Addmath Project Work 2013 (Repaired)

8/12/2019 Addmath Project Work 2013 (Repaired)

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2013

USES OF STATISTIC IN OUR

DAILY LIFENAME : Nur Afaliza Yusaini

CLASS : 5 Harmoni

IC NUMBER : 960726086228

SCHOOL : SMK Kinarut


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T BLE OF CONTENTACKNOWLEDGEMENT

OBJECTIVE

INTRODUCTION

A BRIEF HISTORY OF STATISTICS

PART 1

PART 2

PART 3

FURTHER EXPLORATION

REFLECTION


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First of all, I would like to thank Allah SWT for giving me the strength

to do this Additional Mathematics project work. I would also like to

thank my Additional Mathematics teacher, Mdm. Fadzilah Yahya as she

gives us important guidance and commitment during this project work.

She has been a very supportive figure throughout the whole project. We

had some difficulties in doing this task, but she taught us patiently until

we knew what to do.

Not forgotten, I would also like to thank my parents for giving me

their precious advise upon completing this project. They also supported

me and encouraged me to complete this task so that I will not

procrastinate in doing it.

I also would like to express my gratitude to my fellow friends for

helping me collect the data that I need to complete my project.Last but

not least,I would also like to thank all the other peoples who were

involved directly or indirectly towards making this project a reality.


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The aims of carrying out this project work is :

To apply and adapt a variety of problem-solving strategies to solve

problems.

To improve thinking skills.

To promote effective mathematical communication.

To develop mathematical knowledge through problem-solving in a

way that increases students interest and confidence.

To develop positive attitude towards mathematics.

To use the language of mathematics to express mathematical ideas

precisely.

To provide learning environment that stimulates and enhances

effective learning.

To develop positive attitude towards mathematics


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We as Additional Mathematics learner has been asked to do project

about solving problem using additional mathematics.This year we are

asked to do a research about the statistics of students marks in SMK

Kinarut and I pick to do a research about Form 4 students Chemistry

marks. This project can be done individual or group,and with pleasant I

choose to do individualy.When this project is done I can

Experience classroom environments which are challenging,

interesting and meaningful and hence improve their thinking skills.

Experience a classroom environment where knowledge and skills

used in a meaningful way in solving real-life problems

Experience classroom environments where expressing ones

mathematical thinking, reasoning and communication are highly

encouraged and expected

Acquire mathematical skills effectively through oral and written, and

using the language of mathematics to express mathematical ideas

and accurately

Realize that mathematics is an important and powerful tool in

solving problems in life and to develop positive attitudes towards

mathematics


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Train ourselves to appreciate the intrinsic value of mathematics and

be more creative and innovative

Enhance acquisition of mathematical knowledge and skills through

problem solving in ways that increase interest and confidence

Prepare ourselves for the demand of our future undertakings and in

workplace

Use technology especially the ICT appropriately and effectively

Train ourselves to appreciate the intrinsic values of mathematics and

to become more creative and innovative

We are expected to submit the project work within three weeks from

the first day the task is being administered to us. Failure to submit the

written report will result in us not receiving certificate.


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By the 18th century, the term "statistics" designated thesystematic

collection ofdemographic andeconomic data by states. In the early 19th

century, the meaning of "statistics" broadened to include the discipline

concerned with the collection, summary, and analysis of data. Today

statistics is widely employed in government, business, and all the

sciences. Electroniccomputers have expeditedstatistical computation,

and have allowed statisticians to develop "computer-intensive" methods.

The term "mathematical statistics" designates the mathematical

theories ofprobability andstatistical inference,which are used in

statistical practice.The relation between statistics and probability theory

developed rather late, however. In the 19th century, statistics

increasingly usedprobability theory,whose initial results were found in

the 17th and 18th centuries, particularly in the analysis ofgames of

chance (gambling). By 1800, astronomy used probability models and

statistical theories, particularly themethod of least squares,which was

invented byLegendre andGauss.Early probability theory and statistics

was systematized and extended byLaplace;following Laplace,

probability and statistics have been in continual development. In the

19th century, statistical reasoning and probability models were used by

social scientists to advance the new sciences ofexperimental

psychology andsociology,and by physical scientists in

thermodynamics andstatistical mechanics.The development ofstatistical reasoning was closely associated with the development of

inductive logic and thescientific method.

Statistics can be regarded as not a field ofmathematicsbut an

autonomousmathematical science,likecomputer science andoperations
http://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Official_statisticshttp://en.wikipedia.org/wiki/Official_statisticshttp://en.wikipedia.org/wiki/Demographichttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Computerhttp://en.wikipedia.org/wiki/Computational_statisticshttp://en.wikipedia.org/wiki/Mathematical_statisticshttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Applied_statisticshttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Games_of_chancehttp://en.wikipedia.org/wiki/Games_of_chancehttp://en.wikipedia.org/wiki/Method_of_least_squareshttp://en.wikipedia.org/wiki/Adrien-Marie_Legendrehttp://en.wikipedia.org/wiki/Gausshttp://en.wikipedia.org/wiki/Laplacehttp://en.wikipedia.org/wiki/Experimental_psychologyhttp://en.wikipedia.org/wiki/Experimental_psychologyhttp://en.wikipedia.org/wiki/Sociologyhttp://en.wikipedia.org/wiki/Thermodynamicshttp://en.wikipedia.org/wiki/Statistical_mechanicshttp://en.wikipedia.org/wiki/Inductive_logichttp://en.wikipedia.org/wiki/Scientific_methodhttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Mathematical_sciencehttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Operations_researchhttp://en.wikipedia.org/wiki/Operations_researchhttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Mathematical_sciencehttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Scientific_methodhttp://en.wikipedia.org/wiki/Inductive_logichttp://en.wikipedia.org/wiki/Statistical_mechanicshttp://en.wikipedia.org/wiki/Thermodynamicshttp://en.wikipedia.org/wiki/Sociologyhttp://en.wikipedia.org/wiki/Experimental_psychologyhttp://en.wikipedia.org/wiki/Experimental_psychologyhttp://en.wikipedia.org/wiki/Laplacehttp://en.wikipedia.org/wiki/Gausshttp://en.wikipedia.org/wiki/Adrien-Marie_Legendrehttp://en.wikipedia.org/wiki/Method_of_least_squareshttp://en.wikipedia.org/wiki/Games_of_chancehttp://en.wikipedia.org/wiki/Games_of_chancehttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Applied_statisticshttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Mathematical_statisticshttp://en.wikipedia.org/wiki/Computational_statisticshttp://en.wikipedia.org/wiki/Computerhttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Demographichttp://en.wikipedia.org/wiki/Official_statisticshttp://en.wikipedia.org/wiki/Official_statisticshttp://en.wikipedia.org/wiki/Statistics


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research.Unlike mathematics, statistics had its origins inpublic

administration.It is used indemography andeconomics.With its

emphasis on learning from data and making best predictions, statistics

has a considerable overlap withdecision science andmicroeconomics.With its concerns withdata,statistics has overlap withinformation

science andcomputer science.

