Add Maths Project Sabah

7/27/2019 Add Maths Project Sabah

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PART 1:

1. List the importance of data analysis in daily life.Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal ofhighlighting useful information, suggesting conclusions, and supporting decision making. Data analysis

has multiple facts and approaches, encompassing diverse techniques under a variety of names, indifferent business, science, and social science domains.

Data analysis is used in our daily life for the following field :

Analytics Business intelligence Censoring (statistics) Computational physics Data acquisition Data governance Data mining Data Presentation Architecture Digital signal processing Dimension reduction Early case assessment Exploratory data analysis Fourier Analysis Machine learning Multilinear PCA Multilinear subspace learning Nearest neighbor search Predictive analytics Principal Component Analysis Qualitative research Scientific computing Structured data analysis (statistics) Test method Text analytics Unstructured data Wavelet
http://en.wikipedia.org/wiki/Datahttp://en.wikipedia.org/wiki/Informationhttp://en.wikipedia.org/wiki/Analyticshttp://en.wikipedia.org/wiki/Business_intelligencehttp://en.wikipedia.org/wiki/Censoring_(statistics)http://en.wikipedia.org/wiki/Computational_physicshttp://en.wikipedia.org/wiki/Data_acquisitionhttp://en.wikipedia.org/wiki/Data_governancehttp://en.wikipedia.org/wiki/Data_mininghttp://en.wikipedia.org/wiki/Data_Presentation_Architecturehttp://en.wikipedia.org/wiki/Digital_signal_processinghttp://en.wikipedia.org/wiki/Dimension_reductionhttp://en.wikipedia.org/wiki/Early_case_assessmenthttp://en.wikipedia.org/wiki/Exploratory_data_analysishttp://en.wikipedia.org/wiki/Fourier_Analysishttp://en.wikipedia.org/wiki/Machine_learninghttp://en.wikipedia.org/wiki/Multilinear_principal_component_analysishttp://en.wikipedia.org/wiki/Multilinear_subspace_learninghttp://en.wikipedia.org/wiki/Nearest_neighbor_searchhttp://en.wikipedia.org/wiki/Predictive_analyticshttp://en.wikipedia.org/wiki/Principal_Component_Analysishttp://en.wikipedia.org/wiki/Qualitative_researchhttp://en.wikipedia.org/wiki/Scientific_computinghttp://en.wikipedia.org/wiki/Structured_data_analysis_(statistics)http://en.wikipedia.org/wiki/Test_methodhttp://en.wikipedia.org/wiki/Text_analyticshttp://en.wikipedia.org/wiki/Unstructured_datahttp://en.wikipedia.org/wiki/Wavelethttp://en.wikipedia.org/wiki/Wavelethttp://en.wikipedia.org/wiki/Unstructured_datahttp://en.wikipedia.org/wiki/Text_analyticshttp://en.wikipedia.org/wiki/Test_methodhttp://en.wikipedia.org/wiki/Structured_data_analysis_(statistics)http://en.wikipedia.org/wiki/Scientific_computinghttp://en.wikipedia.org/wiki/Qualitative_researchhttp://en.wikipedia.org/wiki/Principal_Component_Analysishttp://en.wikipedia.org/wiki/Predictive_analyticshttp://en.wikipedia.org/wiki/Nearest_neighbor_searchhttp://en.wikipedia.org/wiki/Multilinear_subspace_learninghttp://en.wikipedia.org/wiki/Multilinear_principal_component_analysishttp://en.wikipedia.org/wiki/Machine_learninghttp://en.wikipedia.org/wiki/Fourier_Analysishttp://en.wikipedia.org/wiki/Exploratory_data_analysishttp://en.wikipedia.org/wiki/Early_case_assessmenthttp://en.wikipedia.org/wiki/Dimension_reductionhttp://en.wikipedia.org/wiki/Digital_signal_processinghttp://en.wikipedia.org/wiki/Data_Presentation_Architecturehttp://en.wikipedia.org/wiki/Data_mininghttp://en.wikipedia.org/wiki/Data_governancehttp://en.wikipedia.org/wiki/Data_acquisitionhttp://en.wikipedia.org/wiki/Computational_physicshttp://en.wikipedia.org/wiki/Censoring_(statistics)http://en.wikipedia.org/wiki/Business_intelligencehttp://en.wikipedia.org/wiki/Analyticshttp://en.wikipedia.org/wiki/Informationhttp://en.wikipedia.org/wiki/Data


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2. (a) Specify

(i) three types of measure of central tendency

Measures of Central Tendency

Introduction

A measure of central tendency is a single value that attempts to describe a set of data by identifying the

central position within that set of data. As such, measures of central tendency are sometimes called

measures of central location. They are also classed as summary statistics. The mean (often called the

average) is most likely the measure of central tendency that you are most familiar with, but there are

others, such as the median and the mode.

