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.


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
(a) If one solves the ordinary differential equation using Euler's method find an expression for the local truncation error. (b) Using the result of (a) above what will

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

Consider a Cournot duopoly with two firms (fi rm 1 and fi rm 2) operating in a market with linear inverse Demand P(Q) = x Q where Q is the sum of the quantities produced by both

Agreement The degree to which different observers, raters or diagnostic the tests agree on the binary classification. Measures of agreement like that of the kappa coefficient qu

Multi stage or Cluster Random sampling  Under this method, the random selection is made of primary, intermediate and final units from a given population. The area of investigat

What would be the cutoff score to indicate a score that is in the top 15% of the scores on a test with a mean of 100 and a standard deviation of 15? This question has multiple p

construction of control chart,n chart

calculate variance and standard deviation of the following sample 12,22,32,13,12,23,34,52,56,23,44,32,11,11

how to interpret results, a good explanation to help me understand.

Choose any published database from the internet or Bethel library (such as those from the Census Bureau or any financial sites). You may opt to use one of the data files provided b