The use of statistical methods dates back to least to the 5th century

BCE. The historianThucydides in hisHistory of the Peloponnesian

War describes how the Athenians calculated the height of the wall

ofPlateaby counting the number of bricks in an unplastered section of

the wall sufficiently near them to be able to count them. The count wasrepeated several times by a number of soldiers. The most frequent value

(in modern terminology - themode ) so determined was taken to be the

most likely value of the number of bricks. Multiplying this value by the

height of the bricks used in the wall allowed the Athenians to determine

the height of the ladders necessary to scale the walls.

The earliest writing on statistics was found in a 9th century book

entitled: "Manuscript on Deciphering Cryptographic Messages", writtenbyAl-Kindi (801873 CE). In his book, Al-Kindi gave a detailed

description of how to usestatistics andfrequency analysis to decipher

encrypted messages, this was the birth of both statistics and

cryptanalysis. The arithmeticmean,although a concept known to the

Greeks, was not generalised to more than two values until the 16th

century. The invention of the decimal system bySimon Stevin in 1585

seems likely to have facilitated these calculations. This method was firstadopted in astronomy byTycho Brahe who was attempting to reduce the

errors in his estimates of the locations of various celestial bodies. The

idea of themedian originated inEdward Wright's book on navigation

(Certaine Errors in Navigation) in 1599 in a section concerning the
http://en.wikipedia.org/wiki/Operations_researchhttp://en.wikipedia.org/wiki/Public_administrationhttp://en.wikipedia.org/wiki/Public_administrationhttp://en.wikipedia.org/wiki/Demographyhttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Decision_sciencehttp://en.wikipedia.org/wiki/Microeconomicshttp://en.wikipedia.org/wiki/Datahttp://en.wikipedia.org/wiki/Information_sciencehttp://en.wikipedia.org/wiki/Information_sciencehttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Thucydideshttp://en.wikipedia.org/wiki/History_of_the_Peloponnesian_Warhttp://en.wikipedia.org/wiki/History_of_the_Peloponnesian_Warhttp://en.wikipedia.org/wiki/Plateahttp://en.wikipedia.org/wiki/Mode_(statistics)http://en.wikipedia.org/wiki/Al-Kindihttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Frequency_analysishttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Simon_Stevinhttp://en.wikipedia.org/wiki/Tycho_Brahehttp://en.wikipedia.org/wiki/Medianhttp://en.wikipedia.org/wiki/Edward_Wright_(mathematician)http://en.wikipedia.org/wiki/Edward_Wright_(mathematician)http://en.wikipedia.org/wiki/Medianhttp://en.wikipedia.org/wiki/Tycho_Brahehttp://en.wikipedia.org/wiki/Simon_Stevinhttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Frequency_analysishttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Al-Kindihttp://en.wikipedia.org/wiki/Mode_(statistics)http://en.wikipedia.org/wiki/Plateahttp://en.wikipedia.org/wiki/History_of_the_Peloponnesian_Warhttp://en.wikipedia.org/wiki/History_of_the_Peloponnesian_Warhttp://en.wikipedia.org/wiki/Thucydideshttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Information_sciencehttp://en.wikipedia.org/wiki/Information_sciencehttp://en.wikipedia.org/wiki/Datahttp://en.wikipedia.org/wiki/Microeconomicshttp://en.wikipedia.org/wiki/Decision_sciencehttp://en.wikipedia.org/wiki/Economicshttp://en.wikipedia.org/wiki/Demographyhttp://en.wikipedia.org/wiki/Public_administrationhttp://en.wikipedia.org/wiki/Public_administrationhttp://en.wikipedia.org/wiki/Operations_research


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determination of location with a compass. Wright felt that this value was

the most likely to be the correct value in a series of observations.

Bayesian statistics.

Statistics today..

During the 20th century, the creation of precise instruments

foragricultural research,public health concerns

(epidemiology,biostatistics,etc.), industrialquality control,and

economic and social purposes (unemployment rate,econometry,etc.)necessitated substantial advances in statistical practices.

Today the use of statistics has broadened far beyond its origins.

Individuals and organizations use statistics to understand data and make

informed decisions throughout the natural and social sciences, medicine,

business, and other areas.

Statistics is generally regarded not as a subfield of mathematics butrather as a distinct, albeit allied, field. Manyuniversities maintain

separate mathematics and statisticsdepartments.Statistics is also taught

in departments as diverse aspsychology,education,andpublic health.
http://en.wikipedia.org/wiki/Agricultural_researchhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Epidemiologyhttp://en.wikipedia.org/wiki/Biostatisticshttp://en.wikipedia.org/wiki/Quality_controlhttp://en.wikipedia.org/wiki/Unemploymenthttp://en.wikipedia.org/wiki/Econometryhttp://en.wikipedia.org/wiki/Universityhttp://en.wikipedia.org/wiki/Academic_departmenthttp://en.wikipedia.org/wiki/Psychologyhttp://en.wikipedia.org/wiki/Educationhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Educationhttp://en.wikipedia.org/wiki/Psychologyhttp://en.wikipedia.org/wiki/Academic_departmenthttp://en.wikipedia.org/wiki/Universityhttp://en.wikipedia.org/wiki/Econometryhttp://en.wikipedia.org/wiki/Unemploymenthttp://en.wikipedia.org/wiki/Quality_controlhttp://en.wikipedia.org/wiki/Biostatisticshttp://en.wikipedia.org/wiki/Epidemiologyhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Agricultural_research


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Founders of statistics..

