THE GOLDEN MEAN

Nowadays insurance education is becoming popular. New insurance agents
are required to undergo training and become well-versed in the theory and practice of insurance so that they can advise their prospects in the right manner. There is an interest and awareness to know the principles of Insurance among the officials and staff of the new private Insurance companies also. Insurance is based on same basic concepts like averages, probability and law of large numbers. An attempt is made in the note to explain these concepts in a simple, easily understandable manner so that both teachers and learners get a clear idea of these matters.

Law of Averages

We use different figures to judge the characteristics of a person. A person is old, middle aged or young depending upon his age. A student is outstanding, good or poor depending upon his marks. A person is rich, middle class or poor depending upon his income. But how to judge the characteristics of a group? For this we use the average of the group as an indicator.

Average is the amount by adding together the characteristics of all the persons in a group and dividing it by the number of members in the group. If the average mark of a class is 60, it indicates a better group of students compared to another group with an average mark of 40. If the average income of a group is 50000, it indicates a better-placed group compared to a group with an average income of 10000. So we decide about the group based on the averages for any particular characteristic.

However this can be misleading in smaller groups. For example if two persons
are earning 100000 and 10000 per month, then their average monthly income is (100000+10000)/2 = 55000. This does not give an indication of the wide variation between the individuals. As the number of members in the group goes on increasing, we get a better and reasonably correct picture of them by taking averages. This is called the law of large numbers in relation to averages.

Law of Probability.

In our daily lives many events take place. Some turn out to be good and some
turn out to be bad. But in nature, the events follow a particular pattern. This pattern is observed by mathematicians and called the law of probability.

Probability is defined as the ratio of happening of a particular outcome to all the outcomes that are likely. For example tossing of a coin has two outcomes, a head or a tail. So in the tossing of a coin, we can say the probability of getting a head is half. But in real events every two tosses of a coin may not produce a head and a tail. It may be both heads and both tails or one head and one tail. In tossing the coin 10 times there may be 6 heads and 4 tails or any other outcome, which may not be exactly half. However, if we go on increasing the number of tosses, the ratio of the number of times head falling to the number of tosses will be going closer and closer to half.

Take another example – a child that is being born can be a male or female, so we can say that the probability of a new child being a male is half and a female is half. In a hundred births there can be 54 males and 46 females. But in a thousand births, the number can be around 520 and 480. In 10000 births it can be around 5125 and 4875. As the number of births go on increasing the numbers will be coming closer and closer to the halfway mark or half the births will be males and half will be females.

In life insurance, the experience of the deaths of the existing policyholders is calculated as so many numbers of deaths at each age for the total number of policyholders at each age. From this each person’s probability of death at each age is calculated, which is called a mortality table. From the mortality table, the actuaries calculate the premiums for different plans of insurance.

But in some events there can be multiple outcomes. For example throwing a die, may result in one of the six numbers 1 to 6 coming on the top. Here we say that the probability of a particular number say 4 coming on the top is 1/6 as there are six possible outcomes. Another example is that of an employee, who can go out of employment by way of resignation, death, retrenchment or retirement.

What is the use of probability in real life?

We all wish that good events should happen and bad events should not happen. But we cannot avoid bad events from happening. A person who hopes that only good events will happen to him is not prepared for any bad event that may happen and gets frustrated and goes on blaming others or planets or his bad luck etc., and his condition worsens as he could not bear the impact of the bad event on his life. An old proverb says “Believe in God but keep your gunpowder dry”. Now we can say, “Believe that good things will happen but be prepared for and insured against the bad events”.

Insurance is devised as a means of protecting people from the effect of bad events or events which may cause an adverse consequence. Here we acknowledge the probability of happening of bad events for anybody. All the persons who are exposed to the happening of bad events contribute small amounts as premium, which is collected by the insurance companies and paid to those who actually suffer from such bad events. In calculating the premiums to be charged, the probabilities are taken into account.


Law of large numbers:

In nature most of the characteristics of people are distributed at the middle or average with a very small number at the extremes. If we take bad to good in a scale of 1 to 100, most of the human beings will be found to be between 40 and 60 with a few at the extremes. Thus there can be one or two like Mahatma Gandhi who are extremely good and a very few like Hitler who are extremely bad. This is called Normal Distribution in Statistics.

When we take a smaller number to test this, we may not be able to find out the way in which the distribution is there, because one or two extreme values that come in the sample can alter the average and we may not get a correct picture. Therefore to judge correctly the characteristics of any group, we have to take sufficiently large number from the group, either to calculate the average or to calculate the probability. This is called the law of large numbers. Thus the law of large numbers become very important in understanding the characteristics of any group by averages or in determining the probability of an event.

Tailpiece: A professor of Maths wanted to cross a stream. He found that the stream is
2 feet deep at the shore and 8 feet deep at the middle point. He quickly calculated the average depth at 4 feet and confidently proceeded to cross as he knew that he was 5
feet 8 inches.

Answering machine message: Hello, this is probably 438-9012, yes, the house of the famous statistician. I'm probably not at home, or not wanting to answer the phone, most probably the latter. According to my latest calculations, supposing that the universe doesn't end in the next 30 seconds, the odds of which I'm still trying to calculate, you can leave your name, phone number, and message, and I'll probably phone you back. So far the probability of that is about 0.645. Have a nice day.