SMK KUHARA TAWAU

NAME : MIMIE SHASHA SYAREEN BINTI MOHD MEM CLASS : 5 ST4 I/C NUMBER : 960414125718 TEACHER : SANTI BINTI MUSA

CONTENTTITLE PAGE

Introduction Acknowledge

History of statisticStatistic today

part 1Part 2Part 3

Further exploration Conclusion Reflection

INTRODUCTION

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 problem.

Experience classroom environments which are challenging,

interesting and meaningful and hence improve their

thinking skills.

Experience classroom environments where knowledge and

skills are applied in meaningful ways in solving real-life

problems.

Experience classroom environments where expressing ones

mathematical thingking, reasoning, and communication are

highly encouraged and expected.

Experience classroom environments that stimulates and

enchanceseffective learning.

Acquire effective mathematical communication through

oral and writing, and to use the language of mathematics to

express mathematical ideas correctly and precisely.

OBJECTIVES

The aims of carrying out this project work are :

To apply and adept a variety of problem solving strategies

to solve problems.

To improve thinking skills.

To promote effective mathematics communication.

To develop mathematics through solving in a way that

increase students interist and confidence.

To develop positive attitude towards mathematics.

ACKNOWLEDGE

Grace be upon to Allah, with his blessing, I can finished my Additoinal Mathematics Project Work. Of course, it was very hard work but the project was most interesting. I have learned a lot from it besides having a chance to sharpen my computer skill. But then again, all of this would not have been possible without a few people in my life.

Firstly, I would like to thank God with all my heart for helping me to finish my project within the time limit. Thank to God for blessing me with a clear understanding of this project, dedicated teachers, helpful parents and the plentiful resources available to me. Of course, they are just too many blessing that I were to mention them all, the list would never be end.

The most important person is none other than my addmaths teacher, Santi Musa. She always strive to give us the best. The next person who played major role in helping me to complete my project is my parents, they have been very helpful and extremely supportive of me. I would like also to thank to both of my parents for the financial support they have given to me.

Last but not least, I would like to thank to all my friends, especially to my closer friends for giving and sharing information with me. Thank you.

HISTORY OF STATISTIC

By the 18th century, the term “statistic” designated the systematic collection of demographic and economic data by states. In the 19th century, the meaning of statistic broadened, the including the discipline concerned with the collection, summary and analysis data. Today statistic is widely employed in government business, and all the sciences. Electronic computers have to expedited statistical computation, and have allowed statisticians to develop “computer intensive” methods. The relation between statistic and probability theory developed rather late, however. In the 19th century, statistic increasingly used probability theory, whose initial results were found in the 17th and 18th centuries. Probability and statistics have been in continual development. In 19th century, social scientist used both statistic and probability model to advance the new science of experimental. The development of statistic was closely associated with the development of inductive logic and the scientific methods. Statistic is not a field of mathematics but an autonomous mathematical science. Unlike mathematics, statistic had its origin in public administration and maintains a special concern with demography and economics. Being concerned with the scientific methods and inductive logic, statistical theory has close association with the philosophy of science, with its

emphasis on learning from data and making best predictions, statistics has great overlap with the decision.

STATISTIC TODAY

During the 20th century, the creation of precise instruments for

agricultural research, public health concerns, industrical quality

control, and economics and social purposes necessitated

substantial advances in statiscal practices. Today the used of

statistic has broadened for beyond its origin. Individuals and

organizations use statistic to understand data and make informed

decisions. Statistics are generally regarded not as the subfield og

mathematics but rather as a distinct, allied, field. Many

universities maintain separate mathematics and statistics

departments. Statistics is also thought in departments as diverse

as pshycology, education and public health.

Part 1

1. The importance of data analysis in daily life.

Structuring the finding from survey research or other

means of data collection.

Break a macro picture into a micro one.

Acquiring meaningful insights from the data set.

Basing critical decisions from the findings.

Ruling out human bias through proper statiscal

treatment.

2. (a) (i) Three types of measure of central tendency.

Mean

The mean is what in everyday conversation is

called the average. It is calculated by simply

adding the values of all the valid cases together

and dividing by the number of valid cases.

OR

Mode

The mode is the attribute of a variable that occurs

most often in the data set for ungrouped data, we

can find mode by finding the modal class and

draw the modal class and two classes adjacent to

the modal class. Two lines from the adjacent we

crossed to find the intersection. The intersection

value is known as the mode.

frequency

8

6

4

2

0 84.5 89.5 94.5 99.5 marks

Median

The median is a measure of central tendency. It

identity the values of the middle case.

