Explain in detail important principles (Law) of statistics.

Ans.

Law of statistical Regularity

Law of Statistical Regularity is based on theory of probability. King has defined this law in these words-“The law of statistical Regularity lays down that a moderately large number of items chosen at random from a very large group are almost sure on the average to have the characteristics of the large group. For example out of 4000 students of a college 400 students are randomly selected and their height is studied then the average height of the sample will be almost same as that of universe.”

Limitations of the Law- The various limitations of this law are-

(i) Random Sampling- This law is applicable when random sampling method is applied to select the samples. It doesn’t apply when deliberate sampling is used.

(ii) Large Size- Sample should be big or large in size as small sample does not represent the universe. The size of sample depends on the size of universe, nature of its units etc-

(iii) True on an Average- This law states a trend which is true on an average. The results of random sampling does not apply entirely to the universe, there can be some difference between the two.

Utility- This law is very useful in the field of statistics. This law is the base of sampling. This is only due to this law that instead of studying the entire universe, through random sampling, the analysis is done and conclusions are derived for entire universe. Moreover through interpolation and extrapolation the future estimates can also be made. This law is applicable in speculations. lotteries, insurance, crime, suicides, accidents etc Thus, it is practically very useful law.

Law of inertia of large numbers

Law of inertia of large numbers is corollary to the law of statistical regularity. According to this law large values are more stable than small values i.e. there are comparatively less changes in large values. In small values the change occur in both the sides due to various reasons and hence it is set off. The result is that when a large value is obtained by combining the small values the quantity of change becomes less and stability becomes more clear. For example, in various districts of U.P. the production of wheat or sugarcane changes in comparison to the previous year but these changes can be positive or negative. In some districts production is less due to adverse conditions and vice-versa. Hence both the changes set off each leaving the production intact i.e. it is stable. In the same manner the birth rate or death rate can change in the individual district but for the country as a whole it usually remains same.

By stability of large numbers or values we should not draw the conclusion that they do not change. In reality, they change in long run in only one direction. But that change is very minute in comparison to the change of small values.

Law of inertia of large numbers occupy a special position in the field of statistics. This law is very useful in random sampling. This is due to this law that accuracy is maintained in large samples. The more values a sample will have then more will be the accuracy and it will represent the universe in whole Hence, this law is very useful in statistics. According to Dr. Bowley “Great numbers and average resulting from then have great inertia. It is the consistency of great numbers that makes statistical measurement possible.”

Drafting of a sample survey for collecting data relating to expenditure pattern of the middle class families of your city:

The following points will be decided :

1. Objective of the Study- Collecting data relating to expenditure pattern of the middle class families of a particular city-

2. Concept and Definition- The concept of middle class family must be clearly defined specifying their income level.

3. Area to be Covered- Middle class families of a particular city.

4. Sampling List- By listing process, a sampling list of all the middle class families will be prepared to known size of the population. All such families will constitute our population.

5. Size of the Sample- Keeping in view of the budget of the survey and the desired accuracy sample size will be decided. Once, the size of the population (Number of middle class families in the city) is known, the sample size is decided.