Practical examples of same mean and different variance

Question

I recently came across this paper : http://projecteuclid.org/download/pdf_1/euclid.aos/1176343959

It proposes a theory about estimating the common mean of several normal populations(which have same mean but different variances), and they have proposed an estimator. But what is the application of this? Where can we have such situation?

One example I can think of is this: Suppose 2 experiments are performed, where there is a random error. We know intuitively that the error will be normally distributed, and somehow we know that the means are same, but the variances depend upon the person. This might serve, but this seems a cooked up example. Can anyone please give some more practical examples? Thanks in advance.

Answer 1

The average person has one testicle and one ovary. This is what high variance means, that "average" rarely happens.

The average person has one head. This is what low variance means.

Answer 2

IQ is the classic example. Both men and women have a common mean IQ of 100, but men have a higher variance.

In practical terms, this means there are more male theoretical physicists and the like, but also more men with intellectual disabilities.