state9 project work statistics pdf may 24 2012-5-25 pm 1 8 meg evozi

7/27/2019 State9 Project Work Statistics PDF May 24 2012-5-25 Pm 1 8 Meg Evozi

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No

Contents

Page

1

PART 1

. Importance of data analysis in daily life

. The types of Measure of CentralTendency and of Measure of Dispersion

3 5

2

PART 2

. Raw data

. Frequency Distribution Table

. Measure of central tendencyi) Meanii) Modeiii) Median

6 11

3

PART 3

. Measure of Dispersion

Interquartile range Standard deviation

12 15

4

PART 4

. Problem solving

17 C 19

5

REFLECTION

20

6


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REFERENCES

21 27

CONTENTS


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PART 1

Importance of data analysis in daily life

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 andrequirements.For example if a school principal wants to know whether there is a relationshipbetween students performance on the district writing assessment and theirsocioeconomic levels. In other words, do students who come from lowersocioeconomic backgrounds perform lower, as we are led to believe? Or are thereother variables responsible for the variance in writing performance? Again, asimple correlation analysis will help describe the students performance and helpexplain the relationship between the issues of performance and socioeconomic level.

Analysis does not have to involve complex statistics. Data analysis in schoolsinvolves collecting data and using that data to improve teaching and learning.Interestingly, principals and teachers have it pretty easy. In most cases, thecollection of data has already been done. Schools regularly collect attendance data,transcript records, discipline referrals, quarterly or semester grades, norm andcriterionreferenced test scores, and a variety of other useful data. Rather thancomplex statistical formulas and tests, it is generally simple counts, averages,percents, and rates that educators are interested in.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 ofdata collection like survey research. It is again very helpful in breaking a macroproblem into micro parts. Data analysis acts like a filter when it comes to acquiringmeaningful insights out of huge dataset. Every researcher has sort out huge pile ofdata that he/she has collected, before reaching to a conclusion of the researchquestion. Mere data collection is of no use to the researcher. Data analysis proves tobe crucial in this process. It provides a meaningful base to critical decisions.

It helpsto create a complete dissertation proposal.

One of the most important uses of data analysis is that it helps in keeping humanbias away from research conclusion with the help of proper statistical treatment.With the help of data analysis a researcher can filter both qualitative and


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quantitative data for an assignment writing projects. Thus, it can be said thatdataanalysis is of utmost importance for both the research and the researcher. Or toputit in another words data analysis is as important to a researcher as it is importantfor a doctor to diagnose the problem of the patient before giving him any treatment


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The types of Measure of Central Tendency and of Measure of Dispersion.Central tendency gets at the typical score on the variable, while dispersion gets athow much variety there is in the scores. When describing the scores on a singlevariable, 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 usedto describe the values of cases on every variable. What choices you have dependonthe variables level of measurement.

Mean

The mean is what in everyday conversation is called the average. It is calculated bysimply adding the values of all the valid cases together and dividing by the numberof valid cases.The mean is an interval/ratio measure of central tendency. Its calculation requires

that the attributes of the variable represent a numeric scaleModeThe mode is the attribute of a variable that occurs most often in the data set.

ffxxorNxx.....

For ungroup data, we can find mode by finding the modal class and draw the modal


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class and two classes adjacent to the modal class. Two lines from the adjacent wecrossed to find the intersection. The intersection value is known as the mode.MedianThe median is a measure of central tendency. It identifies the value of the middlecase when the cases have been placed in order or in line from low to high. Themiddle of the line is as far from being extreme as you can get.

CfFNLmm...............2


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There are as many cases in line in front of the middle case as behind the middlecase. The median is the attribute used by that middle case. When you know thevalue of the median, you know that at least half the cases had that value or a highervalue, 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. Thelarger the value of the range, the more dispersed the cases are on the variable;thesmaller the value of the range, the less dispersed (the more concentrated) the casesare on the variableRange = maximum value C minimum valueInterquartile range (IQR) is the distance between the 75th percentile and the 25thpercentile. The IQR is essentially the range of the middle 50% of the data. Becauseit uses the middle 50%, the IQR is not affected by outliers or extreme values.IQR = Q3 Q1Standard DeviationThe standard deviation tells you the approximate average distance of cases from

themean. This is easier to comprehend than the squared distance of cases from themean. The standard deviation is directly related to the variance.

CfFNLQm...........

..

..433CfFNLQm..

.

.

.

.

..

.

.

.

.

.

..411

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


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22xffx.............


