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SABAH SCIENCE SECONDARY SCHOOL (HIGH PERFORMING SCHOOL)

Statistic Of 5Delta Addmaths Marks NAME:NURUL AINA SHAZWANA CLASS:5D I/C NUMBER:961007-12-5870 TEACHER:MADAM CHIN SIAU LING

CONTENT

ACKNOWLEDGEMENT

OBJECTIVE

INTRODUCTION

TASK SPECIFICATION

PROBLEM SOLVING

FUTHER EXPLORATION

REFLECTION

ACKNOWLEDGEMENT Grace be upon to Allah, with his blessing, I can finished my Additoinal Mathematics Project Work. Of course, it was kind of

hard work but the

project was interesting. I have learned a lot from this project besides having a chance to enchance my computer skill. Nevertheless, all of this would not have been possible without any support from everyone. Firstly, I would like to say thank to 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,Madam Chin Siau Ling. 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.

OBJECTIVES

-The aim of carrying this project work are :1.

To develop mathematical knowledge in a way which increase student’s

interest and confidence. 2. To apply mathematics to everyday situations and to begin to understand the part that mathematics plays in the world in which we live. 3. To improve thinking skill and promote effective mathematical communication. 4. To assist student to develop positive attitude and personalities,intrinsic mathematical values such as accurancy,confidence and system reasoning. 5. To stimulate learning and enhance effective learning.

INTRODUCTION

The History of statistics can be said to start around 1749 although, over time, there have been changes to the interpretation of the word statistics. In early times, the meaning was restricted to information about states. This was later extended to include all collections of information of all types, and later still it was extended to include the analysis and interpretation of such data. In modern terms, "statistics" means both sets of collected information, as in national accounts and temperature records, and analytical work which requires statistical inference.

Statistical activities are often associated with models expressed using probabilities, and require probability theory for them to be put on a firm theoretical basis: see History of probability.

A number of statistical concepts have had an important impact on a wide range of sciences. These include the design of experiments and approaches to statistical inference such as Bayesian inference, each of which can be considered to have their own sequence in the development of the ideas underlying modern statistics.

Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of highlighting useful information, suggesting conclusions, and supporting decision making. Data analysis has multiple facts and approaches, encompassing diverse techniques under a variety of names, in different business, science, and social science domains.

Data analysis is a process used to transform, remodel and revise certain information (data) with a view to reach to a certain conclusion for a given situation or problem. Data analysis can be done by different methods as according to the needs and requirements. For example if a school principal wants to know whether there is a relationship between students’ performance on the district writing assessment and their socioeconomic levels. In other words, do students who come from lower socioeconomic backgrounds perform lower, as we are led to believe? Or are there other variables responsible for the variance in writing performance? Again, a simple correlation analysis will help describe the students’ performance and help explain the relationship between the issues of performance and socioeconomic level. Analysis does not have to involve complex statistics. Data analysis in schools involves collecting data and using that data to improve teaching and learning. Interestingly, principals and teachers have it pretty easy. In most cases, the collection of data has already been done. Schools regularly collect attendance data, transcript records, discipline referrals, quarterly or semester grades, norm- and criterion-referenced test scores, and a variety of other useful data. Rather than complex statistical formulas and tests, it is generally simple counts, averages, percents, and rates that educators are interested in.

PART 1 (IMPORTANCE OF DATA IN DAILY LIFE) Data plays an important role in the information we receive on a daily basis from environmental print, newspapers, television, magazines, the Internet, etc. Other areas of mathematics are deeply embedded into this strand of the curriculum. When working through data analysis activities, students naturally draw upon other mathematical skills such as understanding of number, operations, patterning, and various problem solving strategies. Students view various forms of data in many other areas of the curriculum, such as prediction charts in Science,population

graphs

in

Social

Studies,

or

informational

text

in

LanguageArts. For students, the process of data analysis is not only interesting, but constitutes real problem solving linked to many aspects of theirenvironment. There are many benefits of data analysis however; the most important ones are as follows: - data analysis helps in structuring the findings from different sources of data collection like survey research. It is again very helpful in breaking a macro problem into micro parts. Data analysis acts like a filter when it comes to acquiring meaningful insights out of huge data-set. Every researcher has sort out huge pile of data that he/she has collected, before reaching to a conclusion of the research question. Mere data collection is of no use to the researcher. Data analysis proves to be crucial in this process. It provides a meaningful base to critical decisions. It helps to create a complete dissertation proposal. One of the most important uses of data analysis is that it helps in keeping human bias away from research conclusion with the help of proper statistical treatment. With the help of data analysis a researcher can filter both qualitative and quantitative data for anassignment writing projects. Thus, it can

