Mahesh Godavarti

If you want to describe a population with as few descriptors as possible then mean and variance are the two descriptors you would turn to. Mean gives you a rough idea of what a typical candidate in the population is like and the variance gives you a rough idea of how close to typical the population is in general.

For example, if we say the mean age of people in a town is 54 and the variance is 2, then we know that we won't find young people in the town. In a second town, if the mean age is 54 and the variance is 30, we will expect to find younger people in the 2nd town.

A second example, is that variance gives a confidence level of your estimate. Let's say somebody predicts to find 100 tigers in a national park with a variance of 2. Then we know that they are very confident of their prediction. If, however, they give a variance of 50, then we know that their prediction capabilities are very poor.

Vivekanand Vellanki

Lets say there are 2 athletes A and B.

A's timings on the last 4 400m races is the following: 1 min, 1 min 10 secs, 50 secs, and 1 min 2 secs.

B's timings on the last 4 400m races is the following: 55 secs, 52 secs, 53 secs, and 52 secs

Assuming both were healthy during the 4 races and everything was equal.

Assume that you have to pick one of the two to represent your country. How would you make that choice?

B appears more consistent, but has no chance of winning the gold medal.

A appears more erratic, but has a chance of winning a goal medal.

Would you settle for the more consistent B? or take chances of winning the gold or nothing by picking A?

Statistics and probability are useful in making such decisions.

The above argument of B's consistent behaviour is using the fact that the variance in B's timings is small.

The argument of A having a chance to win a gold is using the fact that in 1/4 races A ran fast enough to win a gold medal (using probability).

When you are picking a team for a team sport, you might want a mixture of consistent performers and erratic yet champion performers.

The same applies in different flavours to decisions in many fields.