Question

4. A student asks, “If the average income of 10 people is $10,000 and one person gets a raise of $10,000, is the median or the mean changed and, if so, by how much?

Answer 1

Since we don't know the specific income of each person in the sample, we don't know for sure if the median will change. Nevertheless, the mean will surely raise.

Since the current average income is $10,000, if one of them gets a raise of $10,000, then the sum of all incomes would be $100,000+$10,000=$110,000. And the new average income will be:

`(110,000)/(10)=11,000`

Then, the mean increases by $1,000, and we can't say anything about the median.