The mean, median and mode are all valid measures of central tendency, but under different conditions,

some measures of central tendency become more appropriate to use than others. In the following

sections, we will look at the mean, mode and median, and learn how to calculate them and under what

conditions they are most appropriate to be used.

Mean (Arithmetic)

The mean (or average) is the most popular and well known measure of central tendency. It can be used

with both discrete and continuous data, although its use is most often with continuous data (see ourType

of Variable guide for data types). The mean is equal to the sum of all the values in the data set divided by

the number of values in the data set. So, if we have n values in a data set and they have values x1, x2, ...,

xn, the sample mean, usually denoted by (pronounced x bar), is:

This formula is usually written in a slightly different manner using the Greek capitol letter, ,

pronounced "sigma", which means "sum of...":
https://statistics.laerd.com/statistical-guides/types-of-variable.phphttps://statistics.laerd.com/statistical-guides/types-of-variable.phphttps://statistics.laerd.com/statistical-guides/types-of-variable.phphttps://statistics.laerd.com/statistical-guides/types-of-variable.php


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You may have noticed that the above formula refers to the sample mean. So, why have we called it a

sample mean? This is because, in statistics, samples and populations have very different meanings and

these differences are very important, even if, in the case of the mean, they are calculated in the same way

To acknowledge that we are calculating the population mean and not the sample mean, we use the Greek

lower case letter "mu", denoted as :

An important property of the mean is that it includes every value in your data set as part of the

calculation. In addition, the mean is the only measure of central tendency where the sum of the deviation

of each value from the mean is always zero.

Median

The median is the middle score for a set of data that has been arranged in order of magnitude. The

median is less affected by outliers and skewed data. In order to calculate the median, suppose we have th

data below:

65 55 89 56 35 14 56 55 87 45 92

We first need to rearrange that data into order of magnitude (smallest first):

14 35 45 55 55 56 56 65 87 89 92

Our median mark is the middle mark - in this case, 56 (highlighted in bold). It is the middle mark becaus

there are 5 scores before it and 5 scores after it. This works fine when you have an odd number of scores

but what happens when you have an even number of scores? What if you had only 10 scores? Well, you

simply have to take the middle two scores and average the result. So, if we look at the example below:

65 55 89 56 35 14 56 55 87 45

We again rearrange that data into order of magnitude (smallest first):


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(ii) at least two types of measure of dispersion

Dispersion

In statistics, there are many techniques that are applied to measure dispersion.

1.Range: Range is the simple measure ofdispersion, which is defined as the difference between the

largest value and the smallest value. Mathematically, the absolute and the relative measure of range can

be written as the following:

R= L - S

Where R= Range, L= largest value, S=smallest value

2.Quartile deviation: This is a measure ofdispersion. In this method, the difference between the upper

quartile and lower quartile is taken and is called the interquartile range. Symbolically it is as follows:

Where Q3= Upper quartile Q1= Lower quartile

3.Standard Deviation: In the measure of dispersion, the standard deviation method is the most widely

used method. In 1983, it was first used by Karl Pearson. Standard deviation is also known as root mean

square deviation. Symbolically it is as follows:

Where

=Deviation
http://www.statisticssolutions.com/descriptive-statistics-and-interpreting-statisticshttp://www.statisticssolutions.com/descriptive-statistics-and-interpreting-statisticshttp://1.bp.blogspot.com/_YaTH7psaq9o/SjFtlEjxRuI/AAAAAAAAAEo/WjPrUxoL5E4/s1600-h/7.jpghttp://1.bp.blogspot.com/_YaTH7psaq9o/SjFthggfdXI/AAAAAAAAAEg/4aOSwVVL5O0/s1600-h/6.jpghttp://3.bp.blogspot.com/_YaTH7psaq9o/SjFsl5Hoq5I/AAAAAAAAAEA/Vo14enHUYhw/s1600-h/2.jpghttp://4.bp.blogspot.com/_YaTH7psaq9o/SjFshE_syZI/AAAAAAAAAD4/bq-g-AEFhXc/s1600-h/1.jpghttp://2.bp.blogspot.com/_YaTH7psaq9o/SjFrDVRp-dI/AAAAAAAAADw/DYDgpYE0KXQ/s1600-h/1.jpghttp://www.statisticssolutions.com/descriptive-statistics-and-interpreting-statisticshttp://www.statisticssolutions.com/descriptive-statistics-and-interpreting-statistics


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(b) For each type of measure of central tendency stated in (a), give examples of

their uses in daily life.

