Additional Mathematics Project 2015

ACKNOWLEDGEMENT

First and foremost, I would like to thank my beloved Additional Mathematics teacher, Miss Yuen Kit Han for all the guidance she had patiently gave me during the period of completing this project.

Next, I would like to give my gratitude to both Mr. Johnny Ng Weng Yuen and Mrs. Yee Siow Chin as my parents who had gave me their full support in this project. Without them, I would have not able to finish this work in time.

I also would like to give my thanks to my fellow friends who had generously share their information that was needed in this project, and for the time we spent together in study groups to finish this project. Last but not least I would like to express my appreciation towards all who had made it possible to complete this coursework.

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INTRODUCTION

We students taking Additional Mathematics are required to carry out a project work while we are in Form 5. This project can be done in groups or individually, but each of us is 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 solving strategies to solve routine and non-routine problems;

Experience classroom environments which are challenging, interesting and meaningful and hence improve our thinking skills.

Experience classroom environments where knowledge and skills are applied in meaningful ways in solving real-life problems

Experience classroom environments where expressing one’s mathematical thinking, reasoning and communication are highly encouraged and expected

Experience a classroom environment that stimulates and enhances effective learning. Acquire effective mathematical communication through oral and writing, and 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 that mathematics is an important and powerful tool in solving real-life

problems and hence develop positive attitude towards mathematics. Train ourselves not only to be independent learners but also to collaborate, to

cooperate, and to share knowledge in an engaging and healthy environment Use technology appropriately and effectively Train ourselves to appreciate the intrinsic values of mathematics and to become more

creative and innovative Realise the importance and the beauty of mathematics

We are expected to submit the project work within three weeks from the first day the task is being administered to us. Failure to submit the written report will result in us not receiving a certificate.

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A BRIEF HISTORY OF HOUSEHOLD EXPENDITURE SURVEY (HES) IN MALAYSIA

The Household Expenditure Survey (HES) was first conducted in the year 1957/58. Beginning 1993/94 it was carried out at an interval of five years and subsequently in 1998/99. The recent survey was undertaken in 2009/2010. The survey covers private households in urban and rural areas.

The main objective of HES is to collect information on the level and pattern of consumption expenditure by households on a comprehensive range of goods and services. This information serves as the basis for determining the goods and services to be included in the basket of the Consumer Price Index (CPI). It is also used to update the CPI weights where the CPI is a measure of the average rate of change in prices of a fixed basket of goods and services which 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.

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USES OF MEAN AND STANDARD DEVIATION IN DAILY LIFE

Mean

In mathematics, mean has several different definitions depending on the context.

In probability and statistics, mean and expected value are used synonymously to refer to one

measure of the central tendency either of a probability distribution or of the random

variable characterized by that distribution. In the case of a discrete probability distribution of

a random variable X, the mean is equal to the sum over every possible value weighted by the

probability of that value; that is, it is computed by taking the product of each possible

value x of X and its probability P(x), and then adding all these products together,

giving  .[2] An analogous formula applies to the case of a continuous

probability distribution. Not every probability distribution has a defined mean; see

the Cauchy distribution for an example. Moreover, for some distributions the mean is infinite:

for example, when the probability of the value   is   for n = 1, 2, 3, ....

For a data set, the terms arithmetic mean, mathematical expectation, and

sometimes average are used synonymously to refer to a central value of a discrete set of

numbers: specifically, the sum of the values divided by the number of values. The arithmetic

mean of a set of numbers x1, x2, ..., xn is typically denoted by  , pronounced "x bar". If the

data set were based on a series of observations obtained by sampling from a statistical

population, the arithmetic mean is termed the sample mean (denoted  ) to distinguish it from

the population mean (denoted   or  ).

For a finite population, the population mean of a property is equal to the arithmetic mean of

the given property while considering every member of the population. For example, the

population mean height is equal to the sum of the heights of every individual divided by the

total number of individuals. The sample mean may differ from the population mean,

especially for small samples. The law of large numbers dictates that the larger the size of the

sample, the more likely it is that the sample mean will be close to the population mean.

