Law of Averages

Random error decreases proportionally as the number of trials increases. So, by the law of averages, after enough trials, the expected outcome is more likely to be achieved. Take the example of tossing a coin. Out of 100 tosses, one expects 50 heads, but, by chance, it will probably be off that number. Say it was off by 5, by chance. If the number of tosses went up to 1,000, the expectation would again be for half heads. But again, by chance, it would probably be off by some number, say 8. The absolute number of errors has increased, from 5 to 8, but the percentage of tosses [Page 558]in error has decreased, from 5% to eight tenths of 1%. In general, the law of averages says that as the number of tosses increases, the overall percentage of random error decreases. Thus, the distribution of the coin toss gets closer to its expected value of 50% heads.