Normal distribution, Applied Statistics

Normal Distribution

Meaning: According  to ya Lun Chou  There perfectly smooth and symmetrical  curve, resulting  from the expansion of the binomial (p+q)n   when n approaches infinity  is known  as the  normal curve. Thus  the normal curve may be considered as the limit  towards  which  the binomial distribution approaches as n increases  to infinity. Alternatively  we may say that the normal curve  represents a continuous and infinite  binomial distribution, or simply a normal distribution .

Normal distribution  is a continuous  probability  distribution. During 18th  century  karl friedrich  gauss  contributed an important role in the development  of normal distribution . so  in his honour this distribution  is often  referred  to as the Gaussian  distribution .This distribution  is also called as normal law  of error  because  gauss  derived its  equation from the stuty  of error in repeated    measurements  of the same.

When n the number  of trails  is very  large or infinite (n-&) and neither p nor q is very small or nearer to equal then binomial distribution  tends  to be a normal distributions.

Properties of Normal Curve

1.      Shape: It is perfectly  symmetrical and bell shaped.

2.      Position of mean, mode and median: Mean ,mode  and median remains  equal  in normal distribution ,they  are found  in the  mid of the distribution , and distribute the area  of curve in   equally two parts.

3.      Asymptotic : As the distance of the curve  from the mean increases, the curve  comes  closer and  closer to the axis  but never  touches it.

4.       Unimodal :  It  has only  one mode  so it sis unimodal.

5.          Continuous Distribution: It is a distribution of continuous  variables.

6.       Equidistance  of Quartiles: The  difference  between third  quartile & median  (Q3-M) = and median  and first   quartile (M-Q1) are  equal.

(Q3-M)=(M-Q1)

7.      Quartile Deviation and Probable Error: Quartile  deviation is equal to probable  error,  which  is about 2/3  of standard  deviation (QD=0.6745)

8.      Mean Deviation: The mean  deviation about  mean is 4/5 of 0.7979

9.      Points of Inflection ; The  points where the curveity  of normal   curve  changes  its direction  are termed as points  of Inflection.

Posted Date: 9/27/2012 7:03:50 AM | Location : United States







Related Discussions:- Normal distribution, Assignment Help, Ask Question on Normal distribution, Get Answer, Expert's Help, Normal distribution Discussions

Write discussion on Normal distribution
Your posts are moderated
Related Questions
Why are graphs and tables useful when examining data? A researcher is comparing two middle school 7th grade classes. One class at one school has participated in an arts program

Index Number Meaning and Definitions of Index Number The index numbers are the special type of averages which are presented in percentages and computed on certain base.

Stratified Random Sampling: This method of sampling is used when the population is comprised of natural subdivision of units, The method consist in classifying the population u

In this problem, we use the CSDATA data set, which is available in 'CSDATA.txt'. We do ne an indicator variable, say HIGPA, to be 1 if the GPA is 3.0 or better and 0 other- wise. S

Lorenz Curve   It is a graphic method of measuring dispersion. This curve was devised by Dr. Max o Lorenz a famous statistician.  He used this technique for wealth it i

The Neatee Eatee Hamburger Joint specializes in soyabean burgers. Customers arrive according to the following inter - arrival times between 11.00 am and 2.00 pm: Interval-arriva

Based on the following graphs (next page) you should write a discussion report (2 pages) on: 1. Determination of whether the open-loop system response is consistent with a 1st o

Types of cost-reimbursable contracts are:   Cost Plus Fixed Fee contract (CPPF): Compensation is based on a fixed sum independent of the final project cost. The customer a

The Harmonic Mean is based on the reciprocals of numbers averaged. It is defined as the reciprocal of the arithmetic mean of the reciprocal of the given individual observations. Th

Geometric Mean is defined as the n th root of the product of numbers to be averaged. The geometric mean of numbers X 1 , X 2 , X 3 .....X n is given as