Question

Describe a situation in which it might be better to use the sample median rather than the sample mean to predict the population mean of a random variable Y , µY .

Answer 1

Note- In general, median is better to use when there is presence of outliers. Median is not affected by outliers whereas mean is affected by outliers.

A practical example is as follows.

Suppose, we want to predict a representative value of per capita income in a country like India (in fact this case is almost similar for all countries where economical diversity is high among people). There are a lot of people who are either below poverty line or in low-income group whereas there are few billionaires too. Suppose, we want to predict per capita income of the people of India using sampling. We follow appropriate sampling procedure to obtain our sample. Income of billionaires are outlier in set of income of people. If we merely calculate mean of income of all people, we shall obtain a higher value (due to those outliers with higher values) which is not at all a good representative of income of most of the people. However median value lies close to the values which occurs most and thus it is a good representative of whole population. Thus use of sample median is better than sample mean to predict population mean in such instance.