MEAN

Mean can be used to see the average mark of the class obtained. This average helps to see how manystudents are above average, how many are average students and how many are below averages. Theteacher tries to help the average and below average students to score more grades in future.

The family finds the average of their expenses to balance their finance. T

The average production of agricultural commodities, the industrial goods, the average exports and

imports help the country to see their developments.

MEDIAN

Median is used to find the students who score less or more than the middle value.

Median is used to find the students who score less or more than the middle value.

Median is calculated to find the distribution of the wages. It is calculated to find the height of the players

in the points scored by players in a series of matches., to find the middle value of the ages of the students

in a class etc.Median

also determines the poverty line.

MODE

It is used to calculate the frequency of the arrival of the public transport, the frequency of the games won

by a team of players.

The mode is also seen in calculation of the wages, in the number of telephone calls received in a minute

by the telephone department, the frequency of the visitors, the frequency of the patients visiting the

hospitals, the mode of travel etc.


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PART 2:1. Get your class marks of any subject in one examination/test. Attach the mark sheet.

Name of Student Marks

Adila 66

Nur Khairani 61Dahiyah 85

Darwin Raj 72

Dayana Syafiqah 68

Endaraha 90

Hoo sze ting 56

Iylia Darweena 62

Noramira 42

Yuganavasan 87

Sarwisan 73

Shobanawathy 80Norshahida 61

Nur Hidayah 95

Nor Syamin 38

Nor Shaheela 75

Nadiah 52

Name of Student Marks

Kirthikaa 96

Jessica 52Nicholas 75

Mohammad Irsyad 46

Nurul Liyana 58

Ruhil Hayati 69

Vigneshwaran 40

Ker De-Sheng 60

Muhd.Adip 65

Wan Zahiran 52

Zulnazmi 88

Candru 74Naim 72


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Summary of statistics

2. Calculate the

(a) mean (b) median , (n+1/2)th value

= 15.5th

value= 67

(c) mode

= highest frequency=52

(d) standard deviation

15.727

bil Ascending order Marks,

1. 38 66 43562. 40 61 37213. 42 85 72254. 46 72 51845. 52 68 46246. 52 90 81007. 52 56 31368. 56 62 38449. 58 42 176410. 60 87 756911. 61 73 532912. 61 80 640013. 62 61 372114. 65 95 902515. 66 38 144416. 68 75 562517. 69 52 270418. 72 96 921619. 72 52 270420. 73 75 562521. 74 46 211622. 75 58 336423. 75 69 476124. 80 40 160025. 85 60 360026. 87 65 422527. 88 52 270428. 90 88 774429. 95 74 547630. 96 72 5184Total


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3. Construct a frequency distribution table as in Table 1 which contains at least five class

intervals of equal size. Choose a suitable class size.

Table 1

(a) From Table 1, find the(i) mean

,

67.5(ii) mode

= 60-69 marks

(iii) median (at least two methods)1

stmethod (by formula)

= lower boundary of the median class 59.5

= frequency of the median class 8

n = sum of frequencies 30F = cumulative frequency just before the median

class

9

c = size of the median class 10

Marks Frequency Mid point cumulativefrequency upperboundary 30-39 1 34.5 34.5 1 39.5 1190.25 1089 1089

40-49 3 44.5 133.5 4 49.5 5940.75 529 1587

50-59 5 54.5 272.5 9 59.5 14851.25 169 845

60-69 8 64.5 516 17 69.5 33282 9 72

70-79 6 74.5 447 23 79.5 33301.5 49 294

80-89 4 84.5 338 27 89.5 28561 289 1156

90-99 3 94.5 283.5 30 99.5 26790.75 729 2187

Total 30 2025 143917.5 2863 7230


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2nd Method

Median, 3rd Method (ogive)

From the graph we got median, m=67

(iv) standard deviation (at least two methods)

1st

method (by formula)

= SQRT(143917.5/30-(67.5)^2) (excel format)