Outside of probability and statistics, a wide range of other notions of "mean" are often used

in geometry and analysis.

(Based on http://en.wikipedia.org/wiki)

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Standard Deviation

In statistics, the standard deviation (SD) (represented by the Greek letter sigma, σ) is a

measure that is used to quantify the amount of variation or dispersion of a set of data values.

A large standard deviation indicates that the data points can spread far from the mean and a

small standard deviation indicates that they are clustered closely around the mean.

For example, each of the three populations {0, 0, 14, 14}, {0, 6, 8, 14} and {6, 6, 8, 8} has a

mean of 7. Their standard deviations are 7, 5, and 1, respectively. The third population has a

much smaller standard deviation than the other two because its values are all close to 7. It

will have the same units as the data points themselves. If, for instance, the data set {0, 6, 8,

14} represents the ages of a population of four siblings in years, the standard deviation is 5

years. As another example, the population {1000, 1006, 1008, 1014} may represent the

distances traveled by four athletes, measured in meters. It has a mean of 1007 meters, and a

standard deviation of 5 meters.

Standard deviation may serve as a measure of uncertainty. In physical science, for example,

the reported standard deviation of a group of repeated measurements gives the precision of

those measurements. When deciding whether measurements agree with a theoretical

prediction, the standard deviation of those measurements is of crucial importance: if the mean

of the measurements is too far away from the prediction (with the distance measured in

standard deviations), then the theory being tested probably needs to be revised. This makes

sense since they fall outside the range of values that could reasonably be expected to occur, if

the prediction were correct and the standard deviation appropriately quantified.

While the standard deviation does measure how far typical values tend to be from the mean,

other measures are available. An example is the mean absolute deviation, which might be

considered a more direct measure of average distance, compared to the root mean square

distance inherent in the standard deviation.

(Based on http://en.wikipedia.org/wiki)

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TASK SPECIFICATION

Page | 6

First Step

I had to research about the history of Household Expenditure Survey (HES) and list down the uses of mean and standard deviation in daily life

Second

Step

I had to gather and analyse the data about my family's income and monthly allocation using three different statistical graphI also had to find the mean and standard deviation of allocation of income by using at least 2 methods

Third Step

I had also collected, tabulated and compared the data from 5 friendsI also had to draw a line graph and bar chart to represent the education and recreation categories for 6 familiesI found the mean and standard deviation for education and recreation categories using at least 2 methods

Fourth

Step

I had to find the weightage in degrees based on the monthly income for my family and my 5 friendsI also had to find the corresponding expected monthly income based on the information given for my five friends and I

Fifth Step

I had to list and compare 20 richest and 20 poorest countries and their literate level (further exploration)

PROBLEM SOLVING

Part A

I was required to get my family’s income and monthly allocation for the following categories: Food, Utility, Transportation, Education, Recreation and others.

My findings are tabulated as below:

Monthly Income

(RM)

Number of family members

Categories Allocation of Income (RM)

Allocation of Income (%)

6000 5 Food 2000 33.33

Utility 500 8.33

Transportation 800 13.33

Education 700 11.67

Recreation 500 8.33

Others (Savings) 1500 25.00

Total 6000 100

Table 1: My Family’s Income and Monthly Allocation

(i) My data is represented using 3 different statistical graphs such as:

bar chart pie chart line graph

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Food Utility Transportation Education Recreation Others0

500

1000

1500

2000

2500

2000

500

800700

500

1500

My Family’s Monthly Allocation of Income

Categories

Allo

catio

n of

Inco

me

(RM

)

Bar Chart 1: My Family’s Monthly Allocation of Income

33.33

8.33

13.33

11.67

8.33

25

My Family's Monthly Allocation

FoodUtilityTransportationEducationRecreationOthers

Pie Chart 1: My Family’s Monthly Allocation of Income

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Line Graph 1: My Family’s Monthly Allocation of Income

(ii) The mean and standard deviation of allocation of income by using at least 2 methods

a) Method 1: Using the mean formulaMean, x = ∑x

N = 2000+500+800+700+500+1500 6 = 6000 6 = RM 1000

Method 2: Using Microsoft Excel

1. I entered the scores in one of the columns on the Excel spreadsheet. After the data has been entered, I selected the Formulas button. Then, I clicked the Function Wizard (fx) button.

