010 should increase by 11.625% basing on the value ofcomposite index (111.625).c) Composite index of the budget for the year 2011 based on 2009

= 111.625 x 111.625 = 124.6100


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Further Exploration

Index numbers are designed to measure the magnitude of economic changes overtime. Because they work in a similar way to percentages they make such changeseasier to compare.

Stock Market index

A stock market index is a method of measuring a section of the stock market. Manyindices are cited by news or financial services firms and are used as benchmarks, tomeasure the performance ofportfolios such as mutual funds.

In stock market Index numbers are basically economic data information that reflectthe price or quantity compared with standard or remnant value. It is normallyexpressed as 100 times the ratio of the base worth that equals 100. Index numbers arevery important for economic analysis. They summarize movements surrounded by agroup of related variables. The consumer Price index is one of the most commonlyused form of index number. It measures the changes in the retail prices. These indexnumbers also used to evaluate the condition of the stock market by economic analysis.The up and down of the stockmarket were identified using index numbers. Therefore index numbers are veryimportant n stock market.

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, ordamages the natural environment into the atmosphere. The atmosphere is a complexdynamic 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 threatto human health as well as to the Earth's ecosystems.

The Air Quality Index (AQI) (also known as the Air Pollution Index (API) orPollutant Standard Index (PSI) is a number used by government agencies tocharacterize the quality of the air at a given location. As the AQI increases, anincreasingly large percentage of the population is likely to experience increasinglysevere adverse health effects .To compute the AQI requires an air pollutant

concentration from a monitor or model .The function used to convert from airpollutant concentration to AQI varies by pollutant, and is different in differentcountries. Air quality index values are divided into ranges, and each range is assigneda descriptor and a color code. Standardized public health advisories are associatedwith 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.
http://en.wikipedia.org/wiki/Stock_markethttp://en.wikipedia.org/wiki/Benchmarkinghttp://en.wikipedia.org/wiki/Portfolio_(finance)http://en.wikipedia.org/wiki/Mutual_fundhttp://en.wikipedia.org/wiki/Stock_markethttp://en.wikipedia.org/wiki/Benchmarkinghttp://en.wikipedia.org/wiki/Portfolio_(finance)http://en.wikipedia.org/wiki/Mutual_fund


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Reflection

While I conducting the project, I had learned some moral values that Ipractice. This project had taught me to responsible on the works that aregiven to me to be completed. This project also had make me felt moreconfidence to do works and not to give easily when we could not find thesolution for the question.

I also learned to be more discipline on time, which I was given about amonth to complete these project and pass up to my teacher just in time. Ialso enjoy doing this project during my school holiday as I spend my timewith friends to complete this project and it had tighten our friendship.

add math project 10

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