Additional Mathematics Project 2015

Teacher’s name : Ms. Yuen

Class : 5 Neptune

ADDITIONAL MATHEMATICS PROJECT 2015Sekolah Menengah Kebangsaan Sri Hartamas

The Household Expenditure Survey (HES) 2015

Name : Nur Farah binti Elias

6/5/2015

No. Content Page Remark

1 Introduction

2 Part A:Family Monthly Income and Its Allocation

I Statistical Graphs

II Mean and Standard Deviation

III Comments

3 Part B:Family Monthly Income and Its Allocation of 5 Friends

I Data and Tables

II Comparison and Comments

III a) Line graph and Bar graph representing education and recreation categoriesb) Comments

IV a) Mean and Standard Deviationb) Comments

4 Part C:Monthly Income Weightage in Six Families

I The Weightage in Pie chart, Bar chart and Ratio Form

II The Change of Allocation of Monthly Income

5 Further Explorations

I 20 Richest and Poorest Countries in the World and their Literal Level

II Conclusion

6 Reflection

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.

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 5Food 3500 35Utility 1500 15

Transportation 500 5Education 1000 10Recreation 1000 10

Others 2500 25Total 10,000 100

Presentation of my family’s monthly income through different statistical graphs.

Food

Utility

Transp

ortation

Educati

on

Recrea

tion

Others0

5

10

15

20

25

30

35

40

Line graph (%)

Allocation of Income (%)

Food Utility Transportation Education Recreation Others0

5

10

15

20

25

30

35

40

Bar graph (%)

35

155

10

10

25

Pie chart (%)

FoodUtilityTransportationEducationRecreationOthers

The mean and standard deviation of allocation of income:

Method 1 Calculator :

Mean = Allocation of Income

Number of Categories

= 3500 + 1500 + 500 + 1000 + 1000 + 25006

= 10,0006

= 1666.67

Standard deviation:

x x² Standard Deviation3500 12,250,000 √Σx² - X²1500 2,250,000 N 500 250,000 = √23,000,000 - (1666.67)²

1000 1,000,000 6 1000 1,000,000 = √1055544.442500 6,250,000

Σx = 10,000 Σx² = 23,000,000 1027.40

Method 2 :

Excel

Mean :

As shown in the image above, the mean is RM 1666.67

Standard deviation :

As show in the image above, the standard deviation is RM 1027.40

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.

PART B:5 different family monthly allocations from 5 friends.

Friend 1:


members



10,000 5Food 3000 30Utility 1000 10


Others 1000 10Total 10,000 100

Friend 2 :


members



10,000 5Food 3000 30Utility 1500 15


Others 2500 25Total 10,000 100

Friend 3 :


members



10,000 6Food 3500 35Utility 1000 10


Others 2000 20Total 10,000 100

Friend 4 :


members



10,000 3Food 1500 15Utility 1500 15


Others 2000 20Total 10,000 100

Friend 5 :


members



10,000 5Food 3000 30Utility 1000 10


Others 3000 30Total 10,000 100

Comparison about my findings:

Family Monthly Income

Number of Family Members

Categories Allocation of

Monthly IncomeFoo

dUtility Trans-

portationEducation Recreation Others

Friend 1 10,000 5 3000 1000 2000 2000 1000 1000 10,000

Friend 2 5 3000 1500 1500 1000 500 2500

Friend 3 6 3500 1000 500 1500 1500 2000

Friend 4 3 1500 1500 2000 2000 500 2500

Friend 5 5 3000 1000 1500 1500 1000 3000

Comments:

Majority of the families has mostly used up their monthly income on food, usually for bigger families- therefore more mouths to feed. The least monthly income used generally for all families are recreational activities because the families are busy with work or school.

Graphs presenting data of education and recreation categories for all six families.

Line graph:

Family 1 Family 2 Family 3 Family 4 Family 5 Family 60

5

10

15

20

25

30

35

RecreationEducation

Bar chart:

Family 1 Family 2 Family 3 Family 4 Family 5 Family 60

5

10

15

20

25

30

35

RecreationEducation

Comments:

Most of the families have spent their monthly income more towards education rather than recreation because the parents of the families need to pay for tutoring classes for the children. Therefore, the families can’t spend much on recreation as everyone is busy with either tutoring classes or earning money for the tutoring classes.

The mean and standard deviation for education and recreation categories:

Education:

Method 1:

Calculator

Mean = Total Education

Number of Families

= 20 + 10 + 15 + 20 + 15 +106

= 906

= 15

Standard Deviation

x x² Standard Deviation20 400 √Σx² - X²10 100 N 15 225 = √1450 - (15)²20 400 6 15 225 = √16.6710 100

Σx = 90 Σx² = 1450 4.08

Method 2 :

Excel

Mean :

As show in the image above, the mean is RM15.

Standard Deviation :

As show in the image above, the standard deviation is RM 4.08.

Recreation :

Method 1:

Calculator

Mean = Total RecreationNumber of

Families= 10 + 5 + 15+ 5 + 10 + 10

6= 55

6= 9.17

Standard Deviation

x x² Standard Deviation10 100 √Σx² - X²5 25 N

15 225 = √575 - (9.17)²5 25 6

10 100 = √45.0810 100

Σx = 55 Σx² = 575 3.44

Method 2 :

Excel

Mean

As show in the image above, the mean is RM 9.16.

Standard Deviation

As show in the image above, the standard deviation is RM 3.44.

Comments

The mean of the education category is higher than the mean of the recreation category. Alongside that, the standard deviation of the education category is also higher than the standard deviation of the recreation category.

PART C:

Monthly Income: Weightage in Degrees for six families

Family Categories Allocation of Monthly

IncomeFood Utility Trans-

portationEducation Recreation Other

My family

126 54 18 36 36 90 360Friend 1 109 36 72 72 36 36

Friend 2 108 54 54 36 18 90

Friend 3 126 36 18 54 54 72

Friend 4 54 54 72 72 18 90

Friend 5 108 36 18 54 36 108

Weightages of any two families in the form of:-

Pie chart:

126

541836

36

90

My family

FoodUtilityTrans-porta-tionEducationRecreationOthers

Friend 1

FoodUtilityTrans-portationEducationRecreationOthers

Bar chart:

Food Utility Transportation Education Recreation Others0

20

40

60

80

100

120

Friend 2Friend 3

Ratio form:

Family CategoriesFood Utility Trans-

portationEducation Recreation Others

Friend 4 15 15 20 20 5 25Friend 5 30 10 5 15 10 30Ratio 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 Allocation of Monthly Income

Food Utility Trans- portation

Education Recreation Others

My family 3850 1575 500 1030 1020 2750 10725Friend 1 3300 1050 2000 2060 980 1100 10490Friend 2 3300 1575 1500 1030 490 2750 10645Friend 3 3850 1050 500 1545 1530 2200 10675Friend 4 1650 1575 2000 2060 490 2200 9975Friend 5 3300 1050 500 1545 980 3300 10675

Further explorations:

The 20 richest and 20 poorest countries in the world and their literate level

The richest:

Rank Country name Literacy level1 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 Level1 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%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 concluded that rich countries are able to achieve high level of literacy, while only rather few poor countries are able to achieve stable literacy level.

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.

Additional Mathematics Project 2015

Education

Transcript of Additional Mathematics Project 2015