2. A dialog box appeared. I click on AVERAGE. Then, I clicked on OK at the bottom of the dialog box.

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Categories

Allocation of Income (RM)

3. I entered the cell range of my data in the number 1 box. I clicked on OK at the bottom of the dialog box.

4. The mean (average) for the list is 1000.

b) Method 1: Using the standard deviation formula

Standard deviation, = (20002 +5002 +8002 +7002 +5002 +15002)

√ 6 = RM 559.76

Method 2: Using a calculator

1. Click on the MODE button twice. Press button “1” to choose “SD”. This puts the calculator in Statistics Mode.

2. Key in the first data, x, which is 2000 into the calculator. Press the SHIFT button, and follow by the “,” button.

3. After that, key in the frequency of the data 2000, which is 1.4. Press the M+ button.

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10002

5. Key in the rest of the data by repeating steps 2,3, and 4.6. After keying in all the data, press SHIFT button again.7. Press button “2”.8. Choose xσn by pressing button “2” for the answer of Standard Deviation of

the data.9. Press “=” button.10. The value of the standard deviation of the data showed on the calculator is

559.76 (after rounding off to the nearest 2 decimal points)

Comment: My family spends the most in the food category. This is because my family

always buys nutritious food as we practice a healthy lifestyle. My family spends the least in the utility and recreation categories. My family

is very thrifty and uses basic necessities with care. The answer for the mean and standard deviation for my family’s allocation of

money in Method 1 and Method 2 are the same. This shows that the results obtain are accurate.

Part B (i) The data from 5 of my friends is tabulated as below:

1. Regina Wong En Ning

Monthly Income Number of family members

Categories Allocation of Income (RM)

Allocation of Income (%)

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(RM)

10000 5 Food 1500 15

Utility 500 5

Transportation 500 5

Education 1500 15

Recreation 1000 10

Others (Savings) 5000 50

Total 10000 100

Table 2: Regina’s Family’s Income and Monthly Allocation

2. Lyxendra Chong Ee Shuen

Monthly Income

(RM)

Number of family members

Categories Allocation of Income (RM)

Allocation of Income (%)

10000 4 Food 1500 15

Utility 200 2

Transportation 600 6

Education 900 9

Recreation 300 3

Others (Savings) 6500 65

Total 10000 100

Table 3: Lyxendra’s Family’s Income and Monthly Allocation

3. Izyan Izzati binti Abd Ghafar

Monthly Income

(RM)

Number of family members

Categories Allocation of Income (RM)

Allocation of Income (%)

4500 11 Food 2475 55

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Utility 450 10

Transportation 450 10

Education 675 15

Recreation 225 5

Others (Savings) 225 5

Total 4500 100

Table 4: Izyan’s Family’s Income and Monthly Allocation

4. Poh Yang Yan

Monthly Income

(RM)

Number of family members

Categories Allocation of Income (RM)

Allocation of Income (%)

10000 4 Food 2000 20

Utility 500 5

Transportation 1000 10

Education 2000 20

Recreation 500 5

Others (Savings) 4000 40

Total 10000 100

Table 5: Yang Yan’s Family’s Income and Monthly Allocation

5. Jessica Chow Jin Wei

Monthly Income

(RM)

Number of family members

Categories Allocation of Income (RM)

Allocation of Income (%)

9000 5 Food 1530 17

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Utility 540 6

Transportation 540 6

Education 990 11

Recreation 1530 17

Others (Savings) 3870 43

Total 9000 100

Table 6: Jessica’s Family’s Income and Monthly Allocation

(ii) A comparison between my friends and I are shown below:

Category

Family

Allocation of Monthly Income (RM) Total Monthly income (RM)

Number of

Family members

Food Utility Transport-ation

Education Recreation Others

Ariana 2000 500 800 700 500 1500 6000 5

Regina 1500 500 500 1500 1000 5000 10000 5

Lyxendra 1500 200 600 900 300 6500 10000 4

Izyan 2475 450 450 675 225 225 4500 11

Yang Yan 2000 500 1000 2000 500 4000 10000 4

Jessica 1530 540 540 990 1530 3870 9000 5

Table 7: My Friends’ and My Family’s Income and Monthly Allocation

Comments: In my findings, most families have more money allocated on ‘Others’ to save money

for the future. However, Izyan’s family have more money allocated on ‘Food’ instead as they have to support a large number of family members.

