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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Substitute into the formula,
( )
( )
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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
4 Harmoni Examination 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
4 Harmoni Examination 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
MARKS UPPER BOUNDARY FREQUENCY,f CUMULATIVEFREQUENCY
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
4 Harmoni Examination Marks
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STANDARD DEVIATION
Formula :
Calculation :
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 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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Substitute into the formula,
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
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 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,
Substitute into the formula,
New Mean = 68.06
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NEW STANDARD DEVIATION
Formula,
Substitute into the 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
MARKS UPPER BOUNDARY FREQUENCY,f CUMULATIVEFREQUENCY
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
4 Harmoni Examination 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.