Name Nationality Birth Death Contribution

Graunt,

John

English 1620 1674 Pioneer

ofdemography

who produced

the firstlife

table

Bayes,

Thomas

English 1702 1761 Developed the

interpretation

ofprobability

now knownasBayes

theorem

Laplace

, Pierre-

Simon

French 1749 1827 Co-

inventedBaye

sian statistics.

Inventedexpo

nential

families (Laplace

transform),con

jugate

prior distributi

ons,asymptoti

c analysis of

estimators

(includingnegligibility of

regular priors).

Usedmaximu

m-

likelihood and
http://en.wikipedia.org/wiki/John_Graunthttp://en.wikipedia.org/wiki/John_Graunthttp://en.wikipedia.org/wiki/John_Graunthttp://en.wikipedia.org/wiki/Demographyhttp://en.wikipedia.org/wiki/Life_tablehttp://en.wikipedia.org/wiki/Life_tablehttp://en.wikipedia.org/wiki/Thomas_Bayeshttp://en.wikipedia.org/wiki/Thomas_Bayeshttp://en.wikipedia.org/wiki/Thomas_Bayeshttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Bayes_theoremhttp://en.wikipedia.org/wiki/Bayes_theoremhttp://en.wikipedia.org/wiki/Pierre-Simon_Laplacehttp://en.wikipedia.org/wiki/Pierre-Simon_Laplacehttp://en.wikipedia.org/wiki/Pierre-Simon_Laplacehttp://en.wikipedia.org/wiki/Pierre-Simon_Laplacehttp://en.wikipedia.org/wiki/Bayesian_statisticshttp://en.wikipedia.org/wiki/Bayesian_statisticshttp://en.wikipedia.org/wiki/Exponential_familyhttp://en.wikipedia.org/wiki/Exponential_familyhttp://en.wikipedia.org/wiki/Exponential_familyhttp://en.wikipedia.org/wiki/Laplace_transformhttp://en.wikipedia.org/wiki/Laplace_transformhttp://en.wikipedia.org/wiki/Laplace_transformhttp://en.wikipedia.org/wiki/Conjugate_priorhttp://en.wikipedia.org/wiki/Conjugate_priorhttp://en.wikipedia.org/wiki/Conjugate_priorhttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Asymptotic_analysishttp://en.wikipedia.org/wiki/Conjugate_priorhttp://en.wikipedia.org/wiki/Conjugate_priorhttp://en.wikipedia.org/wiki/Conjugate_priorhttp://en.wikipedia.org/wiki/Laplace_transformhttp://en.wikipedia.org/wiki/Laplace_transformhttp://en.wikipedia.org/wiki/Laplace_transformhttp://en.wikipedia.org/wiki/Exponential_familyhttp://en.wikipedia.org/wiki/Exponential_familyhttp://en.wikipedia.org/wiki/Exponential_familyhttp://en.wikipedia.org/wiki/Bayesian_statisticshttp://en.wikipedia.org/wiki/Bayesian_statisticshttp://en.wikipedia.org/wiki/Pierre-Simon_Laplacehttp://en.wikipedia.org/wiki/Pierre-Simon_Laplacehttp://en.wikipedia.org/wiki/Pierre-Simon_Laplacehttp://en.wikipedia.org/wiki/Bayes_theoremhttp://en.wikipedia.org/wiki/Bayes_theoremhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Thomas_Bayeshttp://en.wikipedia.org/wiki/Thomas_Bayeshttp://en.wikipedia.org/wiki/Life_tablehttp://en.wikipedia.org/wiki/Life_tablehttp://en.wikipedia.org/wiki/Demographyhttp://en.wikipedia.org/wiki/John_Graunthttp://en.wikipedia.org/wiki/John_Graunt


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posterior-

mode

estimation and

considered

(robust)lossfunctions

Playfair

,

William

Scottish 1759 1823 Pioneer

ofstatistical

graphics

Gauss,

Carl

Friedric

h

German 1777 1855 Inventedleast

squares estima

tion methods

(withLegendre). Usedloss

functions and

maximum-

likelihood esti

mation

Quetelet

,

Adolphe

Belgian 1796 1874 Pioneered the

use of

probabilityand statistics

in thesocial

sciences

Nightin

gale,

Florenc

e

English 1820 1910 Applied

statistical

analysis to

health

problems,

contributing to

the

establishment

of

epidemiology
http://en.wikipedia.org/wiki/Robust_statisticshttp://en.wikipedia.org/wiki/Loss_functionshttp://en.wikipedia.org/wiki/Loss_functionshttp://en.wikipedia.org/wiki/William_Playfairhttp://en.wikipedia.org/wiki/William_Playfairhttp://en.wikipedia.org/wiki/William_Playfairhttp://en.wikipedia.org/wiki/Statistical_graphicshttp://en.wikipedia.org/wiki/Statistical_graphicshttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Least_squareshttp://en.wikipedia.org/wiki/Least_squareshttp://en.wikipedia.org/wiki/Adrien-Marie_Legendrehttp://en.wikipedia.org/wiki/Adrien-Marie_Legendrehttp://en.wikipedia.org/wiki/Loss_functionshttp://en.wikipedia.org/wiki/Loss_functionshttp://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Social_scienceshttp://en.wikipedia.org/wiki/Social_scienceshttp://en.wikipedia.org/wiki/Florence_Nightingalehttp://en.wikipedia.org/wiki/Florence_Nightingalehttp://en.wikipedia.org/wiki/Florence_Nightingalehttp://en.wikipedia.org/wiki/Florence_Nightingalehttp://en.wikipedia.org/wiki/Florence_Nightingalehttp://en.wikipedia.org/wiki/Florence_Nightingalehttp://en.wikipedia.org/wiki/Florence_Nightingalehttp://en.wikipedia.org/wiki/Florence_Nightingalehttp://en.wikipedia.org/wiki/Social_scienceshttp://en.wikipedia.org/wiki/Social_scienceshttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Adolphe_Quetelethttp://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Maximum_likelihoodhttp://en.wikipedia.org/wiki/Loss_functionshttp://en.wikipedia.org/wiki/Loss_functionshttp://en.wikipedia.org/wiki/Adrien-Marie_Legendrehttp://en.wikipedia.org/wiki/Adrien-Marie_Legendrehttp://en.wikipedia.org/wiki/Least_squareshttp://en.wikipedia.org/wiki/Least_squareshttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Statistical_graphicshttp://en.wikipedia.org/wiki/Statistical_graphicshttp://en.wikipedia.org/wiki/William_Playfairhttp://en.wikipedia.org/wiki/William_Playfairhttp://en.wikipedia.org/wiki/William_Playfairhttp://en.wikipedia.org/wiki/Loss_functionshttp://en.wikipedia.org/wiki/Loss_functionshttp://en.wikipedia.org/wiki/Robust_statistics


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and public

health

practice.

