NAME : MOHAMAD HARITH BIN HABIB RAHMAN

CLASS : 5 AKAS

IC NO :

TEACHER : PN. VIJAYALETCHUMY

No. CONTENT Page Remark

1 Introduction

Brief History

2 Part A I Statistical Graphs

Allocation of RM100 Bantuan Khas Awal Persekolahan B13

II Mean and Standard

Deviation

total savings out of RM100 III Comments

3 Part B I Calculation of interest I

II Calculation of interest II

III Comments

4 Part C I Forming equation

II Graph using equation given

III Best Fit Graph

IV

Derive information from graph

5 Further Exploration

Choosing saving plans

6 Reflection

The students of form 5 who are taking Additional Mathematics are

required to carry out this project work. According to the guideline of this project

work, the project work can be either done individually or in groups. However,

I've chose to do this project individually. This project work essentially

contributes 10% of the marks for the trial examination of the Sijil Pelajaran

Malaysia (SPM). The objectives of this project work are as follows:

apply mathematics to everyday situations and appreciate the aesthetical

values of mathematics

develop mathematical knowledge and skills in a way which increases

students interest and confidence

enhance learning effectiveness through less exam-oriented and inquiry-

based learning.

improve problem-solving skills, thinking skills and mathematical reasoning.

Mathematics plays an important role in the human exploration of reality

both in respect of its own kind and other investigation. Mathematics gives the

basis or tool for all sort of discoveries. On the other hand, mathematical

reasoning makes us to be more rational. Mathematics also have a significant

role in dealing with a colossal amount of data such as programming, financial

analysis, accountancy,etc. Mathematics is analogous to a language - the more

one excel in it, the better he/she gets in it. Essentially, this is why our Math

teachers often accentuate us to do a lot of practices on math problems,

particularly on the concepts which we find it hard to grasp. In this coursework,

we're going to dive into the world of statistics which plays an important role in

our daily life.

Statistics Statistics is the study of data - how to collect, summarize and present data. But

what is data in the first place? Data is a collection of facts, such as values or

measurements. It can be numbers, words, measurements, observations or even

just descriptions of things. Data can be qualitative or quantitative.

Qualitative data is descriptive information (it describes something)

Quantitative data, is numerical information (numbers).

Statistics is a set of tools used to organize and analyze data. Data must either be

numeric in origin or transformed by researchers into numbers. For instance,

statistics could be used to analyze percentage scores English students receive on

a grammar test: the percentage scores ranging from 0 to 100 are already in

numeric form. Statistics could also be used to analyze grades on an essay by

assigning numeric values to the letter grades, e.g., A=4, B=3, C=2, D=1, and F=0.

Employing statistics serves two purposes, (1) description and (2) prediction.

Statistics are used to describe the characteristics of groups. These

characteristics are referred to as variables. Data is gathered and recorded for

each variable. Descriptive statistics can then be used to reveal the distribution

of the data in each variable.

Statistics is also frequently used for purposes of prediction. Prediction is based

on the concept of generalizability: if enough data is compiled about a particular

context (e.g., students studying writing in a specific set of classrooms), the

patterns revealed through analysis of the data collected about that context can

be generalized (or predicted to occur in) similar contexts. The prediction of what

will happen in a similar context is probabilistic. That is, the researcher is not

certain that the same things will happen in other contexts; instead, the

researcher can only reasonably expect that the same things will happen.

Prediction is a method employed by individuals throughout daily life. For

instance, if writing students begin class every day for the first half of the

semester with a five-minute freewriting exercise, then they will likely come to

class the first day of the second half of the semester prepared to again freewrite

for the first five minutes of class. The students will have made a prediction

about the class content based on their previous experiences in the class:

Because they began all previous class sessions with freewriting, it would be

probable that their next class session will begin the same way. Statistics is used

to perform the same function; the difference is that precise probabilities are

determined in terms of the percentage chance that an outcome will occur,

complete with a range of error. Prediction is a primary goal of inferential

statistics.