M = L +

Range

- The distance between the minimum and the

maximum is called the range. The larger the

value of the range, the more dispersed the cases

are on the variable; the smaller the value of the

range, the less the range, the less dispersed the

cases are on the variable.

- Range =maximum value – minimum value

- Interquartile range (IQR) is the distance

between the 75th percentile and the 25th

percentile. The interquartile range is essentially

the range of the middle 50%of the data.

Because it uses the middle 50% the IQR is not

affected by outliers or extreme values.

Q1 = L + C Q3 = L + C

Standard deviation

The standard deviation tells you the approximate

average distance of cases from the mean. This is

easier to comprehend than squared distance of

cases from the mean. The standard deviation is

directly related to the variance.

σ =

2)b) - Mean

Calculating the average money used in a month

Determine the average marks achieved by the

students.

- Mode

Determine the marks achieved by a students which

is the most frequent.

- Median

Determine the centre marks achieved by the

students .

Calculate the marks achieved by a class.

Part 21. Monthly Test : BAHASA MALAYSIA ( 5 ST 4 )

NO. NAME MARKS1 STEVELY WILLIAMS PILAI 232 NICOLE YAPP YAP SING 303 DANNY FRED 404 MUHAMAD RUSYAIDI MAZLAN 425 WONG NYUK TING 436 SALMAN BIN YUNUS 447 NUR AINAA AFIFAH BINTI MAHADI 468 NUR ARRDILLA BINTI ARASTAM@RUSTAM 479 SUHAIZA SUHANA BINTI ROY 4710 ZAIREE BIN TANASTA 4811 SYAH RIZAL BIN PUSPA 4912 STEVE PETER 5013 MIMIE SHASHA SYAREEN BINTI MOHD MEM 5014 NUR SHAFINA BINTI MOHD JEFFRY 5115 MOHD MARWAN BIN MARIALI 5116 RAHMAT BIN NASARUDDIN 5217 YUWIE FHATIRA BINTI TOMOYOSHI@MOHD NISIR 5318 SUSANTI BINTI SUDIRMAN 5319 MOHD AIZUDDIN BINTI MOHD YUNUS 5420 ERMA YUSLINA BINTI ANDUN 5421 AZALIZA MARIAM BINTI BASIR 5422 MOHD SYAFIQ BIN USMAN@OSMAN 5523 NUR SYAZADATUL NISMA BONTI SUHURAN 5524 TASMIN BIN MUSTAFA 5625 SUARTINA BINTI ARTSAN 5626 NURHERANI BINTI NURDIN 5627 MANDY CHONG MUN YEE 5628 HISYAMUDDIN BIN ASSANAN 5629 ABDUL HALIM BIN NURDIN 5730 SAIFUL CHOK 5731 NURUL ADIBAH BINTI SUBIR 5832 NUR AFIQAH ZALIENNA BINTI MAHADI 5833 HARIATY BIN HAIRUDDIN 5834 SUMARNI BINTI PASELOI 5935 NURUL AFIQAH BINTI A.AMINULLAH 5936 MOHD HAFIZ BIN ROBERT 6037 LYANA LIM PUI CHING 6038 DAIRUL BIN DABANG 6039 RAMLAH BIN BACO 6140 NUR SYAZWANI BINTI ABDUL TALIB 6241 YEAP KAY FEI 6342 NOOR ASYIKIN BINTI LANANGKA 6343 SITI NUR AZMINA BINTI LAUPE@TOPPEH 6444 LO ZIN MANG 65

45 KHALEEDA BINTI MOHIN 73

2. Calculate the

(a) Mean =

=

= 53.51

(b) Median

Arranging the marks obtained by 45 students in order of magnitude.23, 30, 40, 42, 43, 44, 46, 47, 47, 48, 49, 50, 50, 51, 51, 52, 53, 53, 54, 54, 54, 55, 56, 56, 56, 56, 56, 57, 57, 58, 58, 58, 59, 59, 59, 60, 60, 60, 61, 62, 63, 64, 65, 73

Median = 55

(c) Mode 23, 30, 40, 42, 43, 44, 46, 47, 47, 48, 49, 50, 50, 51, 51, 52, 53, 53, 54, 54, 54, 55, 55, 56,

56, 56, 56, 56, 57, 57, 58, 58, 59, 59, 60, 60, 60, 60, 61, 62, 63, 63, 64, 65, 73

From the data above, the score that appeared with the most frequency is 56.

(d) standard deviation

σ =

= 2

= 8.787

3. Table one

Marks Frequency Midpoint fx Fx2

21- 30 2 25.5 51 1300.5

31-40 1 35.5 35.5 1260.5

41-50 10 45.5 455 20702.5

51-60 25 55.5 1387.5 77006.25

61-70 6 65.5 393 26741.5

71-80 1 75.5 75.5 5700.25

(a) From table one, find

(i) Mean,

=

=

= 53.28

(ii) Mode

The class with the highest frequency is 51-60.

