Population percentages

Question

During my quantitative methods in sociology class, the professor gave the following example, which I don't agree with: essentially, it was the following:

$30\%$ of Californians are drug users, so to find the number of drug users in the US, one simply takes $0.30 \times $the population of the US.

This seems flawed to me because of units perhaps? The $30\%$ figure is not dimensionless it is: $0.30=\frac{\text{Drug users in California}} { \text{population of Californians}}$. This is then multiplied by total American population. So the final answer would have units of Drug users $\times \frac{ \text{Americans }}{ \text{Californians}}$, which is very strange.

Any thoughts?

Answer 1

I think the estimation of number of drug user is biased.

It is assuming that the distribution of drug user is uniform across all states.

Take for example, suppose the percentage of drug user in another state in $40\%$, then we will get another estimate.

Also, the estimate proposed do not take population of each state into consideration.

remark: Percentage is dimensionless. Number of Americans and number of Californians both compute number of people.

Answer 2

1. Percentages are dimensionless, you just have to interpret them correctly. In this case, one might write "30 people in California out of every 100 people in California are drug users." In math-ier looking notation: $$ \frac{30 \text{ people in CA}}{100 \text{ people in CA}} = \frac{3}{10} = 30\%$$ are drug users.

2. That being said, the argument that the number of drug users in the US is equal to $30\%\times(\text{population of the US})$ is flawed because the population of California is not an unbiased subset of the population of the US. There are numerous reasons to suspect that the California average will be different from the national average.