Developedstat

isticalgraphics espec

ially for

mobilizing

public

opinion. First

female

member of

theRoyalStatistical

Society.

Galton,

Francis

English 1822 1911 Invented the

concepts

ofstandard

deviation,corr

elation,regres

sionThiele,

Thorval

d N.

Danish 1838 1910 Introducedcu

mulants and

the term

"likelihood".

Introduced

aKalman

filter intime-

series
http://en.wikipedia.org/wiki/Statistical_graphicshttp://en.wikipedia.org/wiki/Statistical_graphicshttp://en.wikipedia.org/wiki/Statistical_graphicshttp://en.wikipedia.org/wiki/Royal_Statistical_Societyhttp://en.wikipedia.org/wiki/Royal_Statistical_Societyhttp://en.wikipedia.org/wiki/Royal_Statistical_Societyhttp://en.wikipedia.org/wiki/Francis_Galtonhttp://en.wikipedia.org/wiki/Francis_Galtonhttp://en.wikipedia.org/wiki/Francis_Galtonhttp://en.wikipedia.org/wiki/Standard_deviationhttp://en.wikipedia.org/wiki/Standard_deviationhttp://en.wikipedia.org/wiki/Correlationhttp://en.wikipedia.org/wiki/Correlationhttp://en.wikipedia.org/wiki/Regression_analysishttp://en.wikipedia.org/wiki/Regression_analysishttp://en.wikipedia.org/wiki/Thorvald_N._Thielehttp://en.wikipedia.org/wiki/Thorvald_N._Thielehttp://en.wikipedia.org/wiki/Thorvald_N._Thielehttp://en.wikipedia.org/wiki/Thorvald_N._Thielehttp://en.wikipedia.org/wiki/Cumulantshttp://en.wikipedia.org/wiki/Cumulantshttp://en.wikipedia.org/wiki/Likelihood_functionhttp://en.wikipedia.org/wiki/Kalman_filterhttp://en.wikipedia.org/wiki/Kalman_filterhttp://en.wikipedia.org/wiki/Time-serieshttp://en.wikipedia.org/wiki/Time-serieshttp://en.wikipedia.org/wiki/Time-serieshttp://en.wikipedia.org/wiki/Time-serieshttp://en.wikipedia.org/wiki/Kalman_filterhttp://en.wikipedia.org/wiki/Kalman_filterhttp://en.wikipedia.org/wiki/Likelihood_functionhttp://en.wikipedia.org/wiki/Cumulantshttp://en.wikipedia.org/wiki/Cumulantshttp://en.wikipedia.org/wiki/Thorvald_N._Thielehttp://en.wikipedia.org/wiki/Thorvald_N._Thielehttp://en.wikipedia.org/wiki/Thorvald_N._Thielehttp://en.wikipedia.org/wiki/Regression_analysishttp://en.wikipedia.org/wiki/Regression_analysishttp://en.wikipedia.org/wiki/Correlationhttp://en.wikipedia.org/wiki/Correlationhttp://en.wikipedia.org/wiki/Standard_deviationhttp://en.wikipedia.org/wiki/Standard_deviationhttp://en.wikipedia.org/wiki/Francis_Galtonhttp://en.wikipedia.org/wiki/Francis_Galtonhttp://en.wikipedia.org/wiki/Royal_Statistical_Societyhttp://en.wikipedia.org/wiki/Royal_Statistical_Societyhttp://en.wikipedia.org/wiki/Royal_Statistical_Societyhttp://en.wikipedia.org/wiki/Statistical_graphicshttp://en.wikipedia.org/wiki/Statistical_graphicshttp://en.wikipedia.org/wiki/Statistical_graphics


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WHAT IS DATA ANALYSIS ?

Analysis of data is a process of inspecting, cleaning, transforming, and

modelingdata with the goal of highlighting usefulinformation,

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 mining is a particular data analysis technique that focuses on

modeling and knowledge discovery for predictive rather than purelydescriptive purposes.Business intelligencecovers data analysis that

relies heavily on aggregation, focusing on business information.

Instatistical applications,some people divide data analysis

intodescriptive statistics,exploratory data analysis (EDA),

andconfirmatory data analysis (CDA). EDA focuses on discovering new

features in the data and CDA on confirming or falsifying existing

hypothesis.Predictive analytics focuses on application of statistical or

structural models for predictive forecasting or classification, whiletext

analytics applies statistical, linguistic, and structural techniques to

extract and classify information from textual sources, a species

ofunstructured data.All are varieties of data analysis.

