Question

Suppose that a state introduces a state income tax which will be at a flat rate of 3%. The state legislature wishes to estimate how much money they will receive in taxes, and to do this they need to know the average income of residents of the state. Which information would be most useful, the mean income, the median income, or the mode of the incomes? Why?

Answer 1

The mean income is more useful

Explanation:

If you know the mean income, then you can obtain the total income by multiplying for the total population. Once you know the total income, you can deduce the amount of money collected by multiplting the total income by 0.03.

Knowing the median income does only help you so much. The mediam income is only a parameter that says that 50% of the population earn less than that. However, if you dont know how much the richer people earn, you cant deduce how much from taxes will you collect. For a simplified example, the sets A = {1,3,18} and B = {1,3,4} have the same median, 3. however A sums a total of 22, while B only sums 8.

The mode of income alone is also not enough. Again, You can have a lot of salaries ranging from similar values, but if you dont know the exact value of other clusters of salaries, specifically the biggest ones, you will lack a lot of information. As a simplified example, the Sets A = {1,3,3,3,3,3,3, 7, 7,7} and B = {1,3,3,3,3,3,3,3,3,75} have both of them 3 as the most frequent number, however A has a mean of 4, while B has a mean of 10, despite having only 1 mayor cluster of numbers.

Is short, the mean is the bets way to determine the amount of rax collection, because it puts more realistic 'weights' on higher income, and because it lets you obtain exact results for the total amount of income.

I hope this helped you!