This is the most informative single income index giving an immediate evaluation of income distribution, much more efficient than mean and median that are biased by the effective cost of life...
You are correct that mean is very popular measure of central tendency but it may not be a suitable measure everywhere.As far as the age and income distribution is concerned median is a better measure because it will give better representation of population as compared to mean. Say for example we are to find out the average income of households of a country then it is obvious that there would be classes whose income differ significantly from each other say higher class people's avg income is $500000 ,middle class people's income is $30000 lower class people's income is $5000 then if we take an avg of these three then it would give us $180000 (approx) as an average income of a household, which is disastrous to believe because we know that the its not true. On the other hand median as a positional average divides the entire population in two equal parts and then we can say that 50% of the population lie below $***** (whatever the median is) and the remaining 50% lie above the median value. therefore in this context median is a better measure as far as income distribution is concerned..
I may be wrong but sir mode will only be representing the highly frequent observations it will not give any information about the outliers like in our case income of rich persons....Don' t you think so??
For a country, to my opinion, the "outliers" are not so important. If a gouvernment wants to see how much income its citicens have, it should look for the most typical income, which is the income most people have. The median is also not influenced by outliers, though, but for heavily skewed distributions the median will be considerably different to the mode and thus won't represent a typical income. Income distributions are typically heavily right-skewed and the median income thus clearly overestimates a typical income of the citicens.
This is the most informative single income index giving an immediate evaluation of income distribution, much more efficient than mean and median that are biased by the effective cost of life...