Data integration is a precursor to data analysis, and data analysis is

closely linked todata visualization and data dissemination. The

term data analysis is sometimes used as a synonym fordata modeling.
http://en.wikipedia.org/wiki/Datahttp://en.wikipedia.org/wiki/Informationhttp://en.wikipedia.org/wiki/Data_mininghttp://en.wikipedia.org/wiki/Business_intelligencehttp://en.wikipedia.org/wiki/Business_intelligencehttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Descriptive_statisticshttp://en.wikipedia.org/wiki/Exploratory_data_analysishttp://en.wikipedia.org/wiki/Confirmatory_data_analysishttp://en.wikipedia.org/wiki/Predictive_analyticshttp://en.wikipedia.org/wiki/Text_analyticshttp://en.wikipedia.org/wiki/Text_analyticshttp://en.wikipedia.org/wiki/Unstructured_datahttp://en.wikipedia.org/wiki/Data_integrationhttp://en.wikipedia.org/wiki/Data_visualizationhttp://en.wikipedia.org/wiki/Data_modelinghttp://en.wikipedia.org/wiki/Data_modelinghttp://en.wikipedia.org/wiki/Data_visualizationhttp://en.wikipedia.org/wiki/Data_integrationhttp://en.wikipedia.org/wiki/Unstructured_datahttp://en.wikipedia.org/wiki/Text_analyticshttp://en.wikipedia.org/wiki/Text_analyticshttp://en.wikipedia.org/wiki/Predictive_analyticshttp://en.wikipedia.org/wiki/Confirmatory_data_analysishttp://en.wikipedia.org/wiki/Exploratory_data_analysishttp://en.wikipedia.org/wiki/Descriptive_statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Business_intelligencehttp://en.wikipedia.org/wiki/Data_mininghttp://en.wikipedia.org/wiki/Informationhttp://en.wikipedia.org/wiki/Data


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IMPORTANCE OF DATA ANALYSIS

Most research projects need data in order to answer a proposed

research problem. The data that need to be acquired, and the sources of

such data, must be identified as a matter of utmost importance. No

amount or depth of subsequent data analysis can make up for an original

lack of data quantity or quality.

Research problems and objectives (or hypotheses) need to be very

carefully constructed and clearly defined, as they dictate the data that

need to be obtained and analyzed in order to successfully address theobjectives themselves. In addition, the quantity of data, their qualities,

and how they are sampled and measured, have implications for the

choice and effectiveness of the data analysis techniques used in

subsequent analysis.

The collection, analysis and storage of data on the educational system

becomes very important to the school manager for the following reasons.

The school managers have a responsibility to plan ahead for the system.Educational data are very vital tools for planning. For you to plan

adequately for the future you need the data on what the past was and

what the present is like. Also, for the day to day decision making, the

educational manager need data to guide their decisions. Moreover, data

collection, analysis and storage is very important to the school managers

in the assessment of the growth and progress of the educational system.

Further, data collection, analysis and storage enables the school manager

identify areas of staff training and retraining needs. For example the data

on students performance in Mathematics may point to a need to retrainthe Mathematics teacher. If such teacher is an NCE holder it may be a

pointer for a need to recommend him for in-service training for a degree

in Mathematics.


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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 hugedata-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 completedissertation proposal.
http://www.dissertationhelpuk.co.uk/http://www.dissertationhelpuk.co.uk/


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MEASURES OF CENTRAL TENDENCY

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.


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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. 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...":

An estimate, , of themean of the population from which the data are

drawn can be calculated from the grouped data as:

In this formula,xrefers to the midpoint of the class intervals, andfis

the class frequency. Note that the result of this will be different from

thesample mean of the ungrouped data.
http://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Sample_meanhttp://en.wikipedia.org/wiki/Sample_meanhttp://en.wikipedia.org/wiki/Mean


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Median for Grouped Data :

Formula :

Where: is the median

lower boundary of median class

cumulative frequency of the class before the median class frequency of the median class class interval or class width number of observationsExample

Find the median using the age distribution of 30 vacationists in Palawan

Age f

11 - 15 2

16 - 20 3

21 - 25 4

26 - 30 6

31 - 35 336 - 40 5

41 - 45 7


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Solution:

n = 30

The first step in determining the median class is to calculate thecumulative frequency (cf) by adding the frequencies one by one.

The last number must be the same as your n.

Next is to use the formula n/2 to determine which of the classes isthe median class.

30/2 = 15

The median class is the class whose cumulative frequency isgreater than and nearest to n/2. Referring to our first table, we

already have a cf of 15 so our median class is 26 - 30.
http://3.bp.blogspot.com/-5zYWlnvMWCs/T27ZwOjH-0I/AAAAAAAAABg/VuwcAkrieYg/s1600/Table2.JPGhttp://3.bp.blogspot.com/-cEL06a3g3VQ/T27cdAPJYHI/AAAAAAAAABw/KvbhM6uCf6Y/s1600/Table.PNGhttp://3.bp.blogspot.com/-5zYWlnvMWCs/T27ZwOjH-0I/AAAAAAAAABg/VuwcAkrieYg/s1600/Table2.JPGhttp://3.bp.blogspot.com/-cEL06a3g3VQ/T27cdAPJYHI/AAAAAAAAABw/KvbhM6uCf6Y/s1600/Table.PNG


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Next is to calculate the lower boundary of the median class. It isnot necessary to compute the class boundaries for all of the classes

but in case you need it, just subtract .5 from the lower class and

add .5 to the upper class. Since we will be needing the lowerboundary of class 26 - 30, subtract .5 from 26. lb = 25.5

Substitution:

Median = 30.5
http://3.bp.blogspot.com/-rY2OC2K4tRg/T27mnnq6duI/AAAAAAAAACQ/7tyjWboUEwA/s1600/equation3.PNGhttp://2.bp.blogspot.com/-qn616DZIZ8c/T27lS9jh9MI/AAAAAAAAACI/nkwZRO_6Iw4/s1600/equation2.PNGhttp://3.bp.blogspot.com/-twxiUAuTaFk/T27lRzX1CyI/AAAAAAAAACA/xr3XNvoB9Rc/s1600/equation1.PNGhttp://3.bp.blogspot.com/-rY2OC2K4tRg/T27mnnq6duI/AAAAAAAAACQ/7tyjWboUEwA/s1600/equation3.PNGhttp://2.bp.blogspot.com/-qn616DZIZ8c/T27lS9jh9MI/AAAAAAAAACI/nkwZRO_6Iw4/s1600/equation2.PNGhttp://3.bp.blogspot.com/-twxiUAuTaFk/T27lRzX1CyI/AAAAAAAAACA/xr3XNvoB9Rc/s1600/equation1.PNGhttp://3.bp.blogspot.com/-rY2OC2K4tRg/T27mnnq6duI/AAAAAAAAACQ/7tyjWboUEwA/s1600/equation3.PNGhttp://2.bp.blogspot.com/-qn616DZIZ8c/T27lS9jh9MI/AAAAAAAAACI/nkwZRO_6Iw4/s1600/equation2.PNGhttp://3.bp.blogspot.com/-twxiUAuTaFk/T27lRzX1CyI/AAAAAAAAACA/xr3XNvoB9Rc/s1600/equation1.PNGhttp://3.bp.blogspot.com/-rY2OC2K4tRg/T27mnnq6duI/AAAAAAAAACQ/7tyjWboUEwA/s1600/equation3.PNGhttp://2.bp.blogspot.com/-qn616DZIZ8c/T27lS9jh9MI/AAAAAAAAACI/nkwZRO_6Iw4/s1600/equation2.PNGhttp://3.bp.blogspot.com/-twxiUAuTaFk/T27lRzX1CyI/AAAAAAAAACA/xr3XNvoB9Rc/s1600/equation1.PNG