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PART 2

1. March Additional Mathematics test scores for 30 students.

Students

Marks

1

55

2

60

3

63

4

65

5

73

6

74

775

8

75

9

76

10

77

11

78

12

80


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13

81

14

82

15

83

16

84

17

84

18

86

19

86

20

86

21

87

2288

23

88

24

89

25

90

26

90

27

90


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28

91

29

93

30

95


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2. Frequency distributions table:

Marks

Tally

Frequency

55 59

|

1

60 64

||

2

65 69

|

1

70 74

||

2

75 79

||||5

80 84

|||| |

6

85 89

|||| ||

7

90 94

||||

5

95 99


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|

1

a) I) MeanThe mean mark of 30 students can be found by using the formula:

\bar{x}...ffx

Marks

Midpoint,x

Frequencyf

fx

55 59

57

1

57


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60 64

62

2

124

65 69

67

1

67

70 74

72

2

144

75 7977

5

385

80 84

82

6

492

85 89

87

7

609

90 94

92

5

460

95 99

97


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1

97

f = 30

fx = 2435

From the table

f = 30

fx = 2435

Therefore,

mean,= 81.1667 \bar{x}

302435.


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II) Mode

. The modal class is 85 89, i.e., the majority of the students got thatmarks.. To find the mode weight, we draw the modal class and two classesadjacent to the modal class.From the histogram, the mode mark is 86.5

III) MedianMethod 1 C By using formula

. Median is the value of the centre of a set of data

. Median weight for 50 students can be obtained by using theformula:

Median, CfFNLmm......

...

.

.

.

.

..2

Where

L = lower boundary of median class,

N = total frequency,

F = cumulative frequency before the median class,

fm = frequency of median class,

C = class interval size.


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Marks

LowerBoundary

Upperboundary

Frequencyf

CumulativeFrequency

55 59

54.5

59.5

1

1

60 64

59.5

64.5

2

3

65 69

64.569.5

1

4

70 74

69.5

74.5

2

6

75 79

74.5

79.5


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5

11

80 84

79.5

84.5

6

17

85 89

84.5

89.5

7

24

90 94

89.5

94.5

5

29

95 99

94.599.5

1

30

f = 30


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From the table,

Median class = 30 2

= 15th value

= 80 84

L = 79.5 fm = 6 Total frequency N = 30F = 11 C = 69.5 64.5

= 58333.8256112305.79.........

..

.

.

.

..mm

Method 2 C by drawing an ogiveOgive

. Ogive is a graph constructed by plotting the cumulative frequencyof a set of data against the corresponding upper boundary of eachclass.. Not only that, ogive is also the method of calculation, the median,and the interquartile range of a set of data can also be estimatedfrom its ogive.


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b) Mean, x = 81.2 kg Median, m = 82.8333 (or 82.75) Mode = 86.5

From the above measure of central tendency, mean is suitable measure ofcentral tendency because the minimum value of raw data is not extreme wherethe data seems to be clustered, whereas mode and median does not take all thevalues in the data into account which decrease the accuracy of central tendency.


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PART 3

Measure of Dispersion is a measurement to determine how far the values of data ina set of data are spread out from its average value.

a) I) The interquartile rangeMethod I C By using formulaQ1 class = 30 x .CfFNLQm...............411

= 7.5th value= 75 59

L = 74.5 fm = 5 Total frequency N = 30

F = 6 C = 5Q3 class = 30 x .= 22.5 th value= 85 C 89L = 84.5 fm = 7 N = 30

F = 17 C = 5Therefore the Interquartile range,Q3 C Q1 = 88.4286 C 76.0= 12.42860.7655630415.7411........

..

.

.

.

...

.

..

.

..


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QQCfFNLQm...............4334286.88571730435.8433..........

..

.

....

..

.

..QQ


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Method II C By using ogiveFrom the ogiveInterquartile range = 88.5 C 76.25= 12.25


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II) The Standard deviationMethod I

Marks

Midpoint,x

Frequencyf

fx

fx2

55 59

57

1

573249

60 64

62

2

124

7688

65 69

67

1

67

4489

70 74

72

2

144

10368

75 79


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77

5

385

29645

80 84

82

6

492

40344

85 89

87

7

60952938

90 94

92

5

460

42320

95 99

97

1

97

9409

f = 30

fx = 2435

fx2 = 200450


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= 81.1667\bar{x}

v9.6764Method II21667.8130200450....

...

..

..

Marks

Midpointx

Frequencyf

..xx.

..2xx.

..2xxf.