Every family has the least expenditure on ‘Recreation’ besides Jessica’s family. This shows that most families put the least importance on recreation purposes.

(iii) The allocation of income of 6 families in education and recreation are represented as below:

(a) line graph

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Ariana Regina Izyan Lyxendra Yang Yan Jessica0

500

1000

1500

2000

2500

700

1500

675

900

2000

990

500

1000

225300

500

1530

Education

Recreation

Line Graph 2: Monthly Allocation of Income for Education and Recreation for 6 Families

(b) bar chart

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Family

Allocation of Income (RM)

Ariana Regina Lyxendra Izyan Yang Yan Jessica0

500

1000

1500

2000

2500

700

1500

900

675

2000

990

500

1000

300225

500

1530

EducationRecreation

Bar Chart 2: Monthly Allocation of Income for Education and Recreation for 6 Families

Comments: Every family spends more in the education category compared to the recreation

category besides Jessica’s family. Most family believes that education is more important than recreation. By having better education, children can grow into more responsible and successful adults who can contribute to the community.

Yang Yan’s family spends the most on education category. Izyan’s family spends the least on both education and recreation categories. This is

due to the large allocation of money on food as Izyan’s family has 11 family members.

(iv) The mean and standard deviation for education and recreation categories by using at least 2 methods

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Allocation of Income (RM) (RM)

Family

a) Method 1: Using the mean formulaMean of allocation of income in education, x = ∑x

N

= 700+1500+900+675+2000+990 6 = RM1127.50

Mean of allocation of income in recreation, x = ∑x

N

= 500+1000+300+225+500+1530 6 = RM 675.83

Method 2: Using Microsoft Excel

1. I entered the scores in one of the columns on the Excel spreadsheet. After the data has been entered, I selected the Formulas button. Then, I clicked the Function Wizard (fx) button.

2. A dialog box appeared. I click on AVERAGE. Then, I clicked on OK at the bottom of the dialog box.

Page | 17

3. I entered the cell range of my data in the number 1 box. I clicked on OK at the bottom of the dialog box.

4. The mean (average) for the list is 1127.5.5. Step 1 to 4 was repeated to find the mean of recreation category. The answer

stated is 675.83 (after rounding off to the nearest 2 decimal points).

b) Method 1: Using the standard deviation formula

Standard deviation of allocation of income in education,

= (7002 +15002 +9002 +6752 +20002 +9902)

√ 6 = RM475.78

Standard deviation of allocation of income in recreation,

= (5002 +10002 +3002 +2252 +5002 +15302)

√ 6 = RM454.80

Method 2: Using a calculator

1. Click on the MODE button twice. Press button “1” to choose “SD”. This puts the calculator in Statistics Mode.

2. Key in the first data, x, which is 700 into the calculator. Press the SHIFT button, and follow by the “,” button.

3. After that, key in the frequency of the data 700, which is 1.4. Press the M+ button.5. Key in the rest of the data by repeating steps 2,3, and 4.6. After keying in all the data, press SHIFT button again.7. Press button “2”.8. Choose xσn by pressing button “2” for the answer of Standard Deviation of

the data.9. Press “=” button.10. The answer showed on the calculator is 475.78 after rounding off to the

nearest 2 decimal points.11. Repeat step 1 until 9 for the Standard Deviation of allocation of income in

recreation.12. The answer shown on the calculator is 454.79 after rounding off to the nearest

2 decimal points.

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(1127.50)2

(675.83)2

Comments: The answer for the mean for education and recreation categories in Method 1 and

Method 2 are the same. This shows that the results obtain are accurate. The answer for the standard deviation for education category in Method 1 and Method

2 are the same but for recreation category in Method 1 and Method 2 are different (by 0.1). The answer becomes less accurate when certain values are rounded off during the calculations.

