Normal Distribution Final Ppt (1)

7/27/2019 Normal Distribution Final Ppt (1)

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NORMAL DISTRIBUTION



PRESENTED TO:

PROF. FARAH CHOUDHARYTHE BUSINESS SCHOOL

UNIVERSITY OF JAMMU

PRESENTED BY:

•

DIVA SAMNOTRA (12)• IMTIAZ ALI ( 16 )

• LUCKY CHOUDHARY (24)

• SUVIDHA GUPTA (59)



CONTENTS

INTRODUCTION

HISTORY

CHARACTERISTICS

APPLICATIONS

CONDITIONS FOR NORMALITY

GRAPHS OF NORMAL DISTRIBUTION

IMPORTANCE

SIGNIFICANCE

CONSTANTS OF NORMAL DISTRIBUTION



INTRODUCTION

Most useful theoretical distribution

for continuous variables.

Also known as normal probability

distribution.

Cornerstone of modern statistics.



..cont

Descriptive model, defining real worldsituations.

Continuous frequency distribution of infiniterange.

Imp. tool in the analysis of epidemiologicaldata & management science.



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.



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)



CONTD…

Hence Mean= Median

The total area under the curve is 1

(or 100%)

It has the same shape as the

Standard Normal Distribution



CONTD…

In a Standard Normal Distribution:

The Mean = 0

and

Standard Deviation = 1



APPLICATIONS

Its applications goes beyond describing

distribution.

It is used by researchers and modelers.

It helps managers /management in makingdecisions.



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.



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.



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.



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)



GRAPH OF NORMAL DISTRIBUTION



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



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.



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.

Normal Distribution Final Ppt (1)

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