13.2 - Limits of Basic Statistics

Links and useful resources

Average, Median, and Mode are useful, but there are many things they can't tell us.
Average doesn't tell us anything about "fairness" of distribution.
Median doesn't tell us anything about total wealth or extreme values.
Mode is pretty useless in general, I don't know why it's still taught.

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The average wealth of a person in Richville is $$ 150, 000$ and the average wealth of a person in Poorville is $$ 20, 000$ .
- Suppose a person is called “filthy stinking rich” if the person has over one million dollars. Can we tell which town has more filthy stinking rich people?
- Can we tell which town has the higher median wealth?
- If both towns have the same number of people, can we tell which town has the higher total wealth?
- Suppose a person with $$ 1, 000, 000$ and 4 people who have $$ 0$ move into Richville. Will the average wealth of Richville go up or down?
The median wealth of a person in Goldtown is $$ 150, 000$ and the median wealth of a person in Tintown is $$ 20, 000$ . Each town has $8000$ people.
- Suppose a town qualifies for special government subsidies if each of at least half of its residents has less than $$ 60,000$ . Does either town necessarily qualify for the subsidies?
- Can we tell which town has the higher average wealth?
- Suppose a person with $1,000,000,000 and four people with $0 move into town. Will the median wealth go up or down?