Universality: This distribution is a universal distribution because except certain conditione Most in all areas nature of frequency distribution is normal. Sir Francis Galton wrote, ‘I know of barcely anything so to impress the imagination as the wonderful form of cosmic order expressed by whe law of frequency of error.’ WJ Youden a famous statistician, has expressed his admiration of the normal distribution in an artistic fashion (symmetrical) as reproduced below:
LAW OF ERROR
STAND OUT IN THE
EXPERIENCE OF MANKIND
AS ONE OF THE BROADEST
GENERALISATION OF NATURAL
PHILOSOPHY. IT SERVES AS THE
GUIDING INSTRUMENT IN RESEARCHES
IN THE PHYSICAL AND SOCIAL SCIENCES AND
IN MEDICINE AGRICULTURE AND ENGINEERING
IT IS AN INDISPENSABLE TOOL FOR THE ANALYSIS AND THE
INTERPRETATION OF THE BASIC DATA OBTAINED BY
2. Study of Natural Phenomenon: Almost all natural phenomenon possesses the features of normal distribution, such as height of adults, length of leaves of a tree, etc. Therefore, the normal distribution is widely used in the study of natural phenomenon.
3. Approximation to Binomial and Poisson Distribution: The normal distribution serves as a good approximation to binomial and Poisson distribution particularly, when the number of observations increases. It may be mentioned that for large values of n, computation of probability for discrete distribution becomes difficult and in such cases normal distribution can be used with great ease and convenience.
4. Conformity of Sampling Distribution: Almost, all the exact sampling distribution, e.g. students, t-distribution, Fisher’s Z-distribution, Snedecor’s F-distribution and the chi-square distribution conform to normal distribution for large degrees of freedom.
5. Basis of Small Samples: The whole theory of small sample is based on the fundamental assumption that the parent population from which the samples have been drawn follows normal distribution.
6. Statistical Quality Control: It is very useful in statistical quality control where the control limits are set by using this distribution.
7. Determination of Limits of Population Values: The normal distribution is properly stated in the central limit theorem. According to this theorem, we can estimate the upper and lower limits within which a value of population would be. For example, within a range of population, Mean + 3S.D., 99.73% or almost all the items are covered.
Properties of Normal Distribution/Curve
The following are the important properties of normal distribution or normal curve:
1. Bell Shaped: The normal curve is perfectly symmetrical and bell shaped about mean. This means That if we fold the curve along its vertical axis at the centre, the two halves would coincide.
2. Continuous Distribution: Normal distribution is a distribution of continuous variables. Hence, it is called continuous probability distribution.
3. Equality of Central Values : In a normal distribution, all central values are equal, i.e.
Mean = Median= Mode