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Mode

The mode is the most frequent score in the data set. On a histogram it

represents the highest bar in a bar chart or histogram. Example :


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We can see above that the most common form of transport, in this

particular data set, is the bus. However, one of the problems with the

We are now stuck as to which mode best describes the centraltendency of the data. This is particularly problematic when we have

continuous data because we are more likely not to have any one value

that is more frequent than the other. For example, consider measuring 30

peoples' weight (to the nearest 0.1 kg). How likely is it that we will find

two or more people with exactly the same weight (e.g., 67.4 kg)? The

answer, is probably very unlikely - many people might be close, but with

such a small sample (30 people) and a large range of possible weights,you are unlikely to find two people with exactly the same weight; that is,

to the nearest 0.1 kg. This is why the mode is very rarely used with

continuous data.


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Another problem with the mode is that it will not provide us with a

very good measure of central tendency when the most common mark is

far away from the rest of the data in the data set, as depicted in the

diagram below:

In the above diagram the mode has a value of 2. We can clearly see,

however, that the mode is not representative of the data, which is mostly

concentrated around the 20 to 30 value range. To use the mode to

describe the central tendency of this data set would


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RANGE

The rangeis defined as the difference between the largest score in

the set of data and the smallest score in the set of data, XL- XS

The range is used when

have ordinal data or

presenting your results to people with little or no

knowledge of statistics

The range is rarely used in scientific work as it is fairly insensitive

It depends on only two scores in the set of data, XLand XS

INTERQUARTILE RANGE

Indescriptive statistics,the interquartile range (IQR), also called

the midspread or middle fifty, is a measure ofstatistical dispersion,

being equal to the difference between the upper and

lowerquartiles,IQR = Q3 Q1. It is atrimmed estimator,defined

as the 25% trimmedmid-range,and is the most significant

basicrobust measure of scale.It is the 3rd Quartile of a Box and

Whisker plot minus the first quartile.
http://en.wikipedia.org/wiki/Descriptive_statisticshttp://en.wikipedia.org/wiki/Statistical_dispersionhttp://en.wikipedia.org/wiki/Quartilehttp://en.wikipedia.org/wiki/Trimmed_estimatorhttp://en.wikipedia.org/wiki/Mid-rangehttp://en.wikipedia.org/wiki/Robust_measures_of_scalehttp://en.wikipedia.org/wiki/Robust_measures_of_scalehttp://en.wikipedia.org/wiki/Mid-rangehttp://en.wikipedia.org/wiki/Trimmed_estimatorhttp://en.wikipedia.org/wiki/Quartilehttp://en.wikipedia.org/wiki/Statistical_dispersionhttp://en.wikipedia.org/wiki/Descriptive_statistics


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VARIANCE

Variance is defined as the average of the square deviations

Formula :

STANDARD DEVIATION

When the deviate scores are squared in variance, their unit of

measure is squared as well

E.g. If peoples weights are measured in pounds, then the variance

of the weights would be expressed in pounds2

(or squared pounds)

Since squared units of measure are often awkward to deal with, the

square root of variance is often used instead

The standard deviation is the square root of variance

Standard deviation = variance

Variance = standard deviation2

N

X

2

2


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Formula :

Ungrouped data

Grouped data


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USES OF MEASURES OF CENTRAL TENDENCY

Mean

It helps teachers to see the average marks of the students.

It is used in factories, for the authorities to recognize

whether the benefits of the workers is continued or not.

It is also used to contrast the salaries of the workers.

To calculate the average speed of anything.

It is also used by the government to find the income or expenses of

any person.

Using this the family could balance their expenses with their

average income.

Median

It is used to measure the distribution of the earnings

Used to find the players height e.g. football players.

To find the middle age from the class students.

Used to find the poverty line.


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4 HARMONI EXAMINATION MARKS

NAME MARKS

ABDUL MALIK BIN ZAINUDDIN 25

ADAM GABRIEL 58ALOYVIA ANGGOL 65

AMANDA BINTI ALI AMAN 78

ARSAMREE BIN BONG BONG 45

BRYVELEN BENJI 63

DAYANG NOR SYAFIKA AG. MAHMUD 60

DG.UMI SUMIRAH BINTI RAHMAN 75

EFA SUZIANI BINTI ALI 83

FRINGEAL STEPHEN FUNG 78

FRYDOREEN MASMIN 73

IVY KOK 68

JENICA R.JAMES MAJANAU 63JENNYCA MYRNA JUSTINE 55

MAHATHIR BIN RASHID 33

MELANIE JOANNE CHIN 43

MELDAH CHIN MEI YIE 63

MELVOURNE NELFREY GEOFFREY 80

MOHD SHADDAN BIN IBRAHIM 35

MOHD SHAHEDIN BIN BAKHTIAR 55

MUHAMMAD NAIM BIN BASIR 45

MUHD. SYAIT BIN LASEMMAN 73

NADHIRAH BINTI HAMID 63

NASARUDDIN BIN MOHAMMAD 48NATASA GEORGE 53

NORATIKAH BINTI ROSLEE 80

NUR AFALIZA BINTI YUSAINI 95

NUR ZULAIKHA BINTI AHMAD ZULPAKAR 65

NURUL IZZATI ALYA BINTI ABD. KABUL 83

NURUL THAHIRAH BINTI SHAKATALI KHAN 58

PETROZA PITOROS 73

RACHAEL LYNN BONAVENTURE 45

SAIDATUL ATIQAH BINTI AZMI 55

SALMA MATIUS 90

SOLEHA BINTI MOKHTARIFFIN 83STEPHENCIE SINIK 60

SYARMEEN MAZYUNIE MOHD YUSRIN 65

TONNY GUIS JUNIOR 45

VIVIANNIE JIVET 63

YAP LAI WAN 78


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UNGROUPED DATA

MEAN

Formula to calculate mean is :

sum of all the values of the data

total number of values of the data

Calculation :