55 59

57


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1

24.1667

584.0294

584.0294

60 64

62

2

19.1667

367.3624

734.7248

65 69

67

114.1667

200.6954

200.6954

70 74

72

2

9.1667

84.0284

168.0568

75 79

77

5

4.1667

17.3614

86.8069

80 84

82


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6

0.8333

0.6944

4.1663

85 89

87

7

5.8333

34.0274

238.1917

90 94

92

510.8333

117.3604

586.8019

95 99

97

1

15.8333

250.6934

250.6934

f = 30

..1666.28542...xxf


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..fxxf....2.

301666.2854..7539.9..

b) The standard deviation gives a measure of dispersion of the data about the

mean. A direct analogy would be that of the interquartile range, which givesa measure of dispersion about the median. However, the standard deviationis generally more useful than the interquartile range as it includes all data inits calculation. The interquartile range is totally dependent on just two valuesand ignores all the other observations in the data. This reduces the accuracyit extreme value is present in the data. Since the marks does not contain anyextreme value, standard deviation give a better measures compared tointerquartile range.


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PART 4

Students

Marks

1

58

2

63

3

66

4

68

5

76

6

77

7

78

8

789

79

10

80

11

81

12

83

13

84

14


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85

15

86

16

87

17

87

18

89

19

89

20

89

21

90

22

91

23

9124

92

25

93

26

93

27

93

28

94

29


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96

30

98

a) If the teacher adds 3 marks for each student in class for their commitmentand discipline shown,The new marks for 30 students


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New Frequency distributions table:

Marks

LowerBoundary

Midpoint, x

Frequency, f

C.Frequency

fx

fx2

55 59

54.5

571

1

57

3249

60 64

59.5

62

1

2

62

3844

65 69

64.5

67

2

4

134


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8978

70 74

69.5

72

0

4

0

0

75 79

74.5

77

5

9385

29645

80 84

79.5

82

4

13

328

26896

85 89

84.5

87

7

20

609

52983

90 94


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89.5

92

8

28

736

67712

95 99

94.5

97

2

30

194

18818

f = 30

fx = 2505

fx2 = 381495

New mean ,New mode,Modal class = 90 C 94New Mode = 90.755.83302505..

xx


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New MedianMedian class = 80 C 84Class interval remain sameClass interval = 5New interquartile rangeQ1 class = 30 x .= 7.5 th value= 75 C 79Q2 class = 30 x .= 22.5= 85 89Therefore the Interquartile range,Q3 C Q1 = 91.2857 C 78.0= 13.2857New standard deviation,0.875492305.79.........

..

.

.

.

..mm0.7855430415.7411.....

..

.

.

.

.

.

.

...

.

..

.

..

QQ2857.91571330435.8433........


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.

.

.

.

.

...

.

..

.

..QQ25.8330381495.........7908.75..


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b)

Marks

LowerBoundary

Midpoint, x

Frequency, f

C.Frequency

fx

fx2

55 59

54.5

571

1

57

3249

60 64

59.5

62

1

2

62

3844

65 69

64.5

67

2

4

134


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8978

70 74

69.5

72

0

4

0

0

75 79

74.5

77

5

9385

29645

80 84

79.5

82

4

13

328

26896

85 89

84.5

87

7

20

609

52983

90 94


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89.5

92

8

28

736

67712

95 99

94.5

97

3

31

291

28227

f = 31

fx = 2602

fx2 = 390904

New mean ,New standard deviation,Mode, median, and interquartile range are not affected by the adding fornew marks.9355.83312602..

xx29355.8331390904.........5965.74..


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REFLECTION


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REFERENCES

. www.worldteacherspress.com

. www.heartscan.com.my

. www.tips.com.my/article.php

. http://nutriweb.org.my

. http://geminigeek.com/blog/archives/2004/08/addmathprojecttips1

. http://www.sagepub.com/upmdata/43350_4.pdf

. Blog A Form 4 Sasbadi by Pua Kim Teck

. Preston Additional Mathematics Form 4 & 5 reference book by Tan Li Lan

. Fokus Ungu Matematik Tambahan Form 4 & 5 by Wong Teck Sing

. Additional Mathematics Form 4 Text Book.

. Mathematics Form 4 Text Book.


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ADDITIONAL MATHEMATICS PROJECT WORK FOR FORM 5 2012

Vision 2020 aims to produce a balanced human capital in terms of physical, emotional,spiritual and intellectual in accordance with the National Education Philosophy.In orderto expand the intellectual aspect, every individual should have the ability to a

nalyze data.The picture above shows students in a secondary school having their final yearexamination. The School Examination secretary will collect the marks for each subjectsto determine the average grade of the subjects, the average grade school and which willgive the picture of the performance of the school.