= 15.524

0

5

10

15

20

25

30

35

40

39.5 49.5 59.5 69.5 79.5 89.5 99.5

Cu

mulativefrequency

Upper boundary

(marks)


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(v) interquartile range (at least two methods)1

stmethod (by formula)

(IQR) = Q3 - Q1

Q3= 3/4 (30)

= 22.5th

value

69.5

n 30

F 17

6

c 10

Q1= 1/4(30)= 7.5

thvalue

= 22.167

49.5

n 30

F 4

5

c 10


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2nd method (graph)

From the graph, we get = 22.167

0

5

10

15

20

25

30

35

40

39.5 49.5 59.5 69.5 79.5 89.5 99.5

Cumulativefrequency

Upper boundary

(marks)


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3(b) Based on your answers from 3(a) above, state the most appropriate measure of

central tendency that reflect the performance of your class. Give your reasons.

Best Measure of Central Tendency

In all of the types of central tendency we cant just point to a single one and tell which the best measure

is. Each have certain rules are conditions so that they become the best measure.

If the data provided is normally distributed, which means it must be continuous (interval) as well as

symmetric, then the mean becomes usually the best measure of central tendency

The mode is the least used of the measures of central tendency. If the data provided is nominal, then

mode becomes usually the best measure of central tendency.

If the data given are skewed or if they are ordinal data, then the median is the best measure of central

tendency.

Measurement Scale Best Measure of the "Middle"

Nominal

(Categorical)Mode

Ordinal Median

IntervalSymmetrical data: Mean

RatioSymmetrical data: Mean

Skewed data: Median

So for our measure of central tendency which best reflect the performance of the class is mean

because our data is interval which is continuous.


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(c) Measure of dispersion is a measurement used to determine how far the values of data

in a set of data are spread out from its average value.

Explain the advantages of using standard deviation compared to interquartile range as the

better measure of dispersion.

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 gives a measure of dispersion about the median. However, the

standard deviation is generally more useful and appropriate than the interquartile range as it includes all

data in its calculation. In contrast, using the interquartile range immediately discounts 50 per cent of the

data.

4. Ungrouped data and grouped data have been used to obtain the mean and standarddeviation in question (2) and (3) respectively.

(a) Determine which type of data gives a more accurate representation. Give your reasons

Mean: The meanvalue is what we typically call the average. You calculate the mean by adding up all

of the measurements in a group and then dividing by the number of measurements.

standard deviation shows how much variation ordispersion exists from the average (mean), or expected

value. A low standard deviation indicates that the data points tend to be very close to the mean; high

standard deviation indicates that the data points are spread out over a large range of values.

grouped data is more accurate because it has less margin for error. Ungrouped is sometimes flawed and

can harbor more inaccurate data.When it is grouped the correlations are easier to see and more accurate.

(b) State the conditions when grouped data and ungrouped data are preferred.

In statistics, arrangement ofraw data with a wide range of values into groups. This process makes

the data more manageable. Graphs and frequency diagrams can then be drawn showing the class

intervals chosen instead of individual values.

Grouped data is a statistical term used in data analysis. A raw dataset can be organized by constructing a

table showing the frequency distribution of the variable (whose values are given in the raw dataset). Such

a frequency table is often referred to as grouped data.[1]
http://en.wikipedia.org/wiki/Statistical_dispersionhttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Meanhttp://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0097191.htmlhttp://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0000789.htmlhttp://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0006578.htmlhttp://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0097193.htmlhttp://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0026012.htmlhttp://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0026012.htmlhttp://en.wikipedia.org/wiki/Statisticalhttp://en.wikipedia.org/wiki/Data_analysishttp://en.wikipedia.org/wiki/Raw_datahttp://en.wikipedia.org/wiki/Frequency_distributionhttp://en.wikipedia.org/wiki/Frequency_tablehttp://en.wikipedia.org/wiki/Grouped_data#cite_note-1http://en.wikipedia.org/wiki/Grouped_data#cite_note-1http://en.wikipedia.org/wiki/Grouped_data#cite_note-1http://en.wikipedia.org/wiki/Frequency_tablehttp://en.wikipedia.org/wiki/Frequency_distributionhttp://en.wikipedia.org/wiki/Raw_datahttp://en.wikipedia.org/wiki/Data_analysishttp://en.wikipedia.org/wiki/Statisticalhttp://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0026012.htmlhttp://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0026012.htmlhttp://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0097193.htmlhttp://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0006578.htmlhttp://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0000789.htmlhttp://www.talktalk.co.uk/reference/encyclopaedia/hutchinson/m0097191.htmlhttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Statistical_dispersion


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Ungrouped data is the raw data, and correct statistics such as the mean and standard deviations can be

determined. Ungrouped data is usually the starting point of analyses.For ungrouped data, the condition it is preferred is small number of data, lesser than 20 to obtain

statistical analysisFor grouped data, the condition it is preferred is large set of data, more than 20 to obtain statistical

analysis .