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Part C

(i) The weightage in degrees, for each category based on the monthly income for my 5 friends and my family

Category

Family

Allocation of Monthly Income ( ◦) Total Monthly income

( ◦)

Food Utility Transport-ation

Education Recreation Others

Ariana 120.0 30.0 48.0 42.0 30.0 90.0 360

Regina 54.0 18.0 18.0 54.0 36.0 180.0 360

Lyxendra 54.0 7.2 21.6 32.4 10.8 234.0 360

Izyan 198.0 36.0 36.0 54.0 18.0 18.0 360

Yang Yan 72.0 18.0 36.0 72.0 18.0 144.0 360

Jessica 61.2 21.6 21.6 39.6 61.2 154.8 360

Table 8: The Weightage for each Category based on the Monthly Income for my 5 friends and I

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54

7.2

21.6

32.4

10.8230.4

Weightage of Lyxendra's Family's Allocation of Income

FoodUtilityTransportEducationRecreationOthers

198

36

36

54

1818

Weightage of Izyan's Family's Allocation of Income

FoodUtilityTransportationEducationRecreationOthers

Pie Chart 2 and 3: The weightage of Lyxendra’s and Izyan’s Family’s Allocation of Income

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Food Utility Transportation Education Recreation Others0

20

40

60

80

100

120

140

160

180

200

120

30

4842

30

90

54

18 18

54

36

180

My familyRegina's family

Bar Chart 3: The weightage of Regina’s and My Family’s Allocation of Income

The weightage of Yang Yan’s to Jessica’s Family’s Allocation of Income in Degrees using Ratio

Page | 22

Weightage of Family’s Allocation of Income ( ◦)

Categories

Family Weightage ( ◦)

Food Utility Transportation Education Recreation

Others

Yang Yan 72 18 36 72 18 144

4:1:2:4:1:8

Jessica 61.2 21.6 21.6 39.6 61.2 154.8

17:6:6:11:17:43

Simplest ratio

4:1:2:4:1:8 and 17:6:6:11:17:43

Table 9: The weightage of Yang Yan’s Family’s Allocation of Income to that of Jessica’s Family in Ratio

(ii) The allocation of monthly income is expected to change next year as below:

Categories Allocation of Income

Food Increase by 10%

Utility Increase by 5%

Transportation Unchanged

Education Increase by 3%

Recreation Decrease by 2%

Others (Savings) Increase by !0%

The corresponding expected monthly income from the above information for my five friends and I are as below:

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1. My Family

Categories Allocation of Income in 2015

(RM)

Price Index of Allocation of

Income in year 2016 based on year 2015

Allocation of Income in 2016

(RM)

Food 2000 110 2200

Utility 500 105 525

Transportation 800 100 800

Education 700 103 721

Recreation 500 98 490

Others (Savings) 1500 110 1650

TOTAL RM 6386

Table 10: My Family’s Allocation of Monthly Income in 2015 and 2016

The composite index of my family’s total income in the year 2016 based on year 2015:

Ῑ = ∑WI ∑W

=110(120)+105(30)+100(48)+103(42)+98(30)+110(90) 120+30+48+42+30+90

=38316 360

=106.43

Hence, the corresponding expected income for my family in 2016:I = Q1

Q0

106.43 = Q1

RM 6000 Q1 = RM 6385.80

2. Regina Wong En Ning

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x 100

x 100

Categories Allocation of Income in 2015

(RM)

Price Index of Allocation of

Income in year 2016 based on year 2015

Allocation of Income in 2016

(RM)

Food 1500 110 1650

Utility 500 105 525

Transportation 500 100 500

Education 1500 103 1545

Recreation 1000 98 980

Others (Savings) 5000 110 5500

TOTAL RM 10700

Table 11: Regina’s Family Allocation of Monthly Income in 2015 and 2016

The composite index of Regina’s family’s total income in the year 2016 based on year 2015:

