Meaning of Normal distribution or law of error

Binomial and passion distribution are discrete probability distribution. But normal probability distribution commonly called normal distribution. It is theoretical distribution for the continuous variable. The normal distribution was first discovered by English mathematician De Moivre in 1733.later it was rediscovered by Karl Gauss in 1809 and in 1812 by Laplace. Normal distribution is also called Gaussian distribution or Gaussian law of error as this theory describes the accidental error of measurements.

Properties of normal distribution

1)      The normal curve is bell shaped in appearance.

2)      There is one maximum point of normal curve which occur at mean.

3)      As it has only one maximum curve so it is unimodal.

4)      In binomial and possion distribution the variable is discrete while in this it is continuous.

5)      Here mean= median =mode.

6)      The total area of normal curve is 1. The area to the left and the area to the right of the curve is 0.5.

7)      No portion of curve lies below x-axis so probability can never be negative.

8)      The curve becomes parallel to x-axis which is supposed to meet it at infinity.

9)      Here mean deviation = 4/5 standard deviation.

10)  Quartile deviation = 5/6 mean deviation

11)   Quartile deviation : mean deviation : standard deviation

           10                :          12             :        15

12)   4 standard deviation = 5 mean deviation = 6 quartile deviation

 These are the properties of normal distribution.

Importance of normal distribution

1)      It has one of the important properties called central theorem. Central theorem means relationship between shape of population distribution and shape of sampling distribution of mean. This means that sampling distribution of mean approaches normal as sample size increase.

2)      In case the sample size is large the normal distribution serves as good approximation.

3)      Due to its mathematical properties it is more popular and easy to calculate.

4)      It is used in statistical quality control in setting up of control limits.

5)      The whole theory of sample tests t, f and chi-square test is based on the normal distribution.

These are the importance or uses or benefits of normal distribution.