normal distribution final ppt (1)
TRANSCRIPT
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NORMAL DISTRIBUTION
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PRESENTED TO:
PROF. FARAH CHOUDHARYTHE BUSINESS SCHOOL
UNIVERSITY OF JAMMU
PRESENTED BY:
•
DIVA SAMNOTRA (12)• IMTIAZ ALI ( 16 )
• LUCKY CHOUDHARY (24)
• SUVIDHA GUPTA (59)
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CONTENTS
INTRODUCTION
HISTORY
CHARACTERISTICS
APPLICATIONS
CONDITIONS FOR NORMALITY
GRAPHS OF NORMAL DISTRIBUTION
IMPORTANCE
SIGNIFICANCE
CONSTANTS OF NORMAL DISTRIBUTION
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INTRODUCTION
Most useful theoretical distribution
for continuous variables.
Also known as normal probability
distribution.
Cornerstone of modern statistics.
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..cont
Descriptive model, defining real worldsituations.
Continuous frequency distribution of infiniterange.
Imp. tool in the analysis of epidemiologicaldata & management science.
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HISTORY
First described by Abraham Demoivre as thelimiting form of the binomial model in 1733.
Rediscovered by Gauss in 1809 and by Laplacein 1812.
Over the period of time, normal model hasbecome the most imp. probability model instatistical analysis.
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CHARACTERISTICS
It links frequency distribution to probability
distribution.
Has a Bell Shaped Curve.
It is symmetric around the mean i.e twohalves of the curve are the same (mirror
images)
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CONTD…
Hence Mean= Median
The total area under the curve is 1
(or 100%)
It has the same shape as the
Standard Normal Distribution
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CONTD…
In a Standard Normal Distribution:
The Mean = 0
and
Standard Deviation = 1
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APPLICATIONS
Its applications goes beyond describing
distribution.
It is used by researchers and modelers.
It helps managers /management in makingdecisions.
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CONTD..
It plays a major role in statistical inferences.
Many things are actually normally distributed orvery close to it.
For example:
• Height and Intelligence are approximatelynormally distributed.
• Measurement error also often have a normal
distribution.
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CONTD..
The normal Distribution is easy to work with
mathematically.
In many practical cases the methods
developed using normal theory work quite
well even when the distribution is not even.
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CONDITIONS FOR NORMALITITY
Causal forces must be numerous & of approx.
equal weights.
Forces must be homogenous i.e must be the
same over the universe from which the
observations are drawn.
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CONTD..
The forces affecting events must be
independent of one another.
Deviations above as well as below the mean
are balanced as to magnitude and number.
(Condition of symmetry)
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GRAPH OF NORMAL DISTRIBUTION
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Different shapes depending on different
values of μ and σ.
The mean lies at the center of its normal
curve
The two tails of normal distribution extend
indefinitely and never touch the horizontal
axis
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IMPORTANCE
Sampling variability makes statistical
inferences easier.
Determination of min & max limits within
which the population values lie.
Serves as a good approximation of many
discrete distributions.
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SIGNIFICANCE
To approx of “fit” a distribution of
measurement under certain conditions.
To approx. the binomial distribution & others.
To approx. the distribution of means & otherquantities calculated from samples.
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