Additional Mathematics Project 2015
- 1. ADDITIONAL MATHEMATICS PROJECT 2015 Sekolah Menengah Kebangsaan Sri Hartamas The HouseholdExpenditure Survey(HES) 2015 Name : Nur Farah binti Elias 6/5/2015 Teacher’sname : Ms. Yuen Class : 5 Neptune
- 2. 2 No. Content Page Remark 1 Introduction 2 Part A: FamilyMonthly Income andIts Allocation I Statistical Graphs II Mean and StandardDeviation III Comments 3 Part B: Family Monthly Income andIts Allocationof 5 Friends I Data and Tables II ComparisonandComments III a) Line graph and Bar graph representing educationandrecreationcategories b) Comments IV a) Mean andStandard Deviation b) Comments 4 Part C: MonthlyIncome Weightage inSix Families I The Weightage inPie chart,Bar chart and Ratio Form II The Change of Allocationof MonthlyIncome 5 Further Explorations I 20 RichestandPoorestCountriesinthe World and theirLiteral Level II Conclusion 6 Reflection
- 3. 3 INTRODUCTION : The Household Expenditure Survey (HES) was first conducted in the year of 1957/58. Beginning 1993/94 it was carried out at an interval of five years and the recent survey was undertaken in 2009/10. The survey covered private households in urban and rural areas. The main objective of HES was to collect information on the level and pattern of consumption expenditure by households on a comprehensive range of goods and services. This information served as the basis for determining the goods and services to be included in the basket of the Consumer Price Index (CPI). It was also used to represent the expenditure pattern of households in Malaysia. However,over the years, demand for data from the survey has increased and it is now used for several purposes. HES has become an invaluable source of information for government and private sectors, researchers and university students.
- 4. 4 PART A: Family monthly income and its monthly allocation Monthly Income (RM) Number of family members Categories Allocation of income (RM) Allocation of income (%) 10,000 5 Food 3500 35 Utility 1500 15 Transportation 500 5 Education 1000 10 Recreation 1000 10 Others 2500 25 Total 10,000 100 Presentation of my family’s monthly income through different statistical graphs. 0 5 10 15 20 25 30 35 40 Line graph (%) Allocation of Income (%)
- 5. 5 0 5 10 15 20 25 30 35 40 Food Utility Transportation Education Recreation Others Bar graph (%) 35 15 5 10 10 25 Pie chart (%) Food Utility Transportation Education Recreation Others
- 6. 6 The mean and standard deviation of allocation of income: Method 1 Calculator : Mean = Allocation of Income Number of Categories = 3500 + 1500 + 500 + 1000 + 1000 + 2500 6 = 10,000 6 = 1666.67 Standard deviation: x x² Standard Deviation 3500 12,250,000 √Σx² - X² 1500 2,250,000 N 500 250,000 = √23,000,000 - (1666.67)² 1000 1,000,000 6 1000 1,000,000 = √1055544.44 2500 6,250,000 Σx = 10,000 Σx² = 23,000,000 1027.40
- 7. 7 Method2 : Excel Mean : As showninthe image above,the meanis RM1666.67 Standard deviation : As showinthe image above,the standarddeviationis RM1027.40
- 8. 8 Comments: My family mostly use our monthly income on food as there are a lot of people to feed. We cook a lot of big meals that require a lot of ingredients, which can be quite costly. Though, my family used the least money on transportation because petrol costs have not been really high lately, compared to every other item’s cost.
- 9. 9 PART B: 5 different family monthly allocations from 5 friends. Friend 1: Monthly Income (RM) Number of family members Categories Allocation of income (RM) Allocation of income (%) 10,000 5 Food 3000 30 Utility 1000 10 Transportation 2000 20 Education 2000 20 Recreation 1000 10 Others 1000 10 Total 10,000 100 Friend 2 : Monthly Income (RM) Number of family members Categories Allocation of income (RM) Allocation of income (%) 10,000 5 Food 3000 30 Utility 1500 15 Transportation 1500 15 Education 1000 10 Recreation 500 5 Others 2500 25 Total 10,000 100 Friend 3 : Monthly Income (RM) Number of family members Categories Allocation of income (RM) Allocation of income (%) 10,000 6 Food 3500 35
- 10. 10 Utility 1000 10 Transportation 500 5 Education 1500 15 Recreation 1500 15 Others 2000 20 Total 10,000 100 Friend 4 : Monthly Income (RM) Number of family members Categories Allocation of income (RM) Allocation of income (%) 10,000 3 Food 1500 15 Utility 1500 15 Transportation 2000 20 Education 2000 20 Recreation 500 5 Others 2000 20 Total 10,000 100 Friend 5 : Monthly Income (RM) Number of family members Categories Allocation of income (RM) Allocation of income (%) 10,000 5 Food 3000 30 Utility 1000 10 Transportation 500 5 Education 1500 15 Recreation 1000 10 Others 3000 30 Total 10,000 100 Comparison about my findings: Family Monthly Income Number of Family Members Categories Allocation of Monthly IncomeFood Utility Trans- portation Education Recreation Others Friend1 10,000 5 3000 1000 2000 2000 1000 1000 10,000
- 11. 11 Friend2 5 3000 1500 1500 1000 500 2500 Friend3 6 3500 1000 500 1500 1500 2000 Friend4 3 1500 1500 2000 2000 500 2500 Friend5 5 3000 1000 1500 1500 1000 3000 Comments: Majorityof the familieshasmostlyuseduptheirmonthlyincome onfood,usuallyforbigger families- thereforemore mouthstofeed. The leastmonthlyincomeusedgenerallyforall families are recreational activitiesbecause the familiesare busywithworkorschool. Graphs presenting data of education and recreation categories for all six families. Line graph: 0 5 10 15 20 25 30 35 Family 1 Family 2 Family 3 Family 4 Family 5 Family 6 Recreation Education
- 12. 12 Bar chart: Comments: Most of the familieshave spenttheirmonthlyincome more towardseducationratherthan recreationbecause the parentsof the familiesneedtopayfor tutoringclassesforthe children. Therefore,the familiescan’tspendmuchonrecreationaseveryone isbusywitheithertutoring classesor earningmoneyforthe tutoringclasses. The mean and standard deviation for education and recreation categories: 0 5 10 15 20 25 30 35 Family 1 Family 2 Family 3 Family 4 Family 5 Family 6 Recreation Education
- 13. 13 Education: Method1: Calculator Mean = Total Education Number of Families = 20 + 10 + 15 + 20 + 15 +10 6 = 90 6 = 15 StandardDeviation x x² Standard Deviation 20 400 √Σx² - X² 10 100 N 15 225 = √1450 - (15)² 20 400 6 15 225 = √16.67 10 100 Σx = 90 Σx² = 1450 4.08 Method2 : Excel Mean :
- 14. 14 As showinthe image above,the meanis RM15. StandardDeviation: As showinthe image above,the standarddeviationis RM4.08.