Data representation reflects the general characteristics of data that allows ustocompare and thus predict and plan for the future.

PART 1:

1. List the importance of data analysis in daily life.2. Specify the types of Measure of Central Tendency and of Measure of Dispersion.


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PART 2:

1. Get the March Additional Mathematics test scores for your class. Attach thescores sheet.2. Construct a frequency table as in Table 1 which contains at least five classintervals. Choose a suitable class size.

Marks

Tally

Frequency

Table 1

.

a) From Table 1, find

(i) the mean,(ii) the mode,(iii) the median using two methods.


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b) Based on your findings from (a) above, state the appropriate measure of centraltendency to reflect the performance of your class in Additional Mathematics.Explain why.

PART 3:

Measure of Dispersion is a measurement to determine how far the values of data in a setof datais spread out from its average value.

Based on the data from Table 1,

a) using two methods, find(i) the interquartile range(ii) the standard deviation

b) Explain the advantages of using standard deviation compared to interquartilerange to describe the data.


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PART 4:

a. If your teacher wants to make adjustments by adding 3 marks for each studentinyour class for their commitment and discipline shown, find the new value ofmean, mode, median, class interval, interquartile range and standard deviation.Check your answers with other methods.

b. In April 2012, a new student has enrolled in your class. The student has scored97% in the Additional Mathematics March Test in his/her former school. If thestudent scores were taken into account in the analysis of your school March Test,state the effect of the presence of this student to the mean, mode, median,interquartile range and standard deviation.

REFLECTION

What moral values did you put into practice when conducting this project? Prepare acard according to your creativity stating your efforts to increase or maintain theexcellent result for Additional Mathematics in SPM 2012.


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Guidelines for the Implementation of Additional Mathematics Project Work

Form 4 and Form 5

2007

(Students' Edition)

1. Every student taking Additional Mathematics is required to carry out two projectworks, one in Form 4 and another one in Form 5.

2. The aims of carrying out project work are:

i. to apply and adapt a variety of problemsolving strategies to solve problems;

ii. to improve thinking skills;

iii. to promote effective mathematical communication;

iv. to develop mathematical knowledge through problem solving jn a way thatincreases students' interest and confidence;

v. to use the language of mathematics to express mathematical ideas precisely;

vi. to provide learning environment that stimulates and enhances effective

learning;

vii. to develop positive attitude towards mathematics.

3. Project work can be done in groups or individually but each student is expect

ed tosubmit an individually written report which includes the followings:

. Report Presentation:

General Aspect

Introduction

. Task Specification

Specify the task

. Problem Solving :

Procedure Findings

Exploration


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. Conclusion/Generalisation

4. Students are given three weeks to carry out each project work. The written report mustbe submitted by the end of the third week.


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Rubric for Additional Mathematics Project Work 2012

Name:----------------.. Form 4/5 ------

School:----------------..

A. Report Presentation

Range ofmarks

MarkAwarded

Subtotal

A1. General

Aspect (6%)

Appropriate title

1

Contents page

1

Systematic presentation

1 2

Creativity

1 2

A2. Introduction

(7%)

Comprehensive introduction may includehistory/moral/values and other information relevantto the task.


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4 5

Satisfactory introduction.

1 3

Relating given task to reallife situation.

1 2

B. Task Specification

B1. Specific the

Task (10%)

Identify and state all given information andrequired results in proper mathematical statements.

8 10

Identify and state all given information andrequired results only.

4 7

Identify and state given information and requiredresults incompletely.

1 3

C. Problem Solving

C1. Procedure

(47%)

Choose at least two suitable problemsolvingmethods.

4 5


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Choose one suitable problemsolving method.

1 3

Apply at least two of the chosen problemsolvingmethod correctly.

20 30

Apply any one of the chosen problemsolvingmethod correctly.

10 19

Apply any one of the chosen problemsolvingmethod incorrectly / incompletely.

1 9Concise and efficient communication usingsymbols/graph/table/diagrams when necessary.

8 12

Not concise and inefficient communication.

1 7

C2. Findings

(10%)

Answer all questions correctly.

5

Do not answer all questions correctly.

1 4

Detailed discussion of findings.

4 5

Satisfactory discussion on findings.


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1 3

C3. Exploration

(12%)

Explore the task efficiently.

8 12

Explore the task.

1 7

D. Conclusion/ Generalisation

D1. Conclusion/

Generalisation

Check answers using an alternative method.

2 4

Draw conclusion / generalisation.

2 4


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(8%)

Total score ( A1 + A2 + B1+ C1 + C2 + C3+ D1)


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