Ῑ = ∑WI ∑W

=110(54)+105(18)+100(18)+103(54)+98(36)+110(180) 54+18+18+54+36+180

=38520 360

=107

Hence, the corresponding expected income for Regina’s family in 2016:I = Q1

Q0

107 = Q1

RM 10000 Q1 = RM 10700

3. Lyxendra Chong Ee Shuen

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x 100

x 100

Categories Allocation of Income in 2015

(RM)

Price Index of Allocation of

Income in year 2016 based on year 2015

Allocation of Income in 2016

(RM)

Food 1500 110 1650

Utility 200 105 210

Transportation 600 100 600

Education 900 103 927

Recreation 300 98 294

Others (Savings) 6500 110 7150

TOTAL RM 10831

Table 12: Lyxendra’s Family Allocation of Monthly Income in 2015 and 2016

The composite index of Lyxendra’s family’s total income in the year 2016 based on year 2015:

Ῑ = ∑WI ∑W

=110(54)+105(7.2)+100(21.6)+103(32.4)+98(10.8)+110(234) 54+7.2+21.6+32.4+10.8+234

=38991.6 360

=108.31

Hence, the corresponding expected income for Lyxendra’s family in 2016:I = Q1

Q0

108.31 = Q1

RM 10000 Q1 = RM 10831

4. Izyan Izzati binti Abd Ghafar

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x 100

x 100

Categories Allocation of Income in 2015

(RM)

Price Index of Allocation of

Income in year 2016 based on year 2015

Allocation of Income in 2016

(RM)

Food 2475 110 2722.50

Utility 450 105 472.50

Transportation 450 100 450.00

Education 675 103 695.25

Recreation 225 98 220.50

Others (Savings) 225 110 247.50

TOTAL RM 4808.25

Table 13: Izyan’s Family Allocation of Monthly Income in 2015 and 2016

The composite index of Izyan’s family’s total income in the year 2016 based on year 2015:

Ῑ = ∑WI ∑W

=110(198)+105(36)+100(36)+103(54)+98(18)+110(18) 198+36+36+54+18+18

=38446 360

=106.85

Hence, the corresponding expected income for Izyan’s family in 2016:I = Q1

Q0

106.85 = Q1

RM 4500 Q1 = RM 4808.25

5. Poh Yang Yan

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x 100

x 100

Categories Allocation of Income in 2015

(RM)

Price Index of Allocation of

Income in year 2016 based on year 2015

Allocation of Income in 2016

(RM)

Food 2000 110 2200

Utility 500 105 525

Transportation 1000 100 1000

Education 2000 103 2060

Recreation 500 98 490

Others (Savings) 4000 110 4400

TOTAL RM 10675

Table 14: Yang Yan’s Family Allocation of Monthly Income in 2015 and 2016

The composite index of Yang Yan’s family’s total income in the year 2016 based on year 2015:

Ῑ = ∑WI ∑W

=110(72)+105(18)+100(36)+103(72)+98(18)+110(144) 72+18+36+72+18+144

=38430 360

=106.75

Hence, the corresponding expected income for Yang Yan’s family in 2016:I = Q1

Q0

106.75 = Q1

RM 10000 Q1 = RM 10675

6. Jessica Chow Jin Wei

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x 100

x 100

Categories Allocation of Income in 2015

(RM)

Price Index of Allocation of

Income in year 2016 based on year 2015

Allocation of Income in 2016

(RM)

Food 1530 110 1683.00

Utility 540 105 567.00

Transportation 540 100 540.00

Education 990 103 1019.70

Recreation 1530 98 1499.40

Others (Savings) 3870 110 4257.00

TOTAL RM 9566.10

Table 15: Jessica’s Family Allocation of Monthly Income in 2015 and 2016

The composite index of Jessica’s family’s total income in the year 2016 based on year 2015:

Ῑ = ∑WI ∑W

=110(61.2)+105(21.6)+100(21.6)+103(39.6)+98(61.2)+110(154.8) 61.2+21.6+21.6+39.6+61.2+154.8