be said that data analysis is of utmost importance for both the research and the researcher. Or to put it in another words data analysis is as important to a researcher as it is important for a doctor to diagnose the problem of the patient before giving him any treatment. In business,data analysis is important to businesses will be an understatement. In fact, no business can survive without analyzing available data. Visualize the following situations like a pharma company is performing trials on number of patients to test its new drug to fight cancer, number of patients under the trial is well over 500, A company wants to launch new variant of its existing line of fruit juice. It wants to carry out the survey analysis and arrive at some meaningful conclusion. Sales director of a company knows that there is something wrong with one of its successful products, however hasn't yet carried out any market research data analysis. How and what does he conclude? These situations are indicative enough to conclude that data analysis is the lifeline of any business. Whether one wants to arrive at some marketing decisions or fine-tune new product launch strategy, data analysis is the key to all the problems. What is the importance of data analysis - instead, one should say what is not important about data analysis. Merely analyzing data isn't sufficient from the point of view of making a decision. How does one interpret from the analyzed data is more important. Thus, data analysis is not a decision making system, but decision supporting system. Data analysis can offer the following benefits such as structuring the findings from survey research or other means of data collection,break a macro picture into a micro one,Acquiring meaningful insights from the dataset

basing critical decisions from the findings and Ruling out human bias through proper statistical treatment.

1. Types of Measure of Central Tendency and of Measure of Dispersion Central tendency gets at the typical score on the variable, while dispersion gets at how much variety there is in the scores. When describing the scores on a single variable, it is customary to report on both the central tendency and the dispersion. Not all measures of central tendency and not all measures of dispersion can be used to describe the values of cases on every variable. What choices you have depend on the variable’s level of measurement.

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 ̅

∑ ∑

The mean is an interval/ratio measure of central tendency. Its calculation requires that the attributes of the variable represent a numeric scale Mode The mode is the attribute of a variable that occurs most often in the data set.

For ungroup 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. Median

The median is a measure of central tendency. It identifies the value of the middle case when the cases have been placed in order or in line from low to high. The middle of the line is as far from being extreme as you can get.

(

)

There are as many cases in line in front of the middle case as behind the middle case. The median is the attribute used by that middle case. When you know the value of the median, you know that at least half the cases had that value or a higher value, while at least half the cases had that value or a lower value.

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 dispersed (the more concentrated) the cases are on the variable Range = maximum value – minimum value Interquartile range is the distance between the 75th percentile and the 25th percentile. The IQR 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.

(

)

(

)

Interquartile range = Q3 - Q1

Standard Deviation The standard deviation tells you the approximate average distance of cases from the mean. This is easier to comprehend than the squared distance of cases from the mean. The standard deviation is directly related to the variance.

If you know the value of the variance, you can easily figure out the value of the standard deviation. The reverse is also true. If you know the value of the standard deviation, you can easily calculate the value of the variance. The standard deviation is the square root of the variance

∑ √( ∑

)

̅

1. the Mark Additional Mathematics test scores for your class

Student

Marks

1

89

2

86

3

79

4

77

5

71

6

69

7

69

8

68

9

67

10

66

11

65

12

60

13

59

14

57

15

52

16

49

17

47

18

47

19

45

20

43

21

39

22

37

23

35

MARKS

24

31

25

29

26

27

27

26

28

22

29

19

30

15

TALLY

FREQUENCY

0-10

0

11-20

2

21-30

4

31-40

4

41-50

5

51-60

3

61-70

7

71-80

3

81-90

2

91-100

0

1)a)Mean

MARKS

MIDPOINT,x

FREQUENCY,f

Fx

1-10

5.5

0

0

11-20

15.5

2

31

21-30

25.5

4

102

31-40

35.5

4

142

41-50

45.5

5

227.5

51-60

55.5

3

166.5

61-70

65.5

7

458.5

71-80

75.5

3

226.5

81-90

85.5

2

171

91-100

95.5

0

0

TOTAL

30

∑f = 30 ∑fx = 1525 Mean, ̅ = =50.8333

1525

(2) mode

The modal class is 61-70, the majority of the students got that marks.

To find the mode mark, we draw the modal class and two classes adjacent to the modal class.

