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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)
-
7/27/2019 State9 Project Work Statistics PDF May 24 2012-5-25 Pm 1 8 Meg Evozi
57/57