=38264.4 360

=106.29

Hence, the corresponding expected income for Jessica’s family in 2016:I = Q1

Q0

106.29 = Q1

RM 9000 Q1 = RM 9566.10

FURTHER EXPLORATION

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x 100

x 100

1. The list of the 20 richest countries in the world and its literate level are shown below:

Rank Name of Country Literate Level (%)

1. Qatar 96.3

2. Luxembourg 100.0

3. Singapore 95.9

4. Norway 100.0

5. Hong Kong 93.5

6. Brunei Darussalam 95.4

7. United States 99.0

8. Switzerland 99.0

9. Canada 99.0

10. Australia 96.0

11. Austria 98.0

12. Ireland 99.0

13. Netherlands 99.0

14. Sweden 99.0

15. Taiwan 98.3

16. Germany 99.0

17. Iceland 99.0

18. Kuwait 94.0

19. Belgium 99.0

20. Denmark 99.0

(Based on http://www.richestlifestyle.com/richest-countries-in-the-world/10/ and http://en.wikipedia.org/wiki/List_of_countries_by_literacy_rate)

2. The list of the 20 poorest countries in the world and its literate level are shown below:

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Rank Name of Country Literate Level (%)

1. Democratic Republic of the Congo 66.8

2. Zimbabwe 90.7

3. Burundi 67.2

4. Liberia 60.8

5. Eritrea 80.0

6. Central African Republic 56.6

7. Niger 28.7

8. Malawi 74.8

9. Madagascar 64.5

10. Afghanistan 28.1

11. Mali 27.7

12. Togo 60.9

13. Guinea 41.0

14. Ethiopia 39.0

15. Mozambique 56.1

16. Guinea-Bissau 55.3

17. Comoros 75.5

18. South Sudan 27.0

19. Nepal 66.0

20. Haiti 52.9

(Based on http://www.rantlifestyle.com/2014/06/18/20-poorest-countries-in-the-world/ and http://en.wikipedia.org/wiki/List_of_countries_by_literacy_rate)

Conclusion: Rich countries are able to achieve high level of literacy instead only a few poor

countries achieved stable literacy level For example, Zimbabwe is the only poor country which literacy rate is high (at

90.7%) All rich countries have a literacy rate above 93% Hence, we should work together to generate income for our country to improve our

education system. This will increase the literacy rate among Malaysians in the future.

CONCLUSION

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In conclusion, we can conclude using mathematical method, to determine the Household Expenditure Survey (HES) by analyzing the obtained monthly income and its monthly allocation to determine the level and pattern of consumption expenditure by a household. Other than that, we can also use statistical graphs to determine the highest expenditure on a comprehensive range of goods and services by drawing bar chart, line graph and creating a pie chart. This concept can also be used to find out not only the mean of the monthly allocation of income but also its standard deviation for each family. From this we can also observe the advantages of using standard deviation a measurement of dispersion. I have learnt the importance of a composite or a composite index which is a combination of equities or indexes in measuring the overall expenditure in a household. Finally, I also can relate and conclude the countries’ income and its literate level based on the data I have found on the Internet in further exploration.

REFLECTION

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While conducting this project, I have learnt how important data analysis such as mean and standard deviation is in our daily life. Apart from that, this project encourages students to work together and share their knowledge. It is also encourages student to gather information from the internet, improve their thinking skills and promote effective mathematical communication. Based on my findings, I found that the mean mark and standard deviation of the allocation of income in education and recreation of the 6 families are off average and is spread out largely. Next, I was also able to calculate my family and my friends’ corresponding income in 2016 using composite index. Besides that, I also have found out that richer countries have higher literate level compared to that of poorer countries. Hence, we must improve our country’s economy in order to generate more income and thus, able to increase the literate level among Malaysians.

Not only that, I had also learned some moral values during the period of completing this project. This project had taught me how to be responsible on the work that was given to me to be completed .This project also helped me gained more confidence to do work and not to give up easily when we could not find the solution for the question. I also learned to be more punctual, which I was given about 3 weeks to complete this project and pass up to my teacher just in time. I proposed for this project work to be continued as the students will learn many moral values and it also tests the students’ knowledge in Additional Mathematics.

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What I have learned?

Being responsible

Being more confident

Not to easily give up

Being punctual

Thank you!

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