Modal class = (51-60) marks

Mode = 55

(iii) Median

Method 1 using formulae.

N = 45 Median = L + C

L] = 50.5

C = 10 = 50.5 + C

F = 13

fm = 25 = 54.3

(iv) Standard deviation

Method 1

σ = 2

= 2

=

= 9.40

Method 2

σ =

=

=

= 9.40

(v) Interquatile range, Method 1

Q3 – Q1

Q3 = (45) Q3 = C

= 33.75 = 50.5+ 10

L = 50.5 = 58.8

F = 13

fm = 25

C = 10

Q1

Q3 = (45) Q1 = C

= 11.25 = 40.5+ 10

L = 40.5 = 48.75

F = 3

fm = 10

C = 10

Hence, interquatile range = Q3 – Q1

= 58.8 – 48.75

= 10.05

3.(b)

among the measure of the central tendency mean is the

most appropriate measure of central tendency that reflects

the performance of the class.

This is because by using mean all the data’s values are

taken into account when calculated by mean ,the mean

score will reflect the performance of the class.

(c)

Standard deviation is generally more useful than the

interquartile range as it includes all data in its calculation.

The interquartile range is totally dependent on just two

values and ignore all the other observation in the data. This

reduces the accurate it extreme values is present in the data.

Since the marks does not contain any extreme value,

standard deviation give a better measure compared the

interquartile range.

4.(a)

ungrouped data gives a more accurate representation. This

is because ungrouped data in its calculation while grouped

data is totally dependent on the estimated class with its

frequency.

(b)

when there are a lot of data involved of grouped data are

prepared as it is easier to calculate when there are only few

data involved ,ungrouped data are prepared

Part 31.

Students Marks Students Marks 1. 60 30. 642. 57 31. 603. 63 32. 474. 73 33. 675. 57 34 536. 61 35. 267. 59 36. 598. 76 37. 509. 68 38. 6210. 63 39. 5611. 59 40. 5212. 53 41. 5913. 57 42. 4614. 63 43. 6615. 54 44. 5616. 58 45. 5117. 45

18. 33

19. 66

20. 61

21. 49

22. 50

23. 58

24. 65

25. 59

26. 54

27. 62

28. 61

29. 55

Marks Number of students21-30 131-40 141-50 751-60 2161-70 1471-80 1

(a) MEAN

=

=

= 56.39

(b) MODE

Modal class = ( 51-60 )

Mode = 7

(c)MEDIAN

N = 45

L = 50.5

C = 10

F = 9

fm = 21

M = L +

(d) INTERQUARTILE RANGE

IQR = Q3 – Q1

Q1 = 1/4 ( 45 ) Q3 = 3/4 (45)

=11.25

= 33.75

L = 50.5 L = 60.5

F = 9 F = 30

C = 10 C = 10

fm = 21 fm = 14

(e)Standard deviation

2.

Marks Students21-30 131-40 141-50 751-60 2161-70 1471-80 181-90 091-100 1

New mean,

=

=

= 57.24

New standard deviation

6 = - ()2

= 2

= 114.27

FURTHER EXPLORATION

1) Calculation method

Arranging the marks obtained by 45 students in magnitude

Top 20% students

The top 9 students that has higher marco get the rewarded, this is 60, 60, 61, 62,63, 63, 64, 65, 73 is the lowest marco for the group is 60.

2) Mr. Ma’s class achieved a higher mean and a lower

standard deviation in the examination. Thus, Mr.Ma’s class

performed better than my class as Mr.Ma’s class achieved

higher mean which tell that his class has a higher scored

compared to my class which is lower. Furthermore, Mr.

23, 30.40. 42, 43, 44, 46, 47, 47, 48, 49, 50, 50, 51,

51, 52, 53, 53, 54, 54, 54, 55, 56, 56, 56, 56, 56, 57,

57, 58,58, 58, 59, 59, 59, 60, 60, 60, 61, 62, 63, 64,

65, 73,

Ma’s class has a lower standard deviation. This implied that

Mr. Ma’s class score are less dispersed. Thus, his class is

better than mine.

REFLECTION

This project will enhance the knowledge and experience of

applying and adapting mathematics in everyday life. After doing

research, answering questions, completing the table and solve

some problems, I found that the use of mathematics is important

in our daily lives. In conclusion, the creation of the best is to

have an attractive design, reasonable cost and easy to get.

Finally, some important aspects have been found in this design.

Therefore it is not surprising design play a big part to market a

product.