- 15. 15 Recreation: Method1: Calculator Mean = Total Recreation Number of Families = 10 + 5 + 15+ 5 + 10 + 10 6 = 55 6 = 9.17 StandardDeviation x x² Standard Deviation 10 100 √Σx² - X² 5 25 N 15 225 = √575 - (9.17)² 5 25 6 10 100 = √45.08 10 100 Σx = 55 Σx² = 575 3.44 Method2 : Excel Mean
- 16. 16 As showinthe image above,the meanis RM 9.16. StandardDeviation As showinthe image above,the standarddeviationis RM3.44. Comments The mean of the education category is higher than the mean of the recreation category. Alongsidethat, the standard deviation of the education category is also higher than the standard deviation of the recreation category. PART C:
- 17. 17 Monthly Income: Weightage in Degrees for six families Family Categories Allocation of Monthly Income Food Utility Trans- portation Education Recreation Other My family 126 54 18 36 36 90 360 Friend1 109 36 72 72 36 36 Friend2 108 54 54 36 18 90 Friend3 126 36 18 54 54 72 Friend4 54 54 72 72 18 90 Friend5 108 36 18 54 36 108 Weightages of any two families in the form of:- Pie chart: Bar chart: 126 5418 36 36 90 My family Food Utility Trans- portation Education Recreation Others Friend 1 Food Utility Trans- portation Education Recreation Others
- 18. 18 Ratio form: Family Categories Food Utility Trans- portation Education Recreation Others Friend4 15 15 20 20 5 25 Friend5 30 10 5 15 10 30 Ratio 1:2 3:2 4:1 4:3 1:2 5:6 The corresponding expected monthly income based on the information that was given for me and five other friends: Family Categories Allocationof Monthly Income Food Utility Trans- portation Education Recreation Others My family 3850 1575 500 1030 1020 2750 10725 Friend1 3300 1050 2000 2060 980 1100 10490 Friend2 3300 1575 1500 1030 490 2750 10645 Friend3 3850 1050 500 1545 1530 2200 10675 Friend4 1650 1575 2000 2060 490 2200 9975 Friend5 3300 1050 500 1545 980 3300 10675 0 20 40 60 80 100 120 Friend 2 Friend 3
- 19. 19 Further explorations: The 20 richest and 20 poorest countries in the world and their literate level The richest: Rank Country name Literacy level 1 Qatar 96.3% 2 Luxembourg 100% 3 Singapore 95.9% 4 Norway 100% 5 Brunei Darussalam 95.4% 6 Hong Kong 93.5% 7 United States 99% 8 United Arab Emirates 77.9% 9 Switzerland 99% 10 Australia 96% 11 Canada 99% 12 Austria 98% 13 Ireland 99% 14 Netherlands 99% 15 Sweden 99% 16 Iceland 99% 17 Taiwan 98.29% 18 Germany 99% 19 Kuwait 94% 20 Denmark 99% The poorest: Rank Country Name Literacy Level 1 Democratic Republic of the Congo 66.8% 2 Zimbabwe 90.7% 3 Burundi 67.2% 4 Liberia 60.8% 5 Eritrea 80% 6 Central African Republic 56.6% 7 Malawi 74.8% 8 Madagascar 64.5% 9 Afghanistan 28.1% 10 Mali 27.7%
- 20. 20 11 Togo 60.9% 12 Guinea 41% 13 Ethiopia 39% 14 Mozambique 56.1% 15 Guinea-Bissau 55.3% 16 Comoros 75.5% 17 South Sudan 27% 18 Nepal 66% 19 Haiti 52.9% 20 Uganda 66.8% Conclusion: I have concludedthatrich countriesare able toachieve highlevelof literacy,whileonlyratherfew poor countriesare able toachieve stable literacylevel. REFLECTION: While doing this project, I realised that I still have a lot more to learn. Whether it’s through the formulas used above, or the research that was required to gather information- it was overall rather difficult but very interesting to do. Additional Mathematics is very well known as a difficult subject in upper form of Secondary School, but students should not simply give up because they cannot answer the problems given in the subject. Instead, students should understand that Additional Mathematics is one of the many ways to practice having high thinking skills. There’s always a solution if they just try harder.