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PART 3

1.

From table,

a.

Mean,

69.5b. mode = 70-79 marks

c. median

= lower boundary of the median class 59.5

= frequency of the median class 7

n = sum of frequencies 30

F = cumulative frequency just before the medianclass

8

c = size of the median class 10

M= 69.5

Marks

Frequency

Mid point cumulativefrequency

upperboundary

30-39 0 34.5 0 0 39.5 0 1089 040-49 4 44.5 178 4 49.5 7921 529 2116

50-59 4 54.5 218 8 59.5 11881 169 676

60-69 7 64.5 451.5 15 69.5 29121.75 9 63

70-79 8 74.5 596 23 79.5 44402 49 392

80-89 2 84.5 169 25 89.5 14280.5 289 578

90-99 5 94.5 472.5 30 99.5 44651.25 729 3645

total 30 2085 152257.5 2863 7470


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d. Interquartile Range (IQR) = Q3 - Q1

69.5

n 30

F 15

8

C 10

= 20.625

e. Standard Deviation

49.5

n 30

F 4

4

c 10


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2.

Marks Frequency

Mid point

cumulative

frequency

upper

boundary

30-39 0 34.5 0 0 39.5 0 1089 040-49 4 44.5 178 4 49.5 7921 529 211650-59 4 54.5 218 8 59.5 11881 169 676

60-69 7 64.5 451.5 15 69.5 29121.75 9 63

70-79 8 74.5 596 23 79.5 44402 49 392

80-89 2 84.5 169 25 89.5 14280.5 289 578

90-99 6 94.5 567 31 99.5 53581.5 729 4374

Total 31 2179.5 161187.8 2863 8199

Mean,

= 16.01904


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FURTHER EXPLORATION

1. The top 20% of the students in your class will be awarded by the subject teacher.

Calculate the lowest mark for this group of students by using graphical and

calculation methods.

Graphical Method

Calculation Method

we use the same formula as for finding median to calculate for this.

=79.5+(((4*31/5)-23)/2)*10 (excel)

79.5n 31

F 23

2

c 10

0

5

10

15

20

25

30

35

39.5 49.5 59.5 69.5 79.5 89.5 99.5

Cumulative

frequency

Upper boundary


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2. Mr. Mas class scored a mean of 76.79 and a standard deviation of 10.36 in the same

examination. Compare the achievements of your class with Mr. Mas class. Give yourcomments.

Group mean Standard

deviationGroup 1 (Mr.Ma) 70.30 16.01

Group 2 76.79 10.36

My class has obtain an average score of 70.3 marks, whereas Mr.Mas class has achieved an average of

76.79. Mr.Ma had obtain higher mean than my class but still in the grade of B. His standard deviation

score is 10.36 which is smaller than mine which indicate Mr.Ma student performance in Mathematics tes

is greater than mine.


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REFLECTION

How to Improve Classroom PerformanceRead, sing, and talk to your child from infancy. Educators recommend beginning this

process as early as four months old. Use the time that your child feels awake and active toread age-appropriate books and sing. As the child begins to recognize words you'll be able tolengthen the communication time. Early childhood communication becomes crucial toclassroom success, as education is a communication-based activity.

o 2Converse regularly with your child. Communicate ideas and ask questions, allowing forthought and answers. You'll be teaching three crucial components for classroom success: thability to listen, talk, and carry on a conversation. Some children may have learningdifficulties linked to communication problems, so you may need to adjust the speed of your

speech to compensate and make allowances.

o 3Develop a good working relationship with the child's teachers. Ask weekly how your childprogresses, and keep on top of school events and academic progress through weekly, casualvisits to the school. Become involved with parent-teacher organizations.

o 4Track and monitor your child's progress through establishing a homework, project, andstudying schedule. If you have more than one child, make sure to be fair with your

requirements for each child so that they don't resent this school preparation time. Setspecific times each afternoon for homework and keep track of upcoming quizzes and tests sthat you can plan ahead for studying, avoiding last-minute frustrations.


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