Substitute into the formula,


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MEDIAN

Arrange all the marks in increasing order :

MODE

63 - OCCUR 5 TIMES

Median


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Substitute into equation :

Standard Deviation 15.887


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GROUPED DATA

MARKS FREQUENCY

1

20 0

2140 3

4160 14

6180 18

81100 5

MEAN

Formula :

Calculation :

MARKS CLASS MARK,x FREQUENCY,f FREQUENCYCLASS MARK,fx

1 -20 10.5 0 021-40 30.5 3 91.5

41-60 50.5 14 707

61-80 70.5 18 1269

81-100 90.5 5 452.5 40 2520

Mean = 63


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MODE

Modal class : 61-80

From the histogram, mode = 65

0

3

14

18

5

0

2

4

6

8

10

12

14

16

18

20

Category 1

Frequen

cy

Marks

4 Harmoni Examination Marks

0.5 80.560.540.520.5 100.5


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MEDIAN

First Method

Formula :

Calculation :

MARKS LOWER BOUNDARY FREQUENCY,f CUMULATIVE

FREQUENCY

1 -20 0.5 0 0

21-40 20.5 3 3

41-60 40.5 14 17

61-80 60.5 18 35

81-100 80.5 5 40


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( )

( )


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Second Method

Median =

=20th

From the ogive,

Median = 64

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120

CumulativeFrequency

Marks



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STANDARD DEVIATION

First Method

Formula :

Tabulation of data

MARKS CLASS

MARK,x

FREQUENCY,f FREQUENCYCLASS MARK,fx 1 -20 10.5 0 0 0

21-40 30.5 3 91.5 2790.75

41-60 50.5 14 707 35703.5

61-80 70.5 18 1269 89464.5

81-100 90.5 5 452.5 40951.25

40

2520

Calculation :


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Substitue into equation :

Standard deviation = 15.93


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INTERQUARTILE RANGE

FIRST METHOD

Formula : Tabulation of data

MARKS UPPER BOUNDARY FREQUENCY,f CUMULATIVEFREQUENCY

1 -20 20.5 0 0

21-40 40.5 3 341-60 60.5 14 17

61-80 80.5 18 35

81-100 100.5 5 40

Calculation :


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SECOND METHOD

Arrange the data in increasing order

First quartile (Q1) lies between the 10

thand 11

thstudents marks

Second quartile (Q2) lies between the 20th

and the 21ststudents

marks

Third quartile (Q3) lies between the 30thand the 31ststudents marks

Calculation :

First quartile (Q1) =

Second quartile (Q2) =

= 20.5

Third quartile (Q3) =

= 30.5

Interquartile Range = Q3 - Q1

= 30.510.5

= 20


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The mean is a more approriate measure of central tendency to reflect

the performance of my class because it shows the central value around

which the data seems to cluster.

Advantage of using standard deviation compared

to interquartile range as the better measure of

dipersion.

Standard deviation makes use of all data to calculate the spread of data

from average while range only uses two data ie the largest value data

and the smallest value data, so standard deviation is a more accurate

measure.

In addition, standard deviation measures the spread of data from the

mean while range measures only the two extreme values ie the

difference between the largest value and smallest value data.

Thirdly, standard deviation can be used in the statistical analysis eg

hypothesis testing.

Fourthly, standard deviation gives weightage to the deviation of the

data from the mean by squaring it ie the greater the deviation, the

greating the weightage after the squaring.

Fifthly, standard deviation gives weightage to the positive andnegative deviation of the data from the mean too.

Hence, Standard deviation is a more precise measure of spread of data

as compared to the rudimentary range and interquartile range measure of

the spread of data.


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4.a) Determine which type of data gives more accurate representation.

Give your reasons.

Managing and operating on frequency tabulated data is much simpler

than operation on raw data. There are simple algorithms to calculate

median, mean, standard deviation etc. from these tables.

Group data give a more accurate representation because :

It focuses on important subpopulations and ignores irrelevant ones.

Improves the accuracy/efficiency of estimation.

Permits greater balancing of statistical power of tests of differences

between strata by sampling equal numbers from strata varying widely

in size.

Easier to look for patterns.

Certain calculations may be performed that are more difficult on un-

grouped data.

Frequently, business statistics deals with hundreds or even thousands

of values in a set. In dealing with such a large amount of values, it is

often easier to represent the data by dividing the values into equal-

size groups.


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4.b) State the conditions when grouped data and ungrouped data is

preferred.

Ungrouped data is the raw data, and correct statistics such as the mean

and standard deviations can be determined. Ungrouped data is usuallypreferred as the starting point of analyses.

Grouped data means there is less data to work with and my statistics

will be approximate. But we work with grouped data all the time, and so

long as the interval is not too big, there's no problem. It is frequently

necessary to group the data to observe trends. Grouped data is preferred

when there is a large distribution of data to in a data set. It is to

minimizes the mistakes and to enable us to calculate in a more easier

way.

For example:

If there have been 10 million accidents in the last 20 years and 5 million

in the interval from 20 years to 40 years ago, it doesn't tell much.

But if I present data of the number of accidents in the last forty years, by

year, this is grouped data given in a meaningful manner.