(REFER TO HISTOGRAM 1)

Based on the histogram;

Mode = 64.5

Reflection http://dissertation-help-uk.blogspot.com/2011/12/importance-of-data-analysisin-research.html

View more...
Statistic Of 5Delta Addmaths Marks NAME:NURUL AINA SHAZWANA CLASS:5D I/C NUMBER:961007-12-5870 TEACHER:MADAM CHIN SIAU LING

CONTENT

ACKNOWLEDGEMENT

OBJECTIVE

INTRODUCTION

TASK SPECIFICATION

PROBLEM SOLVING

FUTHER EXPLORATION

REFLECTION

ACKNOWLEDGEMENT Grace be upon to Allah, with his blessing, I can finished my Additoinal Mathematics Project Work. Of course, it was kind of

hard work but the

project was interesting. I have learned a lot from this project besides having a chance to enchance my computer skill. Nevertheless, all of this would not have been possible without any support from everyone. Firstly, I would like to say thank to 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,Madam Chin Siau Ling. 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.

OBJECTIVES

-The aim of carrying this project work are :1.

To develop mathematical knowledge in a way which increase student’s

interest and confidence. 2. To apply mathematics to everyday situations and to begin to understand the part that mathematics plays in the world in which we live. 3. To improve thinking skill and promote effective mathematical communication. 4. To assist student to develop positive attitude and personalities,intrinsic mathematical values such as accurancy,confidence and system reasoning. 5. To stimulate learning and enhance effective learning.

INTRODUCTION

The History of statistics can be said to start around 1749 although, over time, there have been changes to the interpretation of the word statistics. In early times, the meaning was restricted to information about states. This was later extended to include all collections of information of all types, and later still it was extended to include the analysis and interpretation of such data. In modern terms, "statistics" means both sets of collected information, as in national accounts and temperature records, and analytical work which requires statistical inference.

Statistical activities are often associated with models expressed using probabilities, and require probability theory for them to be put on a firm theoretical basis: see History of probability.

A number of statistical concepts have had an important impact on a wide range of sciences. These include the design of experiments and approaches to statistical inference such as Bayesian inference, each of which can be considered to have their own sequence in the development of the ideas underlying modern statistics.

Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of highlighting useful information, suggesting conclusions, and supporting decision making. Data analysis has multiple facts and approaches, encompassing diverse techniques under a variety of names, in different business, science, and social science domains.

Data analysis is a process used to transform, remodel and revise certain information (data) with a view to reach to a certain conclusion for a given situation or problem. Data analysis can be done by different methods as according to the needs and requirements. For example if a school principal wants to know whether there is a relationship between students’ performance on the district writing assessment and their socioeconomic levels. In other words, do students who come from lower socioeconomic backgrounds perform lower, as we are led to believe? Or are there other variables responsible for the variance in writing performance? Again, a simple correlation analysis will help describe the students’ performance and help explain the relationship between the issues of performance and socioeconomic level. Analysis does not have to involve complex statistics. Data analysis in schools involves collecting data and using that data to improve teaching and learning. Interestingly, principals and teachers have it pretty easy. In most cases, the collection of data has already been done. Schools regularly collect attendance data, transcript records, discipline referrals, quarterly or semester grades, norm- and criterion-referenced test scores, and a variety of other useful data. Rather than complex statistical formulas and tests, it is generally simple counts, averages, percents, and rates that educators are interested in.

PART 1 (IMPORTANCE OF DATA IN DAILY LIFE) Data plays an important role in the information we receive on a daily basis from environmental print, newspapers, television, magazines, the Internet, etc. Other areas of mathematics are deeply embedded into this strand of the curriculum. When working through data analysis activities, students naturally draw upon other mathematical skills such as understanding of number, operations, patterning, and various problem solving strategies. Students view various forms of data in many other areas of the curriculum, such as prediction charts in Science,population

graphs

in

Social

Studies,

or

informational

text

in

LanguageArts. For students, the process of data analysis is not only interesting, but constitutes real problem solving linked to many aspects of theirenvironment. There are many benefits of data analysis however; the most important ones are as follows: - data analysis helps in structuring the findings from different sources of data collection like survey research. It is again very helpful in breaking a macro problem into micro parts. Data analysis acts like a filter when it comes to acquiring meaningful insights out of huge data-set. Every researcher has sort out huge pile of data that he/she has collected, before reaching to a conclusion of the research question. Mere data collection is of no use to the researcher. Data analysis proves to be crucial in this process. It provides a meaningful base to critical decisions. It helps to create a complete dissertation proposal. One of the most important uses of data analysis is that it helps in keeping human bias away from research conclusion with the help of proper statistical treatment. With the help of data analysis a researcher can filter both qualitative and quantitative data for anassignment writing projects. Thus, it can