PART A

Statistics On October 25 2013, the Prime Minister in tandem with Finance Minister,

Datuk Seri Najib Tun Razak has approved an allocation of RM 540 million for

Bantuan Khas Awal Persekolahan 1Malaysia while presenting the Budget Year

2014. All students from Year 1 to Form 5 for 2014 school session will receive

RM 100 each. As a student receiving such aid, this is how I would use the

money:

I would mostly spend the money on books - reference books, exercise

books and story books. This is to aid my studies and as a preparation for

the upcoming public exam - Sijil Pelajaran Malaysia (SPM).

Following that, I would spend quite a number of the money on

transportation. This is because I often spend some time outdoors after

school - tuition class, co-curricular activities and religious sermons in

mosques.

I would spend the least on food. Most of the time, I would avoid going to

the eateries.

I will save the rest of the money for future expenses in case of an

emergency.

20%

30% 40%

10%

My Expenditure From The Financial Aid

Food

Transportation

Books

Savings

I've conducted an online survey regarding the savings of 5 Akas from the

financial aid and here's the outcome:

Data presentation:

Histogram

TotalSaving (RM)

≤10

≤20

≤30

≤40

≤50

≤60

≤70

≤80

≤90

≤100

Number of Pupils

5

3

2

6

4

1

3

2

2

1

0

1

2

3

4

5

6

7

≤RM10 ≤RM20 ≤RM30 ≤RM40 ≤RM50 ≤RM60 ≤RM70 ≤RM80 ≤RM90 ≤RM100

Nu

mb

er

Of

Pu

pils

Total Savings

Total Savings Of 5 Akas From The Financial Aid

Pie Chart

Frequency Polygon

≤RM10 17%

≤RM20 10%

≤RM30 7%

≤RM40 21%

≤RM50 14%

≤RM60 4%

≤RM70 10%

≤RM80 7% ≤RM90

7%

≤RM100 3%

Total Savings Of 5 Akas From The Financial Aid

0

1

2

3

4

5

6

7

≤RM10 ≤RM20 ≤RM30 ≤RM40 ≤RM50 ≤RM60 ≤RM70 ≤RM80 ≤RM90 ≤RM100

Nu

mb

er

Of

Pu

pils

Total Savings

Total Savings Of 5 Akas From The Financial Aid

Mean And Standard Deviation:

(Ungrouped data)

x̄ = 5(10)+3(20)+2(30)+6(40)+4(50)+1(60)+3(70)+2(80)+2(90)+1(100)

5+3+2+6+4+1+3+2+2+1

= 45.5

≈ 46

δ =

= 25.62

≈ 26

TotalSaving (RM)

10

20

30

40

50

60

70

80

90

100

Number of Pupils

5

3

2

6

4

1

3

2

2

1

Mean,x̄ = Σfx

Σf

Standard deviation,

(Grouped data)

x̄ = 5(5.5)+3(15.5)+2(25.5)+6(35.5)+4(45.5)+1(55.5)+3(65.5)+2(75.5)+2(85.5)+1(95.5)

29

= 41.01

≈ 41

δ =

= 26.49

≈ 27

Total Saving (RM)

1~ 10

11~ 20

21~ 30

31~ 40

41~ 50

51~ 60

61~ 70

71~ 80

81~ 90

91~ 100

Class mark 5.5

15.5

25.5

35.5

45.5

55.5

65.5

75.5

85.5

95.5

Number of Pupils

5

3

2

6

4

1

3

2

2

1

Mean,x̄ = Σfx

Σf

Standard deviation,

Comments: Mean and standard deviation is handy in analysing a large amount of data.

Mean, as a part of central tendency shows the average of a data. Essentially,

mean is the basis of standard deviation which is also a part of measures of

dispersion. Standard deviation indicates how much a data varies from its mean

or average. The average or mean savings of 5 Akas as shown in the ungrouped

data is RM 46. This shows that the overall saving of the students is RM 46. On

the other hand, the standard deviation of the data is 26. This indicates that

each students' savings varies a lot from the mean saving. (Standard deviation is

larger if data varies more).

