Elementary Statistics (1+1)

3.1.5 Law of Inertia of Large Numbers

This law is a corollary of the law of statistical regularity. It is of great significance in the theory of sampling. It states that, other things being equal, larger the size of the sample, more accurate the results are likely to be. This is because large numbers are more stable as compared to small ones. The difference in the aggregate result is likely to be insignificant, when the number in the sample is large, because when large numbers are considered the variations in the component parts tend to balance each other and, therefore, the variation in the aggregate is insignificant. For example, if a coin is tossed 10 times we should expect equal number of heads and tails, i.e., 5 each. But since the experiment is tried a small number of times it is likely that we may not get exactly 5 heads and 5 tails. The result may be a combination of 9 heads and 1 tail, or 8 heads and 2 tails, or 7 heads and 3 tails. If the same experiment is carried out 1,000 times the chance of 500 heads and 500 tails would be very high, i.e., the result would be very near to 50% heads and 50% tails. The basic reason for such likelihood is that the experiment has been carried out sufficiently large number of times and possibility of variation in one direction compensating others in a different direction is greater. If at one time we get continuously 5 heads, it is likely that at other time we may get continuously 5 tails, and so on, and for the experiment as a whole the number of heads and tails may be more or less equal. Similarly, if it is intended to study the variation in the production of rice over a number of years and data are collected from one or two States only, the result would reflect large variations in production due to the favourable factors in operation. If, on the other hand, figures of production are collected for all the States in India, it is quite likely that we find little variation in the aggregate. This does not mean that the production would remain constant for all the years. It only implies that the changes in the production of the individual States will be counterbalanced so as to reflect smaller variations in production for the country as a whole.