be said that data analysis is of utmost importance for both the research and the researcher. Or to put it in another words data analysis is as important to a researcher as it is important for a doctor to diagnose the problem of the patient before giving him any treatment. In business,data analysis is important to businesses will be an understatement. In fact, no business can survive without analyzing available data. Visualize the following situations like a pharma company is performing trials on number of patients to test its new drug to fight cancer, number of patients under the trial is well over 500, A company wants to launch new variant of its existing line of fruit juice. It wants to carry out the survey analysis and arrive at some meaningful conclusion. Sales director of a company knows that there is something wrong with one of its successful products, however hasn't yet carried out any market research data analysis. How and what does he conclude? These situations are indicative enough to conclude that data analysis is the lifeline of any business. Whether one wants to arrive at some marketing decisions or fine-tune new product launch strategy, data analysis is the key to all the problems. What is the importance of data analysis - instead, one should say what is not important about data analysis. Merely analyzing data isn't sufficient from the point of view of making a decision. How does one interpret from the analyzed data is more important. Thus, data analysis is not a decision making system, but decision supporting system. Data analysis can offer the following benefits such as structuring the findings from survey research or other means of data collection,break a macro picture into a micro one,Acquiring meaningful insights from the dataset

basing critical decisions from the findings and Ruling out human bias through proper statistical treatment.

1. Types of Measure of Central Tendency and of Measure of Dispersion Central tendency gets at the typical score on the variable, while dispersion gets at how much variety there is in the scores. When describing the scores on a single variable, it is customary to report on both the central tendency and the dispersion. Not all measures of central tendency and not all measures of dispersion can be used to describe the values of cases on every variable. What choices you have depend on the variable’s level of measurement.

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 ̅

∑ ∑

The mean is an interval/ratio measure of central tendency. Its calculation requires that the attributes of the variable represent a numeric scale Mode The mode is the attribute of a variable that occurs most often in the data set.

For ungroup 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. Median

The median is a measure of central tendency. It identifies the value of the middle case when the cases have been placed in order or in line from low to high. The middle of the line is as far from being extreme as you can get.

(

)

There are as many cases in line in front of the middle case as behind the middle case. The median is the attribute used by that middle case. When you know the value of the median, you know that at least half the cases had that value or a higher value, while at least half the cases had that value or a lower value.

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 dispersed (the more concentrated) the cases are on the variable Range = maximum value – minimum value Interquartile range is the distance between the 75th percentile and the 25th percentile. The IQR 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.

(

)

(

)

Interquartile range = Q3 - Q1

Standard Deviation The standard deviation tells you the approximate average distance of cases from the mean. This is easier to comprehend than the squared distance of cases from the mean. The standard deviation is directly related to the variance.

If you know the value of the variance, you can easily figure out the value of the standard deviation. The reverse is also true. If you know the value of the standard deviation, you can easily calculate the value of the variance. The standard deviation is the square root of the variance

∑ √( ∑

)

̅

1. the Mark Additional Mathematics test scores for your class

Student

Marks

1

89

2

86

3

79

4

77

5

71

6

69

7

69

8

68

9

67

10

66

11

65

12

60

13

59

14

57

15

52

16

49

17

47

18

47

19

45

20

43

21

39

22

37

23

35

MARKS

24

31

25

29

26

27

27

26

28

22

29

19

30

15

TALLY

FREQUENCY

0-10

0

11-20

2

21-30

4

31-40

4

41-50

5

51-60

3

61-70

7

71-80

3

81-90

2

91-100

0

1)a)Mean

MARKS

MIDPOINT,x

FREQUENCY,f

Fx

1-10

5.5

0

0

11-20

15.5

2

31

21-30

25.5

4

102

31-40

35.5

4

142

41-50

45.5

5

227.5

51-60

55.5

3

166.5

61-70

65.5

7

458.5

71-80

75.5

3

226.5

81-90

85.5

2

171

91-100

95.5

0

0

TOTAL

30

∑f = 30 ∑fx = 1525 Mean, ̅ = =50.8333

1525

(2) mode

The modal class is 61-70, the majority of the students got that marks.

To find the mode mark, we draw the modal class and two classes adjacent to the modal class.

(REFER TO HISTOGRAM 1)

Based on the histogram;

Mode = 64.5

Reflection http://dissertation-help-uk.blogspot.com/2011/12/importance-of-data-analysisin-research.html

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