If each student was given an additional RM 50, the new mean is, 50+46 =

RM96. The standard deviation remains the same, that is 26.

PART B

Assuming that I have saved the whole amount of the aid in Bank X which offers

a profit of 3% per annum, this is how I could calculate my total savings after 10

years:

Method 1:

100 x 1.0310 = 134.39

Method 2:

The total savings after 10 years is RM 134.39

Assuming that I have saved the whole amount of the aid in Bank X which offers

a profit of 0.25 per month, this is how I could calculate my total savings after 10

years:

Method 1:

100 x 1.0025120 = 134.94

Method 2:

The total savings after 10 years is RM 134.94

Discussion:

The total savings in both banks increases exponentially. The profit earned in

Bank Y is greater than the profit earned in Bank X by 1.6%.

PART C

Functions

Savings in RM of two students, Ali and Muthu for the first seven months, where

x is Ali's savings and y is Muthu's savings:

Non- linear graph :

x 25 35 51 65 77 90 100

y 50 51 52 54 61 67 73

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100 120

Graph of y against x

Non-linear graph reduced into linear graph:

Both non-linear graph and linear graph represents Ali's and Muthu's

savings which are related by its respective functions . Linear graph is

easier to interpret. Non-linear graph relates the saving of both students

to increase exponentially. Whereas, the linear graph relates the savings

of both student to increase linearly.

0

1000

2000

3000

4000

5000

6000

7000

8000

0 2000 4000 6000 8000 10000 12000

Graph of xy against x2

x2 625 1225 2601 4225 5929 8100 10000

xy 1250 1785 2652 3510 4697 6030 7300

Finding the value of constant k and p :

represents the slope, m of the graph and represents the y-

intercept, c of the graph.

(RM55)2 = RM3025

Muthu's saving is approximately RM2800 when Ali's savings is RM3025.

Further Exploration I've done some researches on basic savings plans from two different

financial institution - MayBank and Bank Simpanan Nasional (BSN).

Rates :

Credit Balance Interest Rate

Up to RM25,000

0.30%

Up to RM50,000

0.40%

Up to RM100,000

0.95%

Up to RM200,000

1.35%

Up to RM500,000

1.56%

Above RM500,000

1.66%

Rates:

Credit Balance Inerest Rate

Up to RM5,000 0.40% Up to RM50,000 0.80%

Above RM50,000 1.10%

Benefits: Earn interest irrespective of account balance No service or maintenance charge as long

as a minimum balance of RM20 is maintained Free mini statement

Benefits: » Ease of account opening with very low initial deposit. » Savings Passbook provided. » Waiver of annual fee for Bank Card / ATM Card. » Free six (6) over the counter visits per month. » Free eight (8) ATM Cash Withdrawals per month. » Free ATM Mini Statement. » No charges imposed upon closing of account.*

My comments:

Based on my comparison of both saving plans, I would choose to

have a Bank Simpanan Nasional account. It is because that the interest

rates provided by this bank is higher than MayBank. Thus, I would be

able to earn more profit.

Reflection This coursework means a lot to me because I was able to learn many stuffs

throughout this coursework. By conducting this coursework, I was able to learn

on how to practically apply mathematical skills in real-life situations. Thus, it

provided me a better understanding of the topics which are being discussed in

this project work.

Apart from that, this coursework has also enhanced my skills in terms of

technology. I had to virtually draw charts, graphs and type out various

mathematical equations which needs some kind of knowledge in computers -

this coursework has provided me that knowledge.

This coursework has also taught me to be independent. Everything that

can be seen in this coursework - words, graphs, charts, and equations are

genuinely drawn and typed by myself though I had referred some sources to

ensure my work is correct. To some degree, the fact that this work of mine is

genuine satisfies me.

Indirectly, I consider this coursework as a revision for my upcoming

examination. It is because, while carrying out this task, I had to revise previous

topics in order to complete this work.