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NAME MARKS NEW MARKS

ABDUL MALIK BIN ZAINUDDIN 25+3 28

ADAM GABRIEL 58+3 61

ALOYVIA ANGGOL 65+3 68

AMANDA BINTI ALI AMAN 78+3 81

ARSAMREE BIN BONG BONG 45+3 48

BRYVELEN BENJI 63+3 66

DAYANG NOR SYAFIKA AG. MAHMUD 60+3 63

DG.UMI SUMIRAH BINTI RAHMAN 75+3 78

EFA SUZIANI BINTI ALI 83+3 86

FRINGEAL STEPHEN FUNG 78+3 81

FRYDOREEN MASMIN 73+3 76

IVY KOK 68+3 71

JENICA R.JAMES MAJANAU 63+3 66

JENNYCA MYRNA JUSTINE 55+3 58

MAHATHIR BIN RASHID 33+3 36

MELANIE JOANNE CHIN 43+3 46

MELDAH CHIN MEI YIE 63+3 66

MELVOURNE NELFREY GEOFFREY 80+3 83MOHD SHADDAN BIN IBRAHIM 35+3 38

MOHD SHAHEDIN BIN BAKHTIAR 55+3 58

MUHAMMAD NAIM BIN BASIR 45+3 48

MUHD. SYAIT BIN LASEMMAN 73+3 76

NADHIRAH BINTI HAMID 63+3 66

NASARUDDIN BIN MOHAMMAD 48+3 51

NATASA GEORGE 53+3 56

NORATIKAH BINTI ROSLEE 80+3 83

NUR AFALIZA BINTI YUSAINI 95+3 98

NUR ZULAIKHA BINTI AHMAD ZULPAKAR 65+3 68

NURUL IZZATI ALYA BINTI ABD. KABUL 83+3 86NURUL THAHIRAH BINTI SHAKATALI KHAN 58+3 61

PETROZA PITOROS 73+3 76

RACHAEL LYNN BONAVENTURE 45+3 48

SAIDATUL ATIQAH BINTI AZMI 55+3 58

SALMA MATIUS 90+3 93

SOLEHA BINTI MOKHTARIFFIN 83+3 86

STEPHENCIE SINIK 60+3 63

SYARMEEN MAZYUNIE MOHD YUSRIN 65+3 68

TONNY GUIS JUNIOR 45+3 48

VIVIANNIE JIVET 63+3 66

YAP LAI WAN 78+3 81


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MEAN

Formula :

MARKS CLASSMARK,x

FREQUENCY,f FREQUENCYCLASS MARK,fx

1 -20 10.5 0 0 021-40 30.5 3 91.5 2790.75

41-60 50.5 10 505 25502.5

61-80 70.5 17 1198.5 84494.25

81-100 90.5 10 905 81902.5 40


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MODE

Modal class : 61-80

Mode = 70.5

0

3

10

17

10

0

2

4

6

8

10

12

14

16

18

Category 1

Frequency

Marks


100.520.5 40.5 60.5 80.50.5


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MEDIAN

Formula :

Calculation :

MARKS LOWER BOUNDARY FREQUENCY,f CUMULATIVE

FREQUENCY1 -20 0.5 0 0

21-40 20.5 3 3

41-60 40.5 10 13

61-80 60.5 17 30

81-100 80.5 10 40

Median Class = 61-80

Substitute into formula,


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( )

(

)

Median = 68.735


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INTERQUARTILE RANGE

Tabulation of data


1 -20 20.5 0 0

21-40 40.5 3 3

41-60 60.5 10 13

61-80 80.5 17 30

81-100 100.5 10 40

Formula,

Calculation


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From the ogive,

Interquartile Range = 80.556

= 24.5

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120

CumulativeFrequency

Marks



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STANDARD DEVIATION

Formula :

Calculation :

MARKS CLASS

MARK,x


1 -20 10.5 0 0 0

21-40 30.5 3 91.5 2790.75

41-60 50.5 10 505 25502.5

61-80 70.5 17 1198.5 84494.25

81-100 90.5 10 905 81902.5

40


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Standard Deviation = 17.64


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2) A new student has just enrolled in your class. The student scored 97% in his/her

former school. If the students mark is taken into account in the analysis of your

school examination/test, calculate the new mean and standard deviation.

Tabulation of data

MARKS CLASSMARK,x


1 -20 10.5 0 0 0

21-40 30.5 3 91.5 2790.75

41-60 50.5 10 505 25502.5

61-80 70.5 17 1198.5 84494.25

81-100 90.5 11 995.5 90092.75

41 2790.5 NEW MEAN

Formula,


New Mean = 68.06


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NEW STANDARD DEVIATION

Formula,


New Standard Deviation = 17.78


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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.

Calculation Method


1 -20 20.5 0 0

21-40 40.5 3 3

41-60 60.5 14 17

61-80 80.5 18 3581-100 100.5 5 40

60.5 +

= 60.5 + = 60.5 + 7.143

= 67.64

= 68


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Graphical Method

Tabulation of data

MARKS UPPER BOUNDARY FREQUENCY,f CUMULATIVE

FREQUENCY

1 -20 20.5 0 0

21-40 40.5 3 3

41-60 60.5 14 17

61-80 80.5 18 35

81-100 100.5 5 40


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Marks

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120

CumulativeFrequency

Marks


Q2

Q1

Q3


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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 your comments.

Students in Mr. Mas class score better than students in our class.Their mean mark is 76.79 which is higher than our mean mark and their

standard deviation is 10.36 which is lower than ours meaning that they

have data that spread out over a wide range of values than our data. So,

their achievement is higher than our class.


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Dear Additional Mathematics,

From the moment I heard your name, I always thought that you would

be my greatest obstacle to achieve my dream in the future. Youre very

famous in high school. Seniors keep telling their juniors about how hard

you would be and that you could put them into a big confusion. I have to

spend many of my times just to a answer less than 5 questions.

But after countless of hours, countless of days, countless of nights,

after sacrificing my time just for you, I realized something that change

my mind about you, something really important about you. I love the

feeling when I manage to get the answer, after the very long working,

and the uncountable crosses on some working.

I realized that you are not that hard as they told, it takes times to

understood you and after spending all my time for you, I finallyunderstand you. You are such a unique subject and I love everything

about you.

I ADDITIONAL MATHEMATICS !!


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After I accomplished this project, I have found that Additional Mathematics is fun

and very useful in daily life. I have learnt the important of perseverance as time will

be inverted to ensure the completion and excellence of this project. On the other

hands , I have learnt the virtue to making together as I have helped and received

help from my fellow peers in the production of this project. I realized the important

to be thankful and appreciative during completing this task. This is because I able to

apply my mathematical knowledge in daily life and appreciate the beauty of

mathematics. This project is a several training stage for me to prepare myself for the

demands of my future undertaking in the university and work life.

Documents

Addmath Project Work 2013 (Repaired)