State the law of statistical regularity. What are the limitations of this law? How it is useful?
State the law of statistical regularity. What are the limitations of this law? How it is useful?
Ans.
Law of Statistical Regularity
This law is derived from the mathematical theory of probability. In the words of king: “the law of statistical regularity lays down that a moderately large number of items chosen at random from a large group are almost sure on the average to possess the characteristics of the large group”. In other words, this law points out that if a sample is taken at random from a population, it is likely to possess almost the same characteristics as that of the population. This law directs our attention to an important point, that is, the desirability of choosing the sample at random.
By random selection we mean a selection where each and every item of the population has an equal chance of being selected in the sample. In other words, the selection must not be made by deliberate exercise of one’s discretion. A sample selected in this manner would be a representative of the population. If this condition is satisfied it is possible for one to depict fairly accurately the characteristics of the population by studying only a part of it. Hence, this law is of great practical significance because it makes possible a considerable reduction of the work necessary before any conclusion is drawn regarding a large universe. For example, if one intends to make a study of the average height of the students of an university it is not necessary to measure the heights of each and every student. A few students may be selected at random from each college, their heights may be measured and the average height of university students in general may be inferred.
It should be noted that the results derived from sample data may be different from that of the population. This is for the simple reason that the sample is only a part of the whole universe. For example, the average height of students of the University may come out to be 160cm. By census method whereas it may be 159cm. or 161cm. for the sample taken. It should be just a coincidence if the height comes out to be exactly 160cm. under both the methods. However, there would not be much difference in the results derived if the sample is a representative of the population.
Limitations: The following are the limitations of this rule:
(i) Random Sampling : This rule is applicable only when the sample units are chosen by random sampling method. This rule is not applicable in case of deliberate sampling.
(ii) Reasonable Size: Size of a sample should be reasonably or moderately large. A small sample does not represent the universe. The reasonable size depends on the size of population and the nature of units.
(iii) Sure on an Average: This rule indicates the trend which is sure on an average. The results of random sampling are not fully applicable to the entire universe. The results of sample and that of entire population may differ to some extent.
Usefulness: This concept is very useful in the area of statistics. On the basis of this rule, it has become possible to study entire population with the help of sample taken by random sampling basis. The results of the study are applicable for the entire population. Predictions can also be made by interprolation and extrapolation for statistical events. This rule is applicable in a game of gambling, insurance business, crimes, suicides and